Peaceful chess queen armies

Peaceful chess queen armies
You are encouraged to solve this task according to the task description, using any language you may know.

In chess, a queen attacks positions from where it is, in straight lines up-down and left-right as well as on both its diagonals. It attacks only pieces not of its own colour.

	⇖	⇑	⇗
⇐	⇐	♛	⇒	⇒
	⇙	⇓	⇘
⇙		⇓		⇘
		⇓

The goal of Peaceful chess queen armies is to arrange m black queens and m white queens on an n-by-n square grid, (the board), so that no queen attacks another of a different colour.

Task

1. Create a routine to represent two-colour queens on a 2-D board. (Alternating black/white background colours, Unicode chess pieces and other embellishments are not necessary, but may be used at your discretion).
2. Create a routine to generate at least one solution to placing m equal numbers of black and white queens on an n square board.
3. Display here results for the m=4, n=5 case.

References

• Peaceably Coexisting Armies of Queens (Pdf) by Robert A. Bosch. Optima, the Mathematical Programming Socity newsletter, issue 62.
• A250000 OEIS

11l

Translation of: D

T.enum Piece
   EMPTY
   BLACK
   WHITE

F isAttacking(queen, pos)
   R queen.x == pos.x
   | queen.y == pos.y
   | abs(queen.x - pos.x) == abs(queen.y - pos.y)

F place(m, n, &pBlackQueens, &pWhiteQueens)
   I m == 0
      R 1B

   V placingBlack = 1B
   L(i) 0 .< n
      L(j) 0 .< n
         V pos = (i, j)
         L(queen) pBlackQueens
            I queen == pos | (!placingBlack & isAttacking(queen, pos))
               L.break
         L.was_no_break
            L(queen) pWhiteQueens
               I queen == pos | (placingBlack & isAttacking(queen, pos))
                  L.break
            L.was_no_break
               I placingBlack
                  pBlackQueens [+]= pos
                  placingBlack = 0B
               E
                  pWhiteQueens [+]= pos
                  I place(m - 1, n, &pBlackQueens, &pWhiteQueens)
                     R 1B
                  pBlackQueens.pop()
                  pWhiteQueens.pop()
                  placingBlack = 1B

   I !placingBlack
      pBlackQueens.pop()
   R 0B

F printBoard(n, blackQueens, whiteQueens)
   V board = [Piece.EMPTY] * (n * n)

   L(queen) blackQueens
      board[queen.x * n + queen.y] = Piece.BLACK

   L(queen) whiteQueens
      board[queen.x * n + queen.y] = Piece.WHITE

   L(b) board
      V i = L.index
      I i != 0 & i % n == 0
         print()
      I b == BLACK
         print(‘B ’, end' ‘’)
      E I b == WHITE
         print(‘W ’, end' ‘’)
      E
         V j = i I/ n
         V k = i - j * n
         I j % 2 == k % 2
            print(‘x ’, end' ‘’)
         E
            print(‘o ’, end' ‘’)
   print("\n")

V nms = [
          (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3),
          (5, 1), (5, 2), (5, 3), (5, 4), (5, 5),
          (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),
          (7, 1), (7, 2), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7)
        ]

L(nm) nms
   print(‘#. black and #. white queens on a #. x #. board:’.format(nm[1], nm[1], nm[0], nm[0]))
   [(Int, Int)] blackQueens, whiteQueens
   I place(nm[1], nm[0], &blackQueens, &whiteQueens)
      printBoard(nm[0], blackQueens, whiteQueens)
   E
      print("No solution exists.\n")

Output:

1 black and 1 white queens on a 2 x 2 board:
No solution exists.

1 black and 1 white queens on a 3 x 3 board:
B o x
o x W
x o x

2 black and 2 white queens on a 3 x 3 board:
No solution exists.

1 black and 1 white queens on a 4 x 4 board:
B o x o
o x W x
x o x o
o x o x

2 black and 2 white queens on a 4 x 4 board:
B o x o
o x W x
B o x o
o x W x

3 black and 3 white queens on a 4 x 4 board:
No solution exists.

1 black and 1 white queens on a 5 x 5 board:
B o x o x
o x W x o
x o x o x
o x o x o
x o x o x

2 black and 2 white queens on a 5 x 5 board:
B o x o B
o x W x o
x W x o x
o x o x o
x o x o x

3 black and 3 white queens on a 5 x 5 board:
B o x o B
o x W x o
x W x o x
o x o B o
x W x o x

4 black and 4 white queens on a 5 x 5 board:
x B x B x
o x o x B
W o W o x
o x o x B
W o W o x

5 black and 5 white queens on a 5 x 5 board:
No solution exists.

1 black and 1 white queens on a 6 x 6 board:
B o x o x o
o x W x o x
x o x o x o
o x o x o x
x o x o x o
o x o x o x

2 black and 2 white queens on a 6 x 6 board:
B o x o B o
o x W x o x
x W x o x o
o x o x o x
x o x o x o
o x o x o x

3 black and 3 white queens on a 6 x 6 board:
B o x o B B
o x W x o x
x W x o x o
o x o x o x
x o W o x o
o x o x o x

4 black and 4 white queens on a 6 x 6 board:
B o x o B B
o x W x o x
x W x o x o
o x o x o B
x o W W x o
o x o x o x

5 black and 5 white queens on a 6 x 6 board:
x B x o B o
o x o B o B
W o x o x o
W x W x o x
x o x o x B
W x W x o x

6 black and 6 white queens on a 6 x 6 board:
No solution exists.

1 black and 1 white queens on a 7 x 7 board:
B o x o x o x
o x W x o x o
x o x o x o x
o x o x o x o
x o x o x o x
o x o x o x o
x o x o x o x

2 black and 2 white queens on a 7 x 7 board:
B o x o B o x
o x W x o x W
x o x o x o x
o x o x o x o
x o x o x o x
o x o x o x o
x o x o x o x

3 black and 3 white queens on a 7 x 7 board:
B o x o B o x
o x W x o x W
B o x o x o x
o x W x o x o
x o x o x o x
o x o x o x o
x o x o x o x

4 black and 4 white queens on a 7 x 7 board:
B o x o B o x
o x W x o x W
B o x o B o x
o x W x o x W
x o x o x o x
o x o x o x o
x o x o x o x

5 black and 5 white queens on a 7 x 7 board:
B o x o B o x
o x W x o x W
B o x o B o x
o x W x o x W
B o x o x o x
o x W x o x o
x o x o x o x

6 black and 6 white queens on a 7 x 7 board:
B o x o B o x
o x W x o x W
B o x o B o x
o x W x o x W
B o x o B o x
o x W x o x W
x o x o x o x

7 black and 7 white queens on a 7 x 7 board:
x B x o x B x
o B o x B x o
x B x o x B x
o x o x B x o
W o W o x o W
o x o W o x o
W o W W x o x

ATS

Translation of: Scheme

The program can print either all solutions or all solutions that are ‘inequivalent’, in the sense of https://oeis.org/A260680

The program also can stop after printing a specified number of solutions, although the default is to print all solutions.

(Commentary by the author: this program suffers similarly of slowness, in eliminating rotational equivalents, as does its Scheme ancestor. Some reasons: it uses backtracking and that is slow; it uses essentially the same inefficient storage format for solutions [one could for instance use integers], and it does not precompute rotational equivalents. However, it does satisfy the task requirements, and might be regarded as a good start. And it can solve the m=5, n=6 case in practical time on a fast machine. m=7, n=7 is a more annoying case.)

(********************************************************************)

#define ATS_DYNLOADFLAG 0

#include "share/atspre_define.hats"
#include "share/atspre_staload.hats"

staload UN = "prelude/SATS/unsafe.sats"

#define NIL list_vt_nil ()
#define :: list_vt_cons

#ifndef NDEBUG #then
  (* Safety is relatively unimportant in this program.
     Therefore I have made it so you can put ‘-DATS NDEBUG=1’ on
     your patscc command line, to skip some assertloc tests. *)
  #define NDEBUG 0
#endif

(********************************************************************)

#define EMPTY 0
#define BLACK 1
#define WHITE ~1

stadef is_color (c : int) : bool = (~1 <= c && c <= 1)
stadef reverse_color (c : int) : int = ~c

typedef color_t (tk : tkind, c : int) =
    [is_color c]
    g1int (tk, c)
typedef color_t (tk : tkind) =
    [c : int | is_color c]
    g1int (tk, c)

fn {tk : tkind}
reverse_color {c : int | is_color c}
              (c : g1int (tk, c)) :<>
    [c_rev : int | is_color c_rev;
                   c_rev == reverse_color c]
    g1int (tk, c_rev) =
  (* This template is a fancy way to say ‘minus’. *)
  ~c

(********************************************************************)

(* Matrix indices will run from 0..n-1 rather than 1..n. *)

#define SIDE_MAX 16             (* The maximum side size. For
                                   efficiency, please make it a
                                   power of two. *)
#define BOARD_SIZE 256          (* The storage size for a board. *)

prval _ = prop_verify {SIDE_MAX * SIDE_MAX == BOARD_SIZE} ()

fn {tk : tkind}
row_index {k : int | 0 <= k; k < BOARD_SIZE}
          (k : g1int (tk, k)) :<>
    [i : int | 0 <= i; i < SIDE_MAX]
    g1int (tk, i) =
  (* Let the C compiler convert this to bitmasking. *)
  g1int_nmod (k, g1i2i SIDE_MAX)

fn {tk : tkind}
column_index {k : int | 0 <= k; k < BOARD_SIZE}
             (k : g1int (tk, k)) :<>
    [i : int | 0 <= i; i < SIDE_MAX]
    g1int (tk, i) =
  (* Let the C compiler convert this to a shift. *)
  k / g1i2i SIDE_MAX

fn {tk : tkind}
storage_index {i, j : int | 0 <= i; i < SIDE_MAX;
                            0 <= j; j < SIDE_MAX}
              (i : g1int (tk, i),
               j : g1int (tk, j)) :<>
    [k : int | 0 <= k; k < BOARD_SIZE]
    g1int (tk, k) =
  (* Let the C compiler convert this to a shift and add. *)
  i + (j * g1i2i SIDE_MAX)

(********************************************************************)

extern fn {tk_index : tkind}
test_equiv$reindex_i
          {i, j : int | 0 <= i; 0 <= j}
          {n : int | 0 <= n; n <= SIDE_MAX;
                     i < n; j < n}
          (i : g1int (tk_index, i),
           j : g1int (tk_index, j),
           n : g1int (tk_index, n)) :<>
    [i1 : int | 0 <= i1; i1 < SIDE_MAX]
    g1int (tk_index, i1)

extern fn {tk_index : tkind}
test_equiv$reindex_j
          {i, j : int | 0 <= i; 0 <= j}
          {n : int | 0 <= n; n <= SIDE_MAX;
                     i < n; j < n}
          (i : g1int (tk_index, i),
           j : g1int (tk_index, j),
           n : g1int (tk_index, n)) :<>
    [j1 : int | 0 <= j1; j1 < SIDE_MAX]
    g1int (tk_index, j1)

extern fn {tk_color : tkind}
test_equiv$recolor
          {c : int | is_color c}
          (c : g1int (tk_color, c)) :<>
    [c1 : int | is_color c1]
    g1int (tk_color, c1)

fn {tk_index, tk_color : tkind}
test_equiv {n : int | 0 <= n; n <= SIDE_MAX}
           (a : &(@[color_t tk_color][BOARD_SIZE]),
            b : &(@[color_t tk_color][BOARD_SIZE]),
            n : g1int (tk_index, n)) :
    bool =
  let
    macdef reindex_i = test_equiv$reindex_i<tk_index>
    macdef reindex_j = test_equiv$reindex_j<tk_index>
    macdef recolor = test_equiv$recolor<tk_color>

    fun
    loopj {j : int | ~1 <= j; j < n} .<j + 1>.
          (a : &(@[color_t tk_color][BOARD_SIZE]),
           b : &(@[color_t tk_color][BOARD_SIZE]),
           n : g1int (tk_index, n),
           j : g1int (tk_index, j)) :
        bool =
      if j < g1i2i 0 then
        true
      else
        let
          fun loopi {i : int | ~1 <= i; i < n} .<i + 1>.
                    (a : &(@[color_t tk_color][BOARD_SIZE]),
                     b : &(@[color_t tk_color][BOARD_SIZE]),
                     n : g1int (tk_index, n),
                     j : g1int (tk_index, j),
                     i : g1int (tk_index, i)) :
              bool =
                if i < g1i2i 0 then
                  true
                else
                  let
                    val ka = storage_index<tk_index> (i, j)
                    val color_a = a[ka]

                    val i1 = test_equiv$reindex_i<tk_index> (i, j, n)
                    val j1 = test_equiv$reindex_j<tk_index> (i, j, n)
                    val kb = storage_index<tk_index> (i1, j1)
                    val color_b = recolor b[kb]
                  in
                    if color_a = color_b then
                      loopi (a, b, n, j, pred i)
                    else
                      false
                  end
        in
          if loopi (a, b, n, j, g1i2i (pred n)) then
            loopj (a, b, n, pred j)
          else
            false
        end
  in
    loopj (a, b, n, g1i2i (pred n))
  end

fn {tk_index, tk_color : tkind}
test_equiv_rotate0
          {n : int | 0 <= n; n <= SIDE_MAX}
          (a : &(@[color_t tk_color][BOARD_SIZE]),
           b : &(@[color_t tk_color][BOARD_SIZE]),
           n : g1int (tk_index, n)) :
    bool =
  let
    (* No rotations or reflections. *)
    implement
    test_equiv$reindex_i<tk_index> (i, j, n) = i
    implement
    test_equiv$reindex_j<tk_index> (i, j, n) = j
  in
    test_equiv<tk_index, tk_color> (a, b, n)
  end

fn {tk_index, tk_color : tkind}
test_equiv_rotate90
          {n : int | 0 <= n; n <= SIDE_MAX}
          (a : &(@[color_t tk_color][BOARD_SIZE]),
           b : &(@[color_t tk_color][BOARD_SIZE]),
           n : g1int (tk_index, n)) :
    bool =
  let
    (* Matrix rotation counterclockwise by 90 degrees. *)
    implement
    test_equiv$reindex_i<tk_index> {i, j} {n} (i, j, n) = pred n - j
    implement
    test_equiv$reindex_j<tk_index> (i, j, n) = i
  in
    test_equiv<tk_index, tk_color> (a, b, n)
  end

fn {tk_index, tk_color : tkind}
test_equiv_rotate180
          {n : int | 0 <= n; n <= SIDE_MAX}
          (a : &(@[color_t tk_color][BOARD_SIZE]),
           b : &(@[color_t tk_color][BOARD_SIZE]),
           n : g1int (tk_index, n)) :
    bool =
  let
    (* Matrix rotation by 180 degrees. *)
    implement
    test_equiv$reindex_i<tk_index> {i, j} {n} (i, j, n) = pred n - i
    implement
    test_equiv$reindex_j<tk_index> {i, j} {n} (i, j, n) = pred n - j
  in
    test_equiv<tk_index, tk_color> (a, b, n)
  end

fn {tk_index, tk_color : tkind}
test_equiv_rotate270
          {n : int | 0 <= n; n <= SIDE_MAX}
          (a : &(@[color_t tk_color][BOARD_SIZE]),
           b : &(@[color_t tk_color][BOARD_SIZE]),
           n : g1int (tk_index, n)) :
    bool =
  let
    (* Matrix rotation counterclockwise by 270 degrees. *)
    implement
    test_equiv$reindex_i<tk_index> (i, j, n) = j
    implement
    test_equiv$reindex_j<tk_index> {i, j} {n} (i, j, n) = pred n - i
  in
    test_equiv<tk_index, tk_color> (a, b, n)
  end

fn {tk_index, tk_color : tkind}
test_equiv_reflecti
          {n : int | 0 <= n; n <= SIDE_MAX}
          (a : &(@[color_t tk_color][BOARD_SIZE]),
           b : &(@[color_t tk_color][BOARD_SIZE]),
           n : g1int (tk_index, n)) :
    bool =
  let
    (* Reverse the order of the rows. *)
    implement
    test_equiv$reindex_i<tk_index> {i, j} {n} (i, j, n) = pred n - i
    implement
    test_equiv$reindex_j<tk_index> (i, j, n) = j
  in
    test_equiv<tk_index, tk_color> (a, b, n)
  end

fn {tk_index, tk_color : tkind}
test_equiv_reflectj
          {n : int | 0 <= n; n <= SIDE_MAX}
          (a : &(@[color_t tk_color][BOARD_SIZE]),
           b : &(@[color_t tk_color][BOARD_SIZE]),
           n : g1int (tk_index, n)) :
    bool =
  let
    (* Reverse the order of the columns. *)
    implement
    test_equiv$reindex_i<tk_index> (i, j, n) = i
    implement
    test_equiv$reindex_j<tk_index> {i, j} {n} (i, j, n) = pred n - j
  in
    test_equiv<tk_index, tk_color> (a, b, n)
  end

fn {tk_index, tk_color : tkind}
test_equiv_reflect_diag_down
          {n : int | 0 <= n; n <= SIDE_MAX}
          (a : &(@[color_t tk_color][BOARD_SIZE]),
           b : &(@[color_t tk_color][BOARD_SIZE]),
           n : g1int (tk_index, n)) :
    bool =
  let
    (* Transpose the matrix around its main diagonal. *)
    implement
    test_equiv$reindex_i<tk_index> (i, j, n) = j
    implement
    test_equiv$reindex_j<tk_index> (i, j, n) = i
  in
    test_equiv<tk_index, tk_color> (a, b, n)
  end

fn {tk_index, tk_color : tkind}
test_equiv_reflect_diag_up
          {n : int | 0 <= n; n <= SIDE_MAX}
          (a : &(@[color_t tk_color][BOARD_SIZE]),
           b : &(@[color_t tk_color][BOARD_SIZE]),
           n : g1int (tk_index, n)) :
    bool =
  let
    (* Transpose the matrix around its main skew diagonal. *)
    implement
    test_equiv$reindex_i<tk_index> {i, j} {n} (i, j, n) = pred n - j
    implement
    test_equiv$reindex_j<tk_index> {i, j} {n} (i, j, n) = pred n - i
  in
    test_equiv<tk_index, tk_color> (a, b, n)
  end

fn {tk_index, tk_color : tkind}
board_equiv {n : int | 0 <= n; n <= SIDE_MAX}
            (a : &(@[color_t tk_color][BOARD_SIZE]),
             b : &(@[color_t tk_color][BOARD_SIZE]),
             n : g1int (tk_index, n),
             rotation_equiv_classes : bool) :
    bool =
  let
    (* Leave the colors unchanged. *)
    implement test_equiv$recolor<tk_color> (c) = c

    (* Test without rotations or reflections. *)
    val equiv = test_equiv_rotate0<tk_index, tk_color> (a, b, n)
  in
    if ~rotation_equiv_classes then
      equiv
    else
      let
        (* Leave the colors unchanged. *)
        implement test_equiv$recolor<tk_color> (c) = c

        val equiv =
          (equiv ||
           test_equiv_rotate90<tk_index, tk_color> (a, b, n) ||
           test_equiv_rotate180<tk_index, tk_color> (a, b, n) ||
           test_equiv_rotate270<tk_index, tk_color> (a, b, n) ||
           test_equiv_reflecti<tk_index, tk_color> (a, b, n) ||
           test_equiv_reflectj<tk_index, tk_color> (a, b, n) ||
           test_equiv_reflect_diag_down<tk_index, tk_color> (a, b, n) ||
           test_equiv_reflect_diag_up<tk_index, tk_color> (a, b, n))

        (* Reverse the colors of b in each test. *)
        implement test_equiv$recolor<tk_color> (c) = reverse_color c

        val equiv =
          (equiv ||
           test_equiv_rotate0<tk_index, tk_color> (a, b, n) ||
           test_equiv_rotate90<tk_index, tk_color> (a, b, n) ||
           test_equiv_rotate180<tk_index, tk_color> (a, b, n) ||
           test_equiv_rotate270<tk_index, tk_color> (a, b, n) ||
           test_equiv_reflecti<tk_index, tk_color> (a, b, n) ||
           test_equiv_reflectj<tk_index, tk_color> (a, b, n) ||
           test_equiv_reflect_diag_down<tk_index, tk_color> (a, b, n) ||
           test_equiv_reflect_diag_up<tk_index, tk_color> (a, b, n))
      in
        equiv
      end
  end

(********************************************************************)

fn {tk_index : tkind}
fprint_rule {n : int | 0 <= n; n <= SIDE_MAX}
            (f : FILEref,
             n : g1int (tk_index, n)) :
    void =
  let
    fun
    loop {j : int | 0 <= j; j <= n} .<n - j>.
         (j : g1int (tk_index, j)) :
        void =
      if j <> n then
        begin
          fileref_puts (f, "----+");
          loop (succ j)
        end
  in
    fileref_puts (f, "+");
    loop (g1i2i 0)
  end

fn {tk_index, tk_color : tkind}
fprint_board {n : int | 0 <= n; n <= SIDE_MAX}
             (f : FILEref,
              a : &(@[color_t tk_color][BOARD_SIZE]),
              n : g1int (tk_index, n)) :
    void =
  if n <> 0 then
    let
      fun
      loopi {i : int | ~1 <= i; i < n} .<i + 1>.
            (f : FILEref,
             a : &(@[color_t tk_color][BOARD_SIZE]),
             n : g1int (tk_index, n),
             i : g1int (tk_index, i)) :
          void =
        if i <> ~1 then
          let
            fun
            loopj {j : int | 0 <= j; j <= n} .<n - j>.
                  (f : FILEref,
                   a : &(@[color_t tk_color][BOARD_SIZE]),
                   n : g1int (tk_index, n),
                   i : g1int (tk_index, i),
                   j : g1int (tk_index, j)) :
                void =
              if j <> n then
                let
                  val k = storage_index<tk_index> (i, j)
                  val color = a[k]
                  val representation =
                    if color = g1i2i BLACK then
                      "|  B "
                    else if color = g1i2i WHITE then
                      "|  W "
                    else
                      "|    "
                in
                  fileref_puts (f, representation);
                  loopj (f, a, n, i, succ j)
                end
          in
            fileref_puts (f, "\n");
            loopj (f, a, n, i, g1i2i 0);
            fileref_puts (f, "|\n");
            fprint_rule (f, n);
            loopi (f, a, n, pred i)
          end
    in
      fprint_rule (f, n);
      loopi (f, a, n, pred n)
    end

(********************************************************************)

(* M2_MAX equals the maximum number of queens of either color.
   Thus it is the maximum of 2*m, where m is the number of queens
   in an army. *)
#define M2_MAX BOARD_SIZE

(* The even-index queens are BLACK, the odd-index queens are WHITE. *)

vtypedef board_record_vt (tk_color : tkind,
                          p        : addr) =
  @{
    pf = @[color_t tk_color][BOARD_SIZE] @ p,
    pfgc = mfree_gc_v p |
    p = ptr p
  }
vtypedef board_record_vt (tk_color : tkind) =
  [p : addr | null < p]
  board_record_vt (tk_color, p)

vtypedef board_record_list_vt (tk_color : tkind,
                               n : int) =
  list_vt (board_record_vt tk_color, n)
vtypedef board_record_list_vt (tk_color : tkind) =
  [n : int]
  board_record_list_vt (tk_color, n)

fn
board_record_vt_free
          {tk_color : tkind}
          {p        : addr}
          (record   : board_record_vt (tk_color, p)) :
    void =
  let
    val @{
          pf = pf,
          pfgc = pfgc |
          p = p
        } = record
  in
    array_ptr_free (pf, pfgc | p)
  end

overload free with board_record_vt_free

fn
board_record_list_vt_free
          {tk_color : tkind}
          {n        : int}
          (lst      : board_record_list_vt (tk_color, n)) :
    void =
  let
    fun
    loop {n   : int | 0 <= n} .<n>.
         (lst : board_record_list_vt (tk_color, n)) :
        void =
      case+ lst of
      | ~ NIL => ()
      | ~ head :: tail =>
        begin
          free head;
          loop tail
        end

    prval _ = lemma_list_vt_param lst
  in
    loop lst
  end

fn {tk_index, tk_color : tkind}
any_board_equiv {n     : int | 0 <= n; n <= SIDE_MAX}
                (board : &(@[color_t tk_color][BOARD_SIZE]),
                 lst   : !board_record_list_vt tk_color,
                 n     : g1int (tk_index, n),
                 rotation_equiv_classes : bool) :
    bool =
  let
    macdef board_equiv = board_equiv<tk_index, tk_color>

    fun
    loop {k : int | 0 <= k} .<k>.
         (board : &(@[color_t tk_color][BOARD_SIZE]),
          lst   : !board_record_list_vt (tk_color, k),
          n     : g1int (tk_index, n)) :
        bool =
      case+ lst of
      | NIL => false
      | head :: tail =>
        if board_equiv (!(head.p), board, n,
                        rotation_equiv_classes) then
          true
        else
          loop (board, tail, n)

    prval _ = lemma_list_vt_param lst
  in
    loop (board, lst, n)
  end

fn {tk_index, tk_color : tkind}
queens_to_board
          {count  : int | 0 <= count; count <= M2_MAX}
          (queens : &(@[g1int tk_index][M2_MAX]),
           count  : int count) :
    [p : addr | null < p]
    board_record_vt (tk_color, p) =
  let
    typedef color_t = color_t tk_color

    fun
    loop {k : int | ~1 <= k; k < count} .<k + 1>.
         (queens : &(@[g1int tk_index][M2_MAX]),
          board  : &(@[color_t tk_color][BOARD_SIZE]),
          k      : int k) :
        void =
      if 0 <= k then
        let
          val [coords : int] coords = queens[k]
          #if NDEBUG <> 0 #then
            prval _ = $UN.prop_assert {0 <= coords} ()
            prval _ = $UN.prop_assert {coords < BOARD_SIZE} ()
          #else
            val _ = assertloc (g1i2i 0 <= coords)
            val _ = assertloc (coords < g1i2i BOARD_SIZE)
          #endif
        in
          if g1int_nmod (k, 2) = 0 then
            board[coords] := g1i2i BLACK
          else
            board[coords] := g1i2i WHITE;
          loop (queens, board, pred k)
        end

    val @(pf, pfgc | p) = array_ptr_alloc<color_t> (i2sz BOARD_SIZE)
    val _ = array_initize_elt<color_t> (!p, i2sz BOARD_SIZE,
                                        g1i2i EMPTY)
    val _ = loop (queens, !p, pred count)
  in
    @{
      pf = pf,
      pfgc = pfgc |
      p = p
    }
  end

fn {tk : tkind}
queen_would_fit_in
          {count  : int | 0 <= count; count <= M2_MAX}
          {i, j   : int | 0 <= i; i < SIDE_MAX;
                          0 <= j; j < SIDE_MAX}
          (queens : &(@[g1int tk][M2_MAX]),
           count  : int count,
           i      : g1int (tk, i),
           j      : g1int (tk, j)) :
    bool =
  (* Would a new queen at (i,j) be feasible? *)
  if count = 0 then
    true
  else
    let
      fun
      loop {k : int | ~1 <= k; k < count}
           (queens : &(@[g1int tk][M2_MAX]),
            k      : int k) :
          bool =
        if k < 0 then
          true
        else
          let
            val [coords : int] coords = queens[k]
            #if NDEBUG <> 0 #then
              prval _ = $UN.prop_assert {0 <= coords} ()
              prval _ = $UN.prop_assert {coords < BOARD_SIZE} ()
            #else
              val _ = assertloc (g1i2i 0 <= coords)
              val _ = assertloc (coords < g1i2i BOARD_SIZE)
            #endif

            val i1 = row_index<tk> coords
            val j1 = column_index<tk> coords
          in
            if g1int_nmod (k, 2) = g1int_nmod (count, 2) then
            (* The two queens are of the same color. They may not
               share the same square. *)
              begin
                if i <> i1 || j <> j1 then
                  loop (queens, pred k)
                else
                  false
              end
            else
              (* The two queens are of different colors. They may not
                 share the same square nor attack each other. *)
              begin
                if (i <> i1 &&
                    j <> j1 &&
                    i + j <> i1 + j1 &&
                    i - j <> i1 - j1) then
                  loop (queens, pred k)
                else
                  false
              end
          end
    in
      loop (queens, pred count)
    end

fn {tk : tkind}
latest_queen_fits_in
          {count  : int | 1 <= count; count <= M2_MAX}
          (queens : &(@[g1int tk][M2_MAX]),
           count  : int count) :
    bool =
  let
    val [coords : int] coords = queens[pred count]
    #if NDEBUG <> 0 #then
      prval _ = $UN.prop_assert {0 <= coords} ()
      prval _ = $UN.prop_assert {coords < BOARD_SIZE} ()
    #else
      val _ = assertloc (g1i2i 0 <= coords)
      val _ = assertloc (coords < g1i2i BOARD_SIZE)
    #endif

    val i = row_index<tk> coords
    val j = column_index<tk> coords
  in
    queen_would_fit_in<tk> (queens, pred count, i, j)
  end

fn {tk_index, tk_color : tkind}
find_solutions
          {m : int | 0 <= m; 2 * m <= M2_MAX}
          {n : int | 0 <= n; n <= SIDE_MAX}
          {max_solutions : int | 0 <= max_solutions}
          (f : FILEref,
           m : int m,
           n : g1int (tk_index, n),
           rotation_equiv_classes : bool,
           max_solutions : int max_solutions) :
    [num_solutions : int | 0 <= num_solutions;
                           num_solutions <= max_solutions]
    @(int num_solutions,
      board_record_list_vt (tk_color, num_solutions)) =
  (* This template function both prints the solutions and returns
     them as a linked list. *)
  if m = 0 then
    @(0, NIL)
  else if max_solutions = 0 then
    @(0, NIL)
  else
    let
      macdef latest_queen_fits_in = latest_queen_fits_in<tk_index>
      macdef queens_to_board = queens_to_board<tk_index, tk_color>
      macdef fprint_board = fprint_board<tk_index, tk_color>
      macdef any_board_equiv = any_board_equiv<tk_index, tk_color>
      macdef row_index = row_index<tk_index>
      macdef column_index = column_index<tk_index>
      macdef storage_index = storage_index<tk_index>

      fnx
      loop {num_solutions : int | 0 <= num_solutions;
                                  num_solutions <= max_solutions}
           {num_queens    : int | 0 <= num_queens;
                                  num_queens <= 2 * m}
           (solutions     : board_record_list_vt (tk_color,
                                                  num_solutions),
            num_solutions : int num_solutions,
            queens        : &(@[g1int tk_index][M2_MAX]),
            num_queens    : int num_queens) :
          [num_solutions1 : int | 0 <= num_solutions1;
                                  num_solutions1 <= max_solutions]
          @(int num_solutions1,
            board_record_list_vt (tk_color, num_solutions1)) =
        if num_queens = 0 then
          @(num_solutions, solutions)
        else if num_solutions = max_solutions then
          @(num_solutions, solutions)
        else if latest_queen_fits_in (queens, num_queens) then
          begin
            if num_queens = 2 * m then
              let
                val board = queens_to_board (queens, num_queens)
                val equiv_solution =
                  any_board_equiv (!(board.p), solutions, n,
                                   rotation_equiv_classes)
              in
                if ~equiv_solution then
                  begin
                    fprintln! (f, "Solution ",
                               succ num_solutions);
                    fprint_board (f, !(board.p), n);
                    fileref_puts (f, "\n\n");
                    move_a_queen (board :: solutions,
                                  succ num_solutions,
                                  queens, num_queens)
                  end
                else
                  begin
                    free board;
                    move_a_queen (solutions, num_solutions,
                                  queens, num_queens)
                  end
              end
            else
              add_another_queen (solutions, num_solutions,
                                 queens, num_queens)
          end
        else
          move_a_queen (solutions, num_solutions,
                        queens, num_queens)
      and
      add_another_queen
                {num_solutions : int |
                                0 <= num_solutions;
                                 num_solutions <= max_solutions}
                {num_queens : int | 0 <= num_queens;
                                    num_queens + 1 <= 2 * m}
                (solutions : board_record_list_vt
                                  (tk_color, num_solutions),
                 num_solutions : int num_solutions,
                 queens     : &(@[g1int tk_index][M2_MAX]),
                 num_queens : int num_queens) :
          [num_solutions1 : int | 0 <= num_solutions1;
                                  num_solutions1 <= max_solutions]
          @(int num_solutions1,
            board_record_list_vt (tk_color, num_solutions1)) =
        let
          val coords = storage_index (g1i2i 0, g1i2i 0)
        in
          queens[num_queens] := coords;
          loop (solutions, num_solutions, queens, succ num_queens)
        end
      and
      move_a_queen {num_solutions : int |
                                0 <= num_solutions;
                                num_solutions <= max_solutions}
                   {num_queens : int | 0 <= num_queens;
                                       num_queens <= 2 * m}
                   (solutions : board_record_list_vt
                                  (tk_color, num_solutions),
                    num_solutions : int num_solutions,
                    queens : &(@[g1int tk_index][M2_MAX]),
                    num_queens : int num_queens) :
          [num_solutions1 : int | 0 <= num_solutions1;
                                  num_solutions1 <= max_solutions]
          @(int num_solutions1,
            board_record_list_vt (tk_color, num_solutions1)) =
        if num_queens = 0 then
          loop (solutions, num_solutions, queens, num_queens)
        else
          let
            val [coords : int] coords = queens[pred num_queens]
            #if NDEBUG <> 0 #then
              prval _ = $UN.prop_assert {0 <= coords} ()
              prval _ = $UN.prop_assert {coords < BOARD_SIZE} ()
            #else
              val _ = assertloc (g1i2i 0 <= coords)
              val _ = assertloc (coords < g1i2i BOARD_SIZE)
            #endif

            val [i : int] i = row_index coords
            val [j : int] j = column_index coords

            prval _ = prop_verify {0 <= i} ()
            prval _ = prop_verify {i < SIDE_MAX} ()

            prval _ = prop_verify {0 <= j} ()
            prval _ = prop_verify {j < SIDE_MAX} ()

            #if NDEBUG <> 0 #then
              prval _ = $UN.prop_assert {i < n} ()
              prval _ = $UN.prop_assert {j < n} ()
            #else
              val _ = $effmask_exn assertloc (i < n)
              val _ = $effmask_exn assertloc (j < n)
            #endif
          in
            if j = pred n then
              begin
                if i = pred n then
                  (* Backtrack. *)
                  move_a_queen (solutions, num_solutions,
                                queens, pred num_queens)
                else
                  let
                    val coords = storage_index (succ i, j)
                  in
                    queens[pred num_queens] := coords;
                    loop (solutions, num_solutions,
                          queens, num_queens)
                  end
              end
            else
              let
                #if NDEBUG <> 0 #then
                  prval _ = $UN.prop_assert {j < n - 1} ()
                #else
                  val _ = $effmask_exn assertloc (j < pred n)
                #endif
              in
                if i = pred n then
                  let
                    val coords = storage_index (g1i2i 0, succ j)
                  in
                    queens[pred num_queens] := coords;
                    loop (solutions, num_solutions,
                          queens, num_queens)
                  end
                else
                  let
                    val coords = storage_index (succ i, j)
                  in
                    queens[pred num_queens] := coords;
                    loop (solutions, num_solutions,
                          queens, num_queens)
                  end
              end
          end

      var queens = @[g1int tk_index][M2_MAX] (g1i2i 0)
    in
      queens[0] := storage_index (g1i2i 0, g1i2i 0);
      loop (NIL, 0, queens, 1)
    end

(********************************************************************)

%{^
#include <stdlib.h>
#include <limits.h>
%}

implement
main0 (argc, argv) =
  let
    stadef tk_index = int_kind
    stadef tk_color = int_kind

    macdef usage_error (status) =
      begin
        println! ("Usage: ", argv[0],
                  " M N IGNORE_EQUIVALENTS [MAX_SOLUTIONS]");
        exit (,(status))
      end

    val max_max_solutions =
      $extval ([i : int | 0 <= i] int i, "INT_MAX")
  in
    if 4 <= argc then
      let
        val m = $extfcall (int, "atoi", argv[1])
        val m = g1ofg0 m
        val _ = if m < 0 then usage_error (2)
        val _ = assertloc (0 <= m)
        val _ =
          if M2_MAX < 2 * m then
            begin
              println! (argv[0], ": M cannot be larger than ",
                        M2_MAX / 2);
              usage_error (2)
            end
        val _ = assertloc (2 * m <= M2_MAX)

        val n = $extfcall (int, "atoi", argv[2])
        val n = g1ofg0 n
        val _ = if n < 0 then usage_error (2)
        val _ = assertloc (0 <= n)
        val _ =
          if SIDE_MAX < n then
            begin
              println! (argv[0], ": N cannot be larger than ",
                        SIDE_MAX);
              usage_error (2)
            end
        val _ = assertloc (n <= SIDE_MAX)

        val ignore_equivalents =
          if argv[3] = "T" || argv[3] = "t" || argv[3] = "1" then
            true
          else if argv[3] = "F" || argv[3] = "f" || argv[3] = "0" then
            false
          else
            begin
              println! (argv[0],
                        ": select T=t=1 or F=f=0 ",
                        "for IGNORE_EQUIVALENTS");
              usage_error (2);
              false
            end
      in
        if argc = 5 then
          let
            val max_solutions = $extfcall (int, "atoi", argv[4])
            val max_solutions = g1ofg0 max_solutions
            val max_solutions = max (0, max_solutions)

            val @(num_solutions, solutions) =
            find_solutions<tk_index, tk_color>
              (stdout_ref, m, n, ignore_equivalents,
               max_solutions)
          in
            board_record_list_vt_free solutions
          end
        else          
          let
            val @(num_solutions, solutions) =
            find_solutions<tk_index, tk_color>
              (stdout_ref, m, n, ignore_equivalents,
               max_max_solutions)
          in
            board_record_list_vt_free solutions
          end
      end
    else
      usage_error (1)
  end

(********************************************************************)

Output:

$ patscc -DATS NDEBUG=1 -O3 -fno-stack-protector -march=native -DATS_MEMALLOC_LIBC -o peaceful_queens peaceful_queens.dats && ./peaceful_queens 4 5 T

Solution 1
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+

Solution 2
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+

Solution 3
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+

C

Translation of: C#

#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>

enum Piece {
    Empty,
    Black,
    White,
};

typedef struct Position_t {
    int x, y;
} Position;

///////////////////////////////////////////////

struct Node_t {
    Position pos;
    struct Node_t *next;
};

void releaseNode(struct Node_t *head) {
    if (head == NULL) return;

    releaseNode(head->next);
    head->next = NULL;

    free(head);
}

typedef struct List_t {
    struct Node_t *head;
    struct Node_t *tail;
    size_t length;
} List;

List makeList() {
    return (List) { NULL, NULL, 0 };
}

void releaseList(List *lst) {
    if (lst == NULL) return;

    releaseNode(lst->head);
    lst->head = NULL;
    lst->tail = NULL;
}

void addNode(List *lst, Position pos) {
    struct Node_t *newNode;

    if (lst == NULL) {
        exit(EXIT_FAILURE);
    }

    newNode = malloc(sizeof(struct Node_t));
    if (newNode == NULL) {
        exit(EXIT_FAILURE);
    }

    newNode->next = NULL;
    newNode->pos = pos;

    if (lst->head == NULL) {
        lst->head = lst->tail = newNode;
    } else {
        lst->tail->next = newNode;
        lst->tail = newNode;
    }

    lst->length++;
}

void removeAt(List *lst, size_t pos) {
    if (lst == NULL) return;

    if (pos == 0) {
        struct Node_t *temp = lst->head;

        if (lst->tail == lst->head) {
            lst->tail = NULL;
        }

        lst->head = lst->head->next;
        temp->next = NULL;

        free(temp);
        lst->length--;
    } else {
        struct Node_t *temp = lst->head;
        struct Node_t *rem;
        size_t i = pos;

        while (i-- > 1) {
            temp = temp->next;
        }

        rem = temp->next;
        if (rem == lst->tail) {
            lst->tail = temp;
        }

        temp->next = rem->next;

        rem->next = NULL;
        free(rem);

        lst->length--;
    }
}

///////////////////////////////////////////////

bool isAttacking(Position queen, Position pos) {
    return queen.x == pos.x
        || queen.y == pos.y
        || abs(queen.x - pos.x) == abs(queen.y - pos.y);
}

bool place(int m, int n, List *pBlackQueens, List *pWhiteQueens) {
    struct Node_t *queenNode;
    bool placingBlack = true;
    int i, j;

    if (pBlackQueens == NULL || pWhiteQueens == NULL) {
        exit(EXIT_FAILURE);
    }

    if (m == 0) return true;
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            Position pos = { i, j };

            queenNode = pBlackQueens->head;
            while (queenNode != NULL) {
                if ((queenNode->pos.x == pos.x && queenNode->pos.y == pos.y) || !placingBlack && isAttacking(queenNode->pos, pos)) {
                    goto inner;
                }
                queenNode = queenNode->next;
            }

            queenNode = pWhiteQueens->head;
            while (queenNode != NULL) {
                if ((queenNode->pos.x == pos.x && queenNode->pos.y == pos.y) || placingBlack && isAttacking(queenNode->pos, pos)) {
                    goto inner;
                }
                queenNode = queenNode->next;
            }

            if (placingBlack) {
                addNode(pBlackQueens, pos);
                placingBlack = false;
            } else {
                addNode(pWhiteQueens, pos);
                if (place(m - 1, n, pBlackQueens, pWhiteQueens)) {
                    return true;
                }
                removeAt(pBlackQueens, pBlackQueens->length - 1);
                removeAt(pWhiteQueens, pWhiteQueens->length - 1);
                placingBlack = true;
            }

        inner: {}
        }
    }
    if (!placingBlack) {
        removeAt(pBlackQueens, pBlackQueens->length - 1);
    }
    return false;
}

void printBoard(int n, List *pBlackQueens, List *pWhiteQueens) {
    size_t length = n * n;
    struct Node_t *queenNode;
    char *board;
    size_t i, j, k;

    if (pBlackQueens == NULL || pWhiteQueens == NULL) {
        exit(EXIT_FAILURE);
    }

    board = calloc(length, sizeof(char));
    if (board == NULL) {
        exit(EXIT_FAILURE);
    }

    queenNode = pBlackQueens->head;
    while (queenNode != NULL) {
        board[queenNode->pos.x * n + queenNode->pos.y] = Black;
        queenNode = queenNode->next;
    }

    queenNode = pWhiteQueens->head;
    while (queenNode != NULL) {
        board[queenNode->pos.x * n + queenNode->pos.y] = White;
        queenNode = queenNode->next;
    }

    for (i = 0; i < length; i++) {
        if (i != 0 && i % n == 0) {
            printf("\n");
        }
        switch (board[i]) {
        case Black:
            printf("B ");
            break;
        case White:
            printf("W ");
            break;
        default:
            j = i / n;
            k = i - j * n;
            if (j % 2 == k % 2) {
                printf("  ");
            } else {
                printf("# ");
            }
            break;
        }
    }

    printf("\n\n");
}

void test(int n, int q) {
    List blackQueens = makeList();
    List whiteQueens = makeList();

    printf("%d black and %d white queens on a %d x %d board:\n", q, q, n, n);
    if (place(q, n, &blackQueens, &whiteQueens)) {
        printBoard(n, &blackQueens, &whiteQueens);
    } else {
        printf("No solution exists.\n\n");
    }

    releaseList(&blackQueens);
    releaseList(&whiteQueens);
}

int main() {
    test(2, 1);

    test(3, 1);
    test(3, 2);

    test(4, 1);
    test(4, 2);
    test(4, 3);

    test(5, 1);
    test(5, 2);
    test(5, 3);
    test(5, 4);
    test(5, 5);

    test(6, 1);
    test(6, 2);
    test(6, 3);
    test(6, 4);
    test(6, 5);
    test(6, 6);

    test(7, 1);
    test(7, 2);
    test(7, 3);
    test(7, 4);
    test(7, 5);
    test(7, 6);
    test(7, 7);

    return EXIT_SUCCESS;
}

Output:

1 black and 1 white queens on a 2 x 2 board:
No solution exists.

1 black and 1 white queens on a 3 x 3 board:
B #
#   W
  #

2 black and 2 white queens on a 3 x 3 board:
No solution exists.

1 black and 1 white queens on a 4 x 4 board:
B #   #
#   W
  #   #
#   #

2 black and 2 white queens on a 4 x 4 board:
B #   #
#   W
B #   #
#   W

3 black and 3 white queens on a 4 x 4 board:
No solution exists.

1 black and 1 white queens on a 5 x 5 board:
B #   #
#   W   #
  #   #
#   #   #
  #   #

2 black and 2 white queens on a 5 x 5 board:
B #   # B
#   W   #
  W   #
#   #   #
  #   #

3 black and 3 white queens on a 5 x 5 board:
B #   # B
#   W   #
  W   #
#   # B #
  W   #

4 black and 4 white queens on a 5 x 5 board:
  B   B
#   #   B
W # W #
#   #   B
W # W #

5 black and 5 white queens on a 5 x 5 board:
No solution exists.

1 black and 1 white queens on a 6 x 6 board:
B #   #   #
#   W   #
  #   #   #
#   #   #
  #   #   #
#   #   #

2 black and 2 white queens on a 6 x 6 board:
B #   # B #
#   W   #
  W   #   #
#   #   #
  #   #   #
#   #   #

3 black and 3 white queens on a 6 x 6 board:
B #   # B B
#   W   #
  W   #   #
#   #   #
  # W #   #
#   #   #

4 black and 4 white queens on a 6 x 6 board:
B #   # B B
#   W   #
  W   #   #
#   #   # B
  # W W   #
#   #   #

5 black and 5 white queens on a 6 x 6 board:
  B   # B #
#   # B # B
W #   #   #
W   W   #
  #   #   B
W   W   #

6 black and 6 white queens on a 6 x 6 board:
No solution exists.

1 black and 1 white queens on a 7 x 7 board:
B #   #   #
#   W   #   #
  #   #   #
#   #   #   #
  #   #   #
#   #   #   #
  #   #   #

2 black and 2 white queens on a 7 x 7 board:
B #   # B #
#   W   #   W
  #   #   #
#   #   #   #
  #   #   #
#   #   #   #
  #   #   #

3 black and 3 white queens on a 7 x 7 board:
B #   # B #
#   W   #   W
B #   #   #
#   W   #   #
  #   #   #
#   #   #   #
  #   #   #

4 black and 4 white queens on a 7 x 7 board:
B #   # B #
#   W   #   W
B #   # B #
#   W   #   W
  #   #   #
#   #   #   #
  #   #   #

5 black and 5 white queens on a 7 x 7 board:
B #   # B #
#   W   #   W
B #   # B #
#   W   #   W
B #   #   #
#   W   #   #
  #   #   #

6 black and 6 white queens on a 7 x 7 board:
B #   # B #
#   W   #   W
B #   # B #
#   W   #   W
B #   # B #
#   W   #   W
  #   #   #

7 black and 7 white queens on a 7 x 7 board:
  B   #   B
# B #   B   #
  B   #   B
#   #   B   #
W # W #   # W
#   # W #   #
W # W W   #

C#

Translation of: D

using System;
using System.Collections.Generic;

namespace PeacefulChessQueenArmies {
    using Position = Tuple<int, int>;

    enum Piece {
        Empty,
        Black,
        White
    }

    class Program {
        static bool IsAttacking(Position queen, Position pos) {
            return queen.Item1 == pos.Item1
                || queen.Item2 == pos.Item2
                || Math.Abs(queen.Item1 - pos.Item1) == Math.Abs(queen.Item2 - pos.Item2);
        }

        static bool Place(int m, int n, List<Position> pBlackQueens, List<Position> pWhiteQueens) {
            if (m == 0) {
                return true;
            }
            bool placingBlack = true;
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    var pos = new Position(i, j);
                    foreach (var queen in pBlackQueens) {
                        if (queen.Equals(pos) || !placingBlack && IsAttacking(queen, pos)) {
                            goto inner;
                        }
                    }
                    foreach (var queen in pWhiteQueens) {
                        if (queen.Equals(pos) || placingBlack && IsAttacking(queen, pos)) {
                            goto inner;
                        }
                    }
                    if (placingBlack) {
                        pBlackQueens.Add(pos);
                        placingBlack = false;
                    } else {
                        pWhiteQueens.Add(pos);
                        if (Place(m - 1, n, pBlackQueens, pWhiteQueens)) {
                            return true;
                        }
                        pBlackQueens.RemoveAt(pBlackQueens.Count - 1);
                        pWhiteQueens.RemoveAt(pWhiteQueens.Count - 1);
                        placingBlack = true;
                    }
                inner: { }
                }
            }
            if (!placingBlack) {
                pBlackQueens.RemoveAt(pBlackQueens.Count - 1);
            }
            return false;
        }

        static void PrintBoard(int n, List<Position> blackQueens, List<Position> whiteQueens) {
            var board = new Piece[n * n];

            foreach (var queen in blackQueens) {
                board[queen.Item1 * n + queen.Item2] = Piece.Black;
            }
            foreach (var queen in whiteQueens) {
                board[queen.Item1 * n + queen.Item2] = Piece.White;
            }

            for (int i = 0; i < board.Length; i++) {
                if (i != 0 && i % n == 0) {
                    Console.WriteLine();
                }
                switch (board[i]) {
                    case Piece.Black:
                        Console.Write("B ");
                        break;
                    case Piece.White:
                        Console.Write("W ");
                        break;
                    case Piece.Empty:
                        int j = i / n;
                        int k = i - j * n;
                        if (j % 2 == k % 2) {
                            Console.Write("  ");
                        } else {
                            Console.Write("# ");
                        }
                        break;
                }
            }

            Console.WriteLine("\n");
        }

        static void Main() {
            var nms = new int[,] {
                {2, 1}, {3, 1}, {3, 2}, {4, 1}, {4, 2}, {4, 3},
                {5, 1}, {5, 2}, {5, 3}, {5, 4}, {5, 5},
                {6, 1}, {6, 2}, {6, 3}, {6, 4}, {6, 5}, {6, 6},
                {7, 1}, {7, 2}, {7, 3}, {7, 4}, {7, 5}, {7, 6}, {7, 7},
            };
            for (int i = 0; i < nms.GetLength(0); i++) {
                Console.WriteLine("{0} black and {0} white queens on a {1} x {1} board:", nms[i, 1], nms[i, 0]);
                List<Position> blackQueens = new List<Position>();
                List<Position> whiteQueens = new List<Position>();
                if (Place(nms[i, 1], nms[i, 0], blackQueens, whiteQueens)) {
                    PrintBoard(nms[i, 0], blackQueens, whiteQueens);
                } else {
                    Console.WriteLine("No solution exists.\n");
                }
            }
        }
    }
}

Output:

1 black and 1 white queens on a 2 x 2 board:
No solution exists.

1 black and 1 white queens on a 3 x 3 board:
B #
#   W
  #

2 black and 2 white queens on a 3 x 3 board:
No solution exists.

1 black and 1 white queens on a 4 x 4 board:
B #   #
#   W
  #   #
#   #

2 black and 2 white queens on a 4 x 4 board:
B #   #
#   W
B #   #
#   W

3 black and 3 white queens on a 4 x 4 board:
No solution exists.

1 black and 1 white queens on a 5 x 5 board:
B #   #
#   W   #
  #   #
#   #   #
  #   #

2 black and 2 white queens on a 5 x 5 board:
B #   # B
#   W   #
  W   #
#   #   #
  #   #

3 black and 3 white queens on a 5 x 5 board:
B #   # B
#   W   #
  W   #
#   # B #
  W   #

4 black and 4 white queens on a 5 x 5 board:
  B   B
#   #   B
W # W #
#   #   B
W # W #

5 black and 5 white queens on a 5 x 5 board:
No solution exists.

1 black and 1 white queens on a 6 x 6 board:
B #   #   #
#   W   #
  #   #   #
#   #   #
  #   #   #
#   #   #

2 black and 2 white queens on a 6 x 6 board:
B #   # B #
#   W   #
  W   #   #
#   #   #
  #   #   #
#   #   #

3 black and 3 white queens on a 6 x 6 board:
B #   # B B
#   W   #
  W   #   #
#   #   #
  # W #   #
#   #   #

4 black and 4 white queens on a 6 x 6 board:
B #   # B B
#   W   #
  W   #   #
#   #   # B
  # W W   #
#   #   #

5 black and 5 white queens on a 6 x 6 board:
  B   # B #
#   # B # B
W #   #   #
W   W   #
  #   #   B
W   W   #

6 black and 6 white queens on a 6 x 6 board:
No solution exists.

1 black and 1 white queens on a 7 x 7 board:
B #   #   #
#   W   #   #
  #   #   #
#   #   #   #
  #   #   #
#   #   #   #
  #   #   #

2 black and 2 white queens on a 7 x 7 board:
B #   # B #
#   W   #   W
  #   #   #
#   #   #   #
  #   #   #
#   #   #   #
  #   #   #

3 black and 3 white queens on a 7 x 7 board:
B #   # B #
#   W   #   W
B #   #   #
#   W   #   #
  #   #   #
#   #   #   #
  #   #   #

4 black and 4 white queens on a 7 x 7 board:
B #   # B #
#   W   #   W
B #   # B #
#   W   #   W
  #   #   #
#   #   #   #
  #   #   #

5 black and 5 white queens on a 7 x 7 board:
B #   # B #
#   W   #   W
B #   # B #
#   W   #   W
B #   #   #
#   W   #   #
  #   #   #

6 black and 6 white queens on a 7 x 7 board:
B #   # B #
#   W   #   W
B #   # B #
#   W   #   W
B #   # B #
#   W   #   W
  #   #   #

7 black and 7 white queens on a 7 x 7 board:
  B   #   B
# B #   B   #
  B   #   B
#   #   B   #
W # W #   # W
#   # W #   #
W # W W   #

C++

Translation of: D

#include <iostream>
#include <vector>

enum class Piece {
    empty,
    black,
    white
};

typedef std::pair<int, int> position;

bool isAttacking(const position &queen, const position &pos) {
    return queen.first == pos.first
        || queen.second == pos.second
        || abs(queen.first - pos.first) == abs(queen.second - pos.second);
}

bool place(const int m, const int n, std::vector<position> &pBlackQueens, std::vector<position> &pWhiteQueens) {
    if (m == 0) {
        return true;
    }
    bool placingBlack = true;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            auto pos = std::make_pair(i, j);
            for (auto queen : pBlackQueens) {
                if (queen == pos || !placingBlack && isAttacking(queen, pos)) {
                    goto inner;
                }
            }
            for (auto queen : pWhiteQueens) {
                if (queen == pos || placingBlack && isAttacking(queen, pos)) {
                    goto inner;
                }
            }
            if (placingBlack) {
                pBlackQueens.push_back(pos);
                placingBlack = false;
            } else {
                pWhiteQueens.push_back(pos);
                if (place(m - 1, n, pBlackQueens, pWhiteQueens)) {
                    return true;
                }
                pBlackQueens.pop_back();
                pWhiteQueens.pop_back();
                placingBlack = true;
            }

        inner: {}
        }
    }
    if (!placingBlack) {
        pBlackQueens.pop_back();
    }
    return false;
}

void printBoard(int n, const std::vector<position> &blackQueens, const std::vector<position> &whiteQueens) {
    std::vector<Piece> board(n * n);
    std::fill(board.begin(), board.end(), Piece::empty);

    for (auto &queen : blackQueens) {
        board[queen.first * n + queen.second] = Piece::black;
    }
    for (auto &queen : whiteQueens) {
        board[queen.first * n + queen.second] = Piece::white;
    }

    for (size_t i = 0; i < board.size(); ++i) {
        if (i != 0 && i % n == 0) {
            std::cout << '\n';
        }
        switch (board[i]) {
        case Piece::black:
            std::cout << "B ";
            break;
        case Piece::white:
            std::cout << "W ";
            break;
        case Piece::empty:
        default:
            int j = i / n;
            int k = i - j * n;
            if (j % 2 == k % 2) {
                std::cout << "x ";
            } else {
                std::cout << "* ";
            }
            break;
        }
    }

    std::cout << "\n\n";
}

int main() {
    std::vector<position> nms = {
        {2, 1}, {3, 1}, {3, 2}, {4, 1}, {4, 2}, {4, 3},
        {5, 1}, {5, 2}, {5, 3}, {5, 4}, {5, 5},
        {6, 1}, {6, 2}, {6, 3}, {6, 4}, {6, 5}, {6, 6},
        {7, 1}, {7, 2}, {7, 3}, {7, 4}, {7, 5}, {7, 6}, {7, 7},
    };

    for (auto nm : nms) {
        std::cout << nm.second << " black and " << nm.second << " white queens on a " << nm.first << " x " << nm.first << " board:\n";
        std::vector<position> blackQueens, whiteQueens;
        if (place(nm.second, nm.first, blackQueens, whiteQueens)) {
            printBoard(nm.first, blackQueens, whiteQueens);
        } else {
            std::cout << "No solution exists.\n\n";
        }
    }

    return 0;
}

Output:

1 black and 1 white queens on a 2 x 2 board:
No solution exists.

1 black and 1 white queens on a 3 x 3 board:
B * x
* x W
x * x

2 black and 2 white queens on a 3 x 3 board:
No solution exists.

1 black and 1 white queens on a 4 x 4 board:
B * x *
* x W x
x * x *
* x * x

2 black and 2 white queens on a 4 x 4 board:
B * x *
* x W x
B * x *
* x W x

3 black and 3 white queens on a 4 x 4 board:
No solution exists.

1 black and 1 white queens on a 5 x 5 board:
B * x * x
* x W x *
x * x * x
* x * x *
x * x * x

2 black and 2 white queens on a 5 x 5 board:
B * x * B
* x W x *
x W x * x
* x * x *
x * x * x

3 black and 3 white queens on a 5 x 5 board:
B * x * B
* x W x *
x W x * x
* x * B *
x W x * x

4 black and 4 white queens on a 5 x 5 board:
x B x B x
* x * x B
W * W * x
* x * x B
W * W * x

5 black and 5 white queens on a 5 x 5 board:
No solution exists.

1 black and 1 white queens on a 6 x 6 board:
B * x * x *
* x W x * x
x * x * x *
* x * x * x
x * x * x *
* x * x * x

2 black and 2 white queens on a 6 x 6 board:
B * x * B *
* x W x * x
x W x * x *
* x * x * x
x * x * x *
* x * x * x

3 black and 3 white queens on a 6 x 6 board:
B * x * B B
* x W x * x
x W x * x *
* x * x * x
x * W * x *
* x * x * x

4 black and 4 white queens on a 6 x 6 board:
B * x * B B
* x W x * x
x W x * x *
* x * x * B
x * W W x *
* x * x * x

5 black and 5 white queens on a 6 x 6 board:
x B x * B *
* x * B * B
W * x * x *
W x W x * x
x * x * x B
W x W x * x

6 black and 6 white queens on a 6 x 6 board:
No solution exists.

1 black and 1 white queens on a 7 x 7 board:
B * x * x * x
* x W x * x *
x * x * x * x
* x * x * x *
x * x * x * x
* x * x * x *
x * x * x * x

2 black and 2 white queens on a 7 x 7 board:
B * x * B * x
* x W x * x W
x * x * x * x
* x * x * x *
x * x * x * x
* x * x * x *
x * x * x * x

3 black and 3 white queens on a 7 x 7 board:
B * x * B * x
* x W x * x W
B * x * x * x
* x W x * x *
x * x * x * x
* x * x * x *
x * x * x * x

4 black and 4 white queens on a 7 x 7 board:
B * x * B * x
* x W x * x W
B * x * B * x
* x W x * x W
x * x * x * x
* x * x * x *
x * x * x * x

5 black and 5 white queens on a 7 x 7 board:
B * x * B * x
* x W x * x W
B * x * B * x
* x W x * x W
B * x * x * x
* x W x * x *
x * x * x * x

6 black and 6 white queens on a 7 x 7 board:
B * x * B * x
* x W x * x W
B * x * B * x
* x W x * x W
B * x * B * x
* x W x * x W
x * x * x * x

7 black and 7 white queens on a 7 x 7 board:
x B x * x B x
* B * x B x *
x B x * x B x
* x * x B x *
W * W * x * W
* x * W * x *
W * W W x * x

D

Translation of: Go

import std.array;
import std.math;
import std.stdio;
import std.typecons;

enum Piece {
    empty,
    black,
    white,
}

alias position = Tuple!(int, "i", int, "j");

bool place(int m, int n, ref position[] pBlackQueens, ref position[] pWhiteQueens) {
    if (m == 0) {
        return true;
    }
    bool placingBlack = true;
    foreach (i; 0..n) {
        inner:
        foreach (j; 0..n) {
            auto pos = position(i, j);
            foreach (queen; pBlackQueens) {
                if (queen == pos || !placingBlack && isAttacking(queen, pos)) {
                    continue inner;
                }
            }
            foreach (queen; pWhiteQueens) {
                if (queen == pos || placingBlack && isAttacking(queen, pos)) {
                    continue inner;
                }
            }
            if (placingBlack) {
                pBlackQueens ~= pos;
                placingBlack = false;
            } else {
                pWhiteQueens ~= pos;
                if (place(m - 1, n, pBlackQueens, pWhiteQueens)) {
                    return true;
                }
                pBlackQueens.length--;
                pWhiteQueens.length--;
                placingBlack = true;
            }
        }
    }
    if (!placingBlack) {
        pBlackQueens.length--;
    }
    return false;
}

bool isAttacking(position queen, position pos) {
    return queen.i == pos.i
        || queen.j == pos.j
        || abs(queen.i - pos.i) == abs(queen.j - pos.j);
}

void printBoard(int n, position[] blackQueens, position[] whiteQueens) {
    auto board = uninitializedArray!(Piece[])(n * n);
    board[] = Piece.empty;

    foreach (queen; blackQueens) {
        board[queen.i * n + queen.j] = Piece.black;
    }
    foreach (queen; whiteQueens) {
        board[queen.i * n + queen.j] = Piece.white;
    }
    foreach (i,b; board) {
        if (i != 0 && i % n == 0) {
            writeln;
        }
        final switch (b) {
            case Piece.black:
                write("B ");
                break;
            case Piece.white:
                write("W ");
                break;
            case Piece.empty:
                int j = i / n;
                int k = i - j * n;

                if (j % 2 == k % 2) {
                    write("• "w);
                } else {
                    write("◦ "w);
                }
                break;
        }
    }
    writeln('\n');
}

void main() {
    auto nms = [
        [2, 1], [3, 1], [3, 2], [4, 1], [4, 2], [4, 3],
        [5, 1], [5, 2], [5, 3], [5, 4], [5, 5],
        [6, 1], [6, 2], [6, 3], [6, 4], [6, 5], [6, 6],
        [7, 1], [7, 2], [7, 3], [7, 4], [7, 5], [7, 6], [7, 7],
    ];
    foreach (nm; nms) {
        writefln("%d black and %d white queens on a %d x %d board:", nm[1], nm[1], nm[0], nm[0]);
        position[] blackQueens;
        position[] whiteQueens;
        if (place(nm[1], nm[0], blackQueens, whiteQueens)) {
            printBoard(nm[0], blackQueens, whiteQueens);
        } else {
            writeln("No solution exists.\n");
        }
    }
}

Output:

1 black and 1 white queens on a 2 x 2 board:
No solution exists.

1 black and 1 white queens on a 3 x 3 board:
B ◦ • 
◦ • W 
• ◦ • 

2 black and 2 white queens on a 3 x 3 board:
No solution exists.

1 black and 1 white queens on a 4 x 4 board:
B ◦ • ◦ 
◦ • W • 
• ◦ • ◦ 
◦ • ◦ • 

2 black and 2 white queens on a 4 x 4 board:
B ◦ • ◦ 
◦ • W • 
B ◦ • ◦ 
◦ • W • 

3 black and 3 white queens on a 4 x 4 board:
No solution exists.

1 black and 1 white queens on a 5 x 5 board:
B ◦ • ◦ • 
◦ • W • ◦ 
• ◦ • ◦ • 
◦ • ◦ • ◦ 
• ◦ • ◦ • 

2 black and 2 white queens on a 5 x 5 board:
B ◦ • ◦ B 
◦ • W • ◦ 
• W • ◦ • 
◦ • ◦ • ◦ 
• ◦ • ◦ • 

3 black and 3 white queens on a 5 x 5 board:
B ◦ • ◦ B 
◦ • W • ◦ 
• W • ◦ • 
◦ • ◦ B ◦ 
• W • ◦ • 

4 black and 4 white queens on a 5 x 5 board:
• B • B • 
◦ • ◦ • B 
W ◦ W ◦ • 
◦ • ◦ • B 
W ◦ W ◦ • 

5 black and 5 white queens on a 5 x 5 board:
No solution exists.

1 black and 1 white queens on a 6 x 6 board:
B ◦ • ◦ • ◦ 
◦ • W • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 

2 black and 2 white queens on a 6 x 6 board:
B ◦ • ◦ B ◦ 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 

3 black and 3 white queens on a 6 x 6 board:
B ◦ • ◦ B B 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ W ◦ • ◦ 
◦ • ◦ • ◦ • 

4 black and 4 white queens on a 6 x 6 board:
B ◦ • ◦ B B 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ B 
• ◦ W W • ◦ 
◦ • ◦ • ◦ • 

5 black and 5 white queens on a 6 x 6 board:
• B • ◦ B ◦ 
◦ • ◦ B ◦ B 
W ◦ • ◦ • ◦ 
W • W • ◦ • 
• ◦ • ◦ • B 
W • W • ◦ • 

6 black and 6 white queens on a 6 x 6 board:
No solution exists.

1 black and 1 white queens on a 7 x 7 board:
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

2 black and 2 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

3 black and 3 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

4 black and 4 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

5 black and 5 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

6 black and 6 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 

7 black and 7 white queens on a 7 x 7 board:
• B • ◦ • B • 
◦ B ◦ • B • ◦ 
• B • ◦ • B • 
◦ • ◦ • B • ◦ 
W ◦ W ◦ • ◦ W 
◦ • ◦ W ◦ • ◦ 
W ◦ W W • ◦ • 

Fortran

Works with: gfortran version 11.2.1

The example demonstrates modern Fortran’s capabilities for integer bit manipulation, by using large machine integers (and their entire bitrange) as bitmaps to represent queen armies. Complicated (but nevertheless single-statement) expressions of such integers represent such operations as rotating a chessboard and checking for any attacks.

There are two Fortran programs and a driver script. One program generates a Fortran module for basic operations; the other program (which must be linked with the generated module) does the actual work. The driver script is for Unix shell.

For speed, armies are represented by 64-bit or 128-bit integers, depending on the value of n. A 1-bit represets a queen. Rotations and reflections of the board are elemental integer operations on an army. Checking for any attacks is an elemental integer-to-boolean operation on the two armies (though the program detects rook-like attacks by a different mechanism). Equivalence under interchange of the colors can be tested by reversing which army gets which integer value.

Here is the first program, peaceful_queens_elements_generator.f90, which generates code (specialized for given m and n) to deal with the representations of the armies as integers:

program peaceful_queens_elements_generator
  use, intrinsic :: iso_fortran_env, only: int64
  use, intrinsic :: iso_fortran_env, only: error_unit

  implicit none

  ! 64-bit integers, for boards up to 8-by-8.
  integer, parameter :: kind8x8 = int64

  ! 128-bit integers, for boards up to 11-by-11.
  ! This value is correct for gfortran.
  integer, parameter :: kind11x11 = 16

  integer(kind = kind11x11), parameter :: one = 1
  integer(kind = kind11x11), parameter :: two = 2

  integer, parameter :: n_max = 11

  integer(kind = kind11x11) :: rook1_masks(0 : n_max - 1)
  integer(kind = kind11x11) :: rook2_masks(0 : n_max - 1)
  integer(kind = kind11x11) :: bishop1_masks(0 : (2 * n_max) - 4)
  integer(kind = kind11x11) :: bishop2_masks(0 : (2 * n_max) - 4)

  ! Combines rook1_masks and rook2_masks.
  integer(kind = kind11x11) :: rook_masks(0 : (2 * n_max) - 1)

  ! Combines bishop1_masks and bishop2_masks.
  integer(kind = kind11x11) :: bishop_masks(0 : (4 * n_max) - 7)

  ! Combines rook and bishop masks.
  integer(kind = kind11x11) :: queen_masks(0 : (6 * n_max) - 7)

  character(len = 16), parameter :: s_kind8x8 = "kind8x8         "
  character(len = 16), parameter :: s_kind11x11 = "kind11x11       "

  character(200) :: arg
  integer :: arg_count

  integer :: m, n, max_solutions
  integer :: board_kind

  arg_count = command_argument_count ()
  if (arg_count /= 3) then
     call get_command_argument (0, arg)
     write (error_unit, '("Usage: ", A, " M N MAX_SOLUTIONS")') trim (arg)
     stop 1
  end if

  call get_command_argument (1, arg)
  read (arg, *) m
  if (m < 1) then
     write (error_unit, '("M must be between 1 or greater.")')
     stop 2
  end if

  call get_command_argument (2, arg)
  read (arg, *) n
  if (n < 3 .or. 11 < n) then
     write (error_unit, '("N must be between 3 and ", I0, ", inclusive.")') n_max
     stop 2
  end if

  call get_command_argument (3, arg)
  read (arg, *) max_solutions

  write (*, '("module peaceful_queens_elements")')
  write (*, '()')
  write (*, '("  use, intrinsic :: iso_fortran_env, only: int64")')
  write (*, '()')
  write (*, '("  implicit none")')
  write (*, '("  private")')
  write (*, '()')
  write (*, '("  integer, parameter, public :: m = ", I0)') m
  write (*, '("  integer, parameter, public :: n = ", I0)') n
  write (*, '("  integer, parameter, public :: max_solutions = ", I0)') max_solutions
  write (*, '()')
  if (n <= 8) then
     write (*, '("  ! 64-bit integers, for boards up to 8-by-8.")')
     write (*, '("  integer, parameter, private :: kind8x8 = int64")')
  else
     write (*, '("  ! 128-bit integers, for boards up to 11-by-11.")')
     write (*, '("  integer, parameter, private :: kind11x11 = ", I0)') kind11x11
  end if
  write (*, '("  integer, parameter, public :: board_kind = ", A)') trim (s_kindnxn (n))
  write (*, '()')
  write (*, '()')
  write (*, '("  public :: rooks1_attack_check")')
  write (*, '("  public :: rooks2_attack_check")')
  write (*, '("  public :: rooks_attack_check")')
  write (*, '("  public :: bishops1_attack_check")')
  write (*, '("  public :: bishops2_attack_check")')
  write (*, '("  public :: bishops_attack_check")')
  write (*, '("  public :: queens_attack_check")')
  write (*, '()')
  write (*, '("  public :: board_rotate90")')
  write (*, '("  public :: board_rotate180")')
  write (*, '("  public :: board_rotate270")')
  write (*, '("  public :: board_reflect1")')
  write (*, '("  public :: board_reflect2")')
  write (*, '("  public :: board_reflect3")')
  write (*, '("  public :: board_reflect4")')
  write (*, '()')

  call write_rook1_masks
  call write_rook2_masks
  call write_bishop1_masks
  call write_bishop2_masks
  call write_rook_masks
  call write_bishop_masks
  call write_queen_masks

  write (*, '("contains")')
  write (*, '()')

  call write_rooks1_attack_check
  call write_rooks2_attack_check
  call write_bishops1_attack_check
  call write_bishops2_attack_check
  call write_rooks_attack_check
  call write_bishops_attack_check
  call write_queens_attack_check

  call write_board_rotate90
  call write_board_rotate180
  call write_board_rotate270
  call write_board_reflect1
  call write_board_reflect2
  call write_board_reflect3
  call write_board_reflect4

  call write_insert_zeros
  call write_reverse_insert_zeros

  write (*, '("end module peaceful_queens_elements")')

contains

  subroutine write_rook1_masks
    integer :: i

    call fill_masks (n)
    do i = 0, n - 1
       write (*, '("  integer(kind = ", A, "), parameter :: rook1_mask_",&
            & I0, "x", I0, "_", I0, " = int (z''", Z0.32, "'', kind &
            &= ", A, ")")') trim (s_kindnxn (n)), n, n, i,&
            & rook1_masks(i), trim (s_kindnxn (n))
    end do
    write (*, '()')
  end subroutine write_rook1_masks

  subroutine write_rook2_masks
    integer :: i

    call fill_masks (n)
    do i = 0, n - 1
       write (*, '("  integer(kind = ", A, "), parameter :: rook2_mask_",&
            & I0, "x", I0, "_", I0, " = int (z''", Z0.32, "'', kind &
            &= ", A, ")")') trim (s_kindnxn (n)), n, n, i,&
            & rook2_masks(i), trim (s_kindnxn (n))
    end do
    write (*, '()')
  end subroutine write_rook2_masks

  subroutine write_bishop1_masks
    integer :: i

    call fill_masks (n)
    do i = 0, (2 * n) - 4
       write (*, '("  integer(kind = ", A, "), parameter :: bishop1_mask_",&
            & I0, "x", I0, "_", I0, " = int (z''", Z0.32, "'', kind &
            &= ", A, ")")') trim (s_kindnxn (n)), n, n, i,&
            & bishop1_masks(i), trim (s_kindnxn (n))
    end do
    write (*, '()')
  end subroutine write_bishop1_masks

  subroutine write_bishop2_masks
    integer :: i

    call fill_masks (n)
    do i = 0, (2 * n) - 4
       write (*, '("  integer(kind = ", A, "), parameter :: bishop2_mask_",&
            & I0, "x", I0, "_", I0, " = int (z''", Z0.32, "'', kind &
            &= ", A, ")")') trim (s_kindnxn (n)), n, n, i,&
            & bishop2_masks(i), trim (s_kindnxn (n))
    end do
    write (*, '()')
  end subroutine write_bishop2_masks

  subroutine write_rook_masks
    integer :: i

    call fill_masks (n)
    do i = 0, (2 * n) - 1
       write (*, '("  integer(kind = ", A, "), parameter :: rook_mask_",&
            & I0, "x", I0, "_", I0, " = int (z''", Z0.32, "'', kind &
            &= ", A, ")")') trim (s_kindnxn (n)), n, n, i,&
            & rook_masks(i), trim (s_kindnxn (n))
    end do
    write (*, '()')
  end subroutine write_rook_masks

  subroutine write_bishop_masks
    integer :: i

    call fill_masks (n)
    do i = 0, (4 * n) - 7
       write (*, '("  integer(kind = ", A, "), parameter :: bishop_mask_",&
            & I0, "x", I0, "_", I0, " = int (z''", Z0.32, "'', kind &
            &= ", A, ")")') trim (s_kindnxn (n)), n, n, i,&
            & bishop_masks(i), trim (s_kindnxn (n))
    end do
    write (*, '()')
  end subroutine write_bishop_masks

  subroutine write_queen_masks
    integer :: i

    call fill_masks (n)
    do i = 0, (6 * n) - 7
       write (*, '("  integer(kind = ", A, "), parameter :: queen_mask_",&
            & I0, "x", I0, "_", I0, " = int (z''", Z0.32, "'', kind &
            &= ", A, ")")') trim (s_kindnxn (n)), n, n, i,&
            & queen_masks(i), trim (s_kindnxn (n))
    end do
    write (*, '()')
  end subroutine write_queen_masks

  subroutine write_rooks1_attack_check
    integer :: i

    write (*, '("  elemental function rooks1_attack_check (army1, army2) result (attacking)")')
    write (*, '("    integer(kind = ", A, "), value :: army1, army2")') trim (s_kindnxn (n))
    write (*, '("    logical :: attacking")')
    write (*, '()')
    write (*, '("    attacking = ((iand (army1, rook1_mask_", I0, "x", I0,&
         & "_0) /= 0) .and. (iand (army2, rook1_mask_", I0, "x", I0, "_0) /=&
         & 0)) .or. &")') n, n, n, n
    do i = 1, n - 1
       write (*, '("              & ((iand (army1, rook1_mask_", I0, "x",&
            & I0, "_", I0, ") /= 0) .and. (iand (army2, rook1_mask_", I0,&
            & "x", I0, "_", I0, ") /= 0))")', advance = 'no') n, n, i, n, n, i
       if (i /= n - 1) then
          write (*, '(" .or. &")')
       else
          write (*, '()')
       end if
    end do
    write (*, '("  end function rooks1_attack_check")')
    write (*, '()')
  end subroutine write_rooks1_attack_check

  subroutine write_rooks2_attack_check
    integer :: i

    write (*, '("  elemental function rooks2_attack_check (army1, army2) result (attacking)")')
    write (*, '("    integer(kind = ", A, "), value :: army1, army2")') trim (s_kindnxn (n))
    write (*, '("    logical :: attacking")')
    write (*, '()')
    write (*, '("    attacking = ((iand (army1, rook2_mask_", I0, "x", I0,&
         & "_0) /= 0) .and. (iand (army2, rook2_mask_", I0, "x", I0, "_0) /=&
         & 0)) .or. &")') n, n, n, n
    do i = 1, n - 1
       write (*, '("              & ((iand (army1, rook2_mask_", I0, "x",&
            & I0, "_", I0, ") /= 0) .and. (iand (army2, rook2_mask_", I0,&
            & "x", I0, "_", I0, ") /= 0))")', advance = 'no') n, n, i, n, n, i
       if (i /= n - 1) then
          write (*, '(" .or. &")')
       else
          write (*, '()')
       end if
    end do
    write (*, '("  end function rooks2_attack_check")')
    write (*, '()')
  end subroutine write_rooks2_attack_check

  subroutine write_bishops1_attack_check
    integer :: i

    write (*, '("  elemental function bishops1_attack_check (army1, army2) result (attacking)")')
    write (*, '("    integer(kind = ", A, "), value :: army1, army2")') trim (s_kindnxn (n))
    write (*, '("    logical :: attacking")')
    write (*, '()')
    write (*, '("    attacking = ((iand (army1, bishop1_mask_", I0, "x", I0,&
         & "_0) /= 0) .and. (iand (army2, bishop1_mask_", I0, "x", I0, "_0) /=&
         & 0)) .or. &")') n, n, n, n
    do i = 1, (2 * n) - 4
       write (*, '("              & ((iand (army1, bishop1_mask_", I0, "x",&
            & I0, "_", I0, ") /= 0) .and. (iand (army2, bishop1_mask_", I0,&
            & "x", I0, "_", I0, ") /= 0))")', advance = 'no') n, n, i, n, n, i
       if (i /= (2 * n) - 4) then
          write (*, '(" .or. &")')
       else
          write (*, '()')
       end if
    end do
    write (*, '("  end function bishops1_attack_check")')
    write (*, '()')
  end subroutine write_bishops1_attack_check

  subroutine write_bishops2_attack_check
    integer :: i

    write (*, '("  elemental function bishops2_attack_check (army1, army2) result (attacking)")')
    write (*, '("    integer(kind = ", A, "), value :: army1, army2")') trim (s_kindnxn (n))
    write (*, '("    logical :: attacking")')
    write (*, '()')
    write (*, '("    attacking = ((iand (army1, bishop2_mask_", I0, "x", I0,&
         & "_0) /= 0) .and. (iand (army2, bishop2_mask_", I0, "x", I0, "_0) /=&
         & 0)) .or. &")') n, n, n, n
    do i = 1, (2 * n) - 4
       write (*, '("              & ((iand (army1, bishop2_mask_", I0, "x",&
            & I0, "_", I0, ") /= 0) .and. (iand (army2, bishop2_mask_", I0,&
            & "x", I0, "_", I0, ") /= 0))")', advance = 'no') n, n, i, n, n, i
       if (i /= (2 * n) - 4) then
          write (*, '(" .or. &")')
       else
          write (*, '()')
       end if
    end do
    write (*, '("  end function bishops2_attack_check")')
    write (*, '()')
  end subroutine write_bishops2_attack_check

  subroutine write_rooks_attack_check
    integer :: i

    write (*, '("  elemental function rooks_attack_check (army1, army2) result (attacking)")')
    write (*, '("    integer(kind = ", A, "), value :: army1, army2")') trim (s_kindnxn (n))
    write (*, '("    logical :: attacking")')
    write (*, '()')
    write (*, '("    attacking = ((iand (army1, rook_mask_", I0, "x", I0,&
         & "_0) /= 0) .and. (iand (army2, rook_mask_", I0, "x", I0, "_0) /=&
         & 0)) .or. &")') n, n, n, n
    do i = 1, (2 * n) - 1
       write (*, '("              & ((iand (army1, rook_mask_", I0, "x",&
            & I0, "_", I0, ") /= 0) .and. (iand (army2, rook_mask_", I0,&
            & "x", I0, "_", I0, ") /= 0))")', advance = 'no') n, n, i, n, n, i
       if (i /= (2 * n) - 1) then
          write (*, '(" .or. &")')
       else
          write (*, '()')
       end if
    end do
    write (*, '("  end function rooks_attack_check")')
    write (*, '()')
  end subroutine write_rooks_attack_check

  subroutine write_bishops_attack_check
    integer :: i

    write (*, '("  elemental function bishops_attack_check (army1, army2) result (attacking)")')
    write (*, '("    integer(kind = ", A, "), value :: army1, army2")') trim (s_kindnxn (n))
    write (*, '("    logical :: attacking")')
    write (*, '()')
    write (*, '("    attacking = ((iand (army1, bishop_mask_", I0, "x", I0,&
         & "_0) /= 0) .and. (iand (army2, bishop_mask_", I0, "x", I0, "_0) /=&
         & 0)) .or. &")') n, n, n, n
    do i = 1, (4 * n) - 7
       write (*, '("              & ((iand (army1, bishop_mask_", I0, "x",&
            & I0, "_", I0, ") /= 0) .and. (iand (army2, bishop_mask_", I0,&
            & "x", I0, "_", I0, ") /= 0))")', advance = 'no') n, n, i, n, n, i
       if (i /= (4 * n) - 7) then
          write (*, '(" .or. &")')
       else
          write (*, '()')
       end if
    end do
    write (*, '("  end function bishops_attack_check")')
    write (*, '()')
  end subroutine write_bishops_attack_check

  subroutine write_queens_attack_check
    integer :: i

    write (*, '("  elemental function queens_attack_check (army1, army2) result (attacking)")')
    write (*, '("    integer(kind = ", A, "), value :: army1, army2")') trim (s_kindnxn (n))
    write (*, '("    logical :: attacking")')
    write (*, '()')
    write (*, '("    attacking = ((iand (army1, queen_mask_", I0, "x", I0,&
         & "_0) /= 0) .and. (iand (army2, queen_mask_", I0, "x", I0, "_0) /=&
         & 0)) .or. &")') n, n, n, n
    do i = 1, (6 * n) - 7
       write (*, '("              & ((iand (army1, queen_mask_", I0, "x",&
            & I0, "_", I0, ") /= 0) .and. (iand (army2, queen_mask_", I0,&
            & "x", I0, "_", I0, ") /= 0))")', advance = 'no') n, n, i, n, n, i
       if (i /= (6 * n) - 7) then
          write (*, '(" .or. &")')
       else
          write (*, '()')
       end if
    end do
    write (*, '("  end function queens_attack_check")')
    write (*, '()')
  end subroutine write_queens_attack_check

  subroutine write_board_rotate90
    integer :: i, j

    write (*, '("  elemental function board_rotate90 (a) result (b)")')
    write (*, '("    integer(kind = ", A, "), value :: a")') trim (s_kindnxn (n))
    write (*, '("    integer(kind = ", A, ") :: b")') trim (s_kindnxn (n))
    write (*, '()')
    write (*, '("    ! Rotation 90 degrees in one of the orientations.")')
    write (*, '()')
    do i = 0, n - 1
       if (i == 0) then
          write (*, '("    b = ")', advance = 'no')
       else
          write (*, '("      & ")', advance = 'no')
          do j = 1, i
             write (*, '("  ")', advance = 'no')
          end do
       end if
       if (i /= n - 1) then
          write (*, '("ior (ishft (reverse_insert_zeros_", I0, " (ishft&
               & (iand (rook1_mask_", I0, "x", I0, "_", I0, ", a), ",&
               & I0, ")), ", I0, "), &")') n, n, n, i, -i * n, i
       else
          write (*, '("   ishft (reverse_insert_zeros_", I0, " (ishft&
               & (iand (rook1_mask_", I0, "x", I0, "_", I0, ", a), ",&
               & I0, ")), ", I0, ")")', advance = 'no') n, n, n, i, -i * n, i
          do j = 1, n - 1
             write (*, '(")")', advance = 'no')
          end do
          write (*, '()')
       end if
    end do
    write (*, '("  end function board_rotate90")')
    write (*, '()')
  end subroutine write_board_rotate90

  subroutine write_board_rotate180
    write (*, '("  elemental function board_rotate180 (a) result (b)")')
    write (*, '("    integer(kind = ", A, "), value :: a")') trim (s_kindnxn (n))
    write (*, '("    integer(kind = ", A, ") :: b")') trim (s_kindnxn (n))
    write (*, '()')
    write (*, '("    ! Rotation 180 degrees.")')
    write (*, '()')
    write (*, '("    b = board_reflect1 (board_reflect2 (a))")')
    write (*, '("  end function board_rotate180")')
    write (*, '()')
  end subroutine write_board_rotate180

  subroutine write_board_rotate270
    integer :: i, j

    write (*, '("  elemental function board_rotate270 (a) result (b)")')
    write (*, '("    integer(kind = ", A, "), value :: a")') trim (s_kindnxn (n))
    write (*, '("    integer(kind = ", A, ") :: b")') trim (s_kindnxn (n))
    write (*, '()')
    write (*, '("    ! Rotation 270 degrees in one of the orientations.")')
    write (*, '()')
    do i = 0, n - 1
       if (i == 0) then
          write (*, '("    b = ")', advance = 'no')
       else
          write (*, '("      & ")', advance = 'no')
          do j = 1, i
             write (*, '("  ")', advance = 'no')
          end do
       end if
       if (i /= n - 1) then
          write (*, '("ior (ishft (insert_zeros_", I0, " (ishft&
               & (iand (rook1_mask_", I0, "x", I0, "_", I0, ", a), ",&
               & I0, ")), ", I0, "), &")') n, n, n, i, -i * n, n - 1 - i
       else
          write (*, '("   ishft (insert_zeros_", I0, " (ishft&
               & (iand (rook1_mask_", I0, "x", I0, "_", I0, ", a), ",&
               & I0, ")), ", I0, ")")', advance = 'no') n, n, n, i, -i * n, n - 1 - i
          do j = 1, n - 1
             write (*, '(")")', advance = 'no')
          end do
          write (*, '()')
       end if
    end do
    write (*, '("  end function board_rotate270")')
    write (*, '()')
  end subroutine write_board_rotate270

  subroutine write_board_reflect1
    integer :: i, j

    write (*, '("  elemental function board_reflect1 (a) result (b)")')
    write (*, '("    integer(kind = ", A, "), value :: a")') trim (s_kindnxn (n))
    write (*, '("    integer(kind = ", A, ") :: b")') trim (s_kindnxn (n))
    write (*, '()')
    write (*, '("    ! Reflection of rows or columns.")')
    write (*, '()')
    do i = 0, n - 1
       if (i == 0) then
          write (*, '("    b = ")', advance = 'no')
       else
          write (*, '("      & ")', advance = 'no')
          do j = 1, i
             write (*, '("     ")', advance = 'no')
          end do
       end if
       if (i /= n - 1) then
          write (*, '("ior (ishft (iand (rook2_mask_", I0, "x", I0, "_", I0, ", a), ", I0, "), &")') &
               & n, n, i, (n - 1) - (2 * i)
       else
          write (*, '("ishft (iand (rook2_mask_", I0, "x", I0, "_", I0, ", a), ", I0, ")")', advance = 'no') &
               & n, n, i, (n - 1) - (2 * i)
          do j = 1, n - 1
             write (*, '(")")', advance = 'no')
          end do
          write (*, '()')
       end if
    end do
    write (*, '("  end function board_reflect1")')
    write (*, '()')
  end subroutine write_board_reflect1

  subroutine write_board_reflect2
    integer :: i, j

    write (*, '("  elemental function board_reflect2 (a) result (b)")')
    write (*, '("    integer(kind = ", A, "), value :: a")') trim (s_kindnxn (n))
    write (*, '("    integer(kind = ", A, ") :: b")') trim (s_kindnxn (n))
    write (*, '()')
    write (*, '("    ! Reflection of rows or columns.")')
    write (*, '()')
    do i = 0, n - 1
       if (i == 0) then
          write (*, '("    b = ")', advance = 'no')
       else
          write (*, '("      & ")', advance = 'no')
          do j = 1, i
             write (*, '("     ")', advance = 'no')
          end do
       end if
       if (i /= n - 1) then
          write (*, '("ior (ishft (iand (rook1_mask_", I0, "x", I0, "_", I0, ", a), ", I0, "), &")') &
               & n, n, i, n * ((n - 1) - (2 * i))
       else
          write (*, '("ishft (iand (rook1_mask_", I0, "x", I0, "_", I0, ", a), ", I0, ")")', advance = 'no') &
               & n, n, i, n * ((n - 1) - (2 * i))
          do j = 1, n - 1
             write (*, '(")")', advance = 'no')
          end do
          write (*, '()')
       end if
    end do
    write (*, '("  end function board_reflect2")')
    write (*, '()')
  end subroutine write_board_reflect2

  subroutine write_board_reflect3
    integer :: i, j

    write (*, '("  elemental function board_reflect3 (a) result (b)")')
    write (*, '("    integer(kind = ", A, "), value :: a")') trim (s_kindnxn (n))
    write (*, '("    integer(kind = ", A, ") :: b")') trim (s_kindnxn (n))
    write (*, '()')
    write (*, '("    ! Reflection around one of the two main diagonals.")')
    write (*, '()')
    do i = 0, n - 1
       if (i == 0) then
          write (*, '("    b = ")', advance = 'no')
       else
          write (*, '("      & ")', advance = 'no')
          do j = 1, i
             write (*, '("  ")', advance = 'no')
          end do
       end if
       if (i /= n - 1) then
          write (*, '("ior (ishft (insert_zeros_", I0, " (ishft&
               & (iand (rook1_mask_", I0, "x", I0, "_", I0, ", a), ",&
               & I0, ")), ", I0, "), &")') n, n, n, i, -i * n, i
       else
          write (*, '("   ishft (insert_zeros_", I0, " (ishft&
               & (iand (rook1_mask_", I0, "x", I0, "_", I0, ", a), ",&
               & I0, ")), ", I0, ")")', advance = 'no') n, n, n, i, -i * n, i
          do j = 1, n - 1
             write (*, '(")")', advance = 'no')
          end do
          write (*, '()')
       end if
    end do
    write (*, '("  end function board_reflect3")')
    write (*, '()')
  end subroutine write_board_reflect3

  subroutine write_board_reflect4
    integer :: i, j

    write (*, '("  elemental function board_reflect4 (a) result (b)")')
    write (*, '("    integer(kind = ", A, "), value :: a")') trim (s_kindnxn (n))
    write (*, '("    integer(kind = ", A, ") :: b")') trim (s_kindnxn (n))
    write (*, '()')
    write (*, '("    ! Reflection around one of the two main diagonals.")')
    write (*, '()')
    do i = 0, n - 1
       if (i == 0) then
          write (*, '("    b = ")', advance = 'no')
       else
          write (*, '("      & ")', advance = 'no')
          do j = 1, i
             write (*, '("  ")', advance = 'no')
          end do
       end if
       if (i /= n - 1) then
          write (*, '("ior (ishft (reverse_insert_zeros_", I0, " (ishft&
               & (iand (rook1_mask_", I0, "x", I0, "_", I0, ", a), ",&
               & I0, ")), ", I0, "), &")') n, n, n, i, -i * n, n - 1 - i
       else
          write (*, '("   ishft (reverse_insert_zeros_", I0, " (ishft&
               & (iand (rook1_mask_", I0, "x", I0, "_", I0, ", a), ",&
               & I0, ")), ", I0, ")")', advance = 'no') n, n, n, i, -i * n, n - 1 - i
          do j = 1, n - 1
             write (*, '(")")', advance = 'no')
          end do
          write (*, '()')
       end if
    end do
    write (*, '("  end function board_reflect4")')
    write (*, '()')
  end subroutine write_board_reflect4

  subroutine write_insert_zeros
    integer :: i, j

    write (*, '("  elemental function insert_zeros_", I0, " (a) result (b)")') n
    write (*, '("    integer(kind = ", A, "), value :: a")') trim (s_kindnxn (n))
    write (*, '("    integer(kind = ", A, ") :: b")') trim (s_kindnxn (n))
    write (*, '()')
    do i = 0, n - 1
       if (i == 0) then
          write (*, '("    b = ")', advance = 'no')
       else
          write (*, '("      & ")', advance = 'no')
          do j = 1, i
             write (*, '("     ")', advance = 'no')
          end do
       end if
       if (i /= n - 1) then
          write (*, '("ior (ishft (ibits (a, ", I0, ", 1), ", I0, "), &")') i, i * n
       else
          write (*, '("ishft (ibits (a, ", I0, ", 1), ", I0, ")")', advance = 'no') i, i * n
          do j = 1, n - 1
             write (*, '(")")', advance = 'no')
          end do
          write (*, '()')
       end if
    end do
    write (*, '("  end function insert_zeros_", I0)') n
    write (*, '()')
  end subroutine write_insert_zeros

  subroutine write_reverse_insert_zeros
    integer :: i, j

    write (*, '("  elemental function reverse_insert_zeros_", I0, " (a) result (b)")') n
    write (*, '("    integer(kind = ", A, "), value :: a")') trim (s_kindnxn (n))
    write (*, '("    integer(kind = ", A, ") :: b")') trim (s_kindnxn (n))
    write (*, '()')
    do i = 0, n - 1
       if (i == 0) then
          write (*, '("    b = ")', advance = 'no')
       else
          write (*, '("      & ")', advance = 'no')
          do j = 1, i
             write (*, '("     ")', advance = 'no')
          end do
       end if
       if (i /= n - 1) then
          write (*, '("ior (ishft (ibits (a, ", I0, ", 1), ", I0, "), &")') n - 1 - i, i * n
       else
          write (*, '("ishft (ibits (a, ", I0, ", 1), ", I0, ")")', advance = 'no') n - 1 - i, i * n
          do j = 1, n - 1
             write (*, '(")")', advance = 'no')
          end do
          write (*, '()')
       end if
    end do
    write (*, '("  end function reverse_insert_zeros_", I0)') n
    write (*, '()')
  end subroutine write_reverse_insert_zeros

  function s_kindnxn (n) result (s)
    integer, intent(in) :: n
    character(len = 16) :: s

    if (n <= 8) then
       s = s_kind8x8
    else
       s = s_kind11x11
    end if
  end function s_kindnxn

  subroutine fill_masks (n)
    integer, intent(in) :: n

    call fill_rook1_masks (n)
    call fill_rook2_masks (n)
    call fill_bishop1_masks (n)
    call fill_bishop2_masks (n)
    call fill_rook_masks (n)
    call fill_bishop_masks (n)
    call fill_queen_masks (n)
  end subroutine fill_masks

  subroutine fill_rook1_masks (n)
    integer, intent(in) :: n

    integer :: i
    integer(kind = kind11x11) :: mask

    mask = (two ** n) - 1
    do i = 0, n - 1
       rook1_masks(i) = mask
       mask = ishft (mask, n)
    end do
  end subroutine fill_rook1_masks

  subroutine fill_rook2_masks (n)
    integer, intent(in) :: n

    integer :: i
    integer(kind = kind11x11) :: mask

    mask = 0
    do i = 0, n - 1
       mask = ior (ishft (mask, n), one)
    end do
    do i = 0, n - 1
       rook2_masks(i) = mask
       mask = ishft (mask, 1)
    end do
  end subroutine fill_rook2_masks
  
  subroutine fill_bishop1_masks (n)
    integer, intent(in) :: n

    integer :: i, j, k
    integer(kind = kind11x11) :: mask0, mask1

    ! Masks for diagonals. Put them in order from most densely
    ! populated to least densely populated.

    do k = 0, n - 2
       mask0 = 0
       mask1 = 0
       do i = k, n - 1
          j = i - k
          mask0 = ior (mask0, ishft (one, i + (j * n)))
          mask1 = ior (mask1, ishft (one, j + (i * n)))
       end do
       if (k == 0) then
          bishop1_masks(0) = mask0
       else
          bishop1_masks((2 * k) - 1) = mask0
          bishop1_masks(2 * k) = mask1
       end if
    end do
  end subroutine fill_bishop1_masks

  subroutine fill_bishop2_masks (n)
    integer, intent(in) :: n

    integer :: i, j, k
    integer :: i1, j1
    integer(kind = kind11x11) :: mask0, mask1

    ! Masks for skew diagonals. Put them in order from most densely
    ! populated to least densely populated.

    do k = 0, n - 2
       mask0 = 0
       mask1 = 0
       do i = k, n - 1
          j = i - k
          i1 = n - 1 - i
          j1 = n - 1 - j
          mask0 = ior (mask0, ishft (one, j + (i1 * n)))
          mask1 = ior (mask1, ishft (one, i + (j1 * n)))
       end do
       if (k == 0) then
          bishop2_masks(0) = mask0
       else
          bishop2_masks((2 * k) - 1) = mask0
          bishop2_masks(2 * k) = mask1
       end if
    end do
  end subroutine fill_bishop2_masks

  subroutine fill_rook_masks (n)
    integer, intent(in) :: n

    rook_masks(0 : n - 1) = rook1_masks
    rook_masks(n : (2 * n) - 1) = rook2_masks
  end subroutine fill_rook_masks

  subroutine fill_bishop_masks (n)
    integer, intent(in) :: n

    integer :: i

    ! Put the masks in order from most densely populated to least
    ! densely populated.

    do i = 0, (2 * n) - 4
       bishop_masks(2 * i) = bishop1_masks(i)
       bishop_masks((2 * i) + 1) = bishop2_masks(i)
    end do
  end subroutine fill_bishop_masks

  subroutine fill_queen_masks (n)
    integer, intent(in) :: n

    queen_masks(0 : (2 * n) - 1) = rook_masks
    queen_masks(2 * n : (6 * n) - 7) = bishop_masks
  end subroutine fill_queen_masks

end program peaceful_queens_elements_generator

Here is the second program, peaceful_queens.f90:

module peaceful_queens_support
  use, non_intrinsic :: peaceful_queens_elements

  implicit none
  private

  public :: write_board
  public :: write_board_without_spaces
  public :: write_board_with_spaces

  public :: save_a_solution

  interface write_board
     module procedure write_board_without_spaces
     module procedure write_board_with_spaces
  end interface write_board

contains

  subroutine write_board_without_spaces (unit, army_b, army_w)
    integer, intent(in) :: unit
    integer(kind = board_kind), intent(in) :: army_b, army_w

    call write_board_with_spaces (unit, army_b, army_w, 0)
  end subroutine write_board_without_spaces

  subroutine write_board_with_spaces (unit, army_b, army_w, num_spaces)
    integer, intent(in) :: unit
    integer(kind = board_kind), intent(in) :: army_b, army_w
    integer, intent(in) :: num_spaces

    integer(kind = board_kind), parameter :: zero = 0
    integer(kind = board_kind), parameter :: one = 1

    integer :: i, j
    integer(kind = board_kind) :: rank_b, rank_w
    integer(kind = board_kind) :: mask

    character(1), allocatable :: queens(:)
    character(4), allocatable :: rules(:)
    character(1), allocatable :: spaces(:)

    allocate (queens(0 : n - 1))
    allocate (rules(0 : n - 1))
    allocate (spaces(1 : num_spaces))

    rules = "----"
    if (0 < num_spaces) then
       spaces = " "             ! For putting spaces after newlines.
    end if

    mask = not (ishft (not (zero), n))
    write (unit, '("+", 100(A4, "+"))') rules
    do i = 0, n - 1
       rank_b = iand (mask, ishft (army_b, -i * n))
       rank_w = iand (mask, ishft (army_w, -i * n))
       do j = 0, n - 1
          if (iand (rank_b, ishft (one, j)) /= 0) then
             queens(j) = "B"
          else if (iand (rank_w, ishft (one, j)) /= 0) then
             queens(j) = "W"
          else
             queens(j) = " "
          end if
       end do
       write (unit, '(100A1)', advance = 'no') spaces
       write (unit, '("|", 100(A3, " |"))') queens
       write (unit, '(100A1)', advance = 'no') spaces
       if (i /= n - 1) then
          write (unit, '("+", 100(A4, "+"))') rules
       else
          write (unit, '("+", 100(A4, "+"))', advance = 'no') rules
       end if
    end do
  end subroutine write_board_with_spaces

  subroutine save_a_solution (army1, army2, num_solutions, armies1, armies2)
    integer(kind = board_kind), intent(in) :: army1, army2
    integer, intent(inout) :: num_solutions
    integer(kind = board_kind), intent(inout) :: armies1(1:8, 1:max_solutions)
    integer(kind = board_kind), intent(inout) :: armies2(1:8, 1:max_solutions)

    ! A sanity check.
    if (queens_attack_check (army1, army2)) then
       error stop
    end if

    num_solutions = num_solutions + 1

    armies1(1, num_solutions) = army1
    armies1(2, num_solutions) = board_rotate90 (army1)
    armies1(3, num_solutions) = board_rotate180 (army1)
    armies1(4, num_solutions) = board_rotate270 (army1)
    armies1(5, num_solutions) = board_reflect1 (army1)
    armies1(6, num_solutions) = board_reflect2 (army1)
    armies1(7, num_solutions) = board_reflect3 (army1)
    armies1(8, num_solutions) = board_reflect4 (army1)

    armies2(1, num_solutions) = army2
    armies2(2, num_solutions) = board_rotate90 (army2)
    armies2(3, num_solutions) = board_rotate180 (army2)
    armies2(4, num_solutions) = board_rotate270 (army2)
    armies2(5, num_solutions) = board_reflect1 (army2)
    armies2(6, num_solutions) = board_reflect2 (army2)
    armies2(7, num_solutions) = board_reflect3 (army2)
    armies2(8, num_solutions) = board_reflect4 (army2)
  end subroutine save_a_solution

end module peaceful_queens_support

module peaceful_queens_solver
  use, non_intrinsic :: peaceful_queens_elements
  use, non_intrinsic :: peaceful_queens_support

  implicit none
  private

  public :: solve_peaceful_queens

  integer(kind = board_kind), parameter :: zero = 0_board_kind
  integer(kind = board_kind), parameter :: one = 1_board_kind
  integer(kind = board_kind), parameter :: two = 2_board_kind

contains

  subroutine solve_peaceful_queens (unit, show_equivalents, &
       &                            num_solutions, armies1, armies2)
    integer, intent(in) :: unit
    logical, intent(in) :: show_equivalents
    integer, intent(out) :: num_solutions
    integer(kind = board_kind), intent(out) :: armies1(1:8, 1:max_solutions)
    integer(kind = board_kind), intent(out) :: armies2(1:8, 1:max_solutions)

    call solve (zero, 0, 0, zero, 0, 0, 0)

  contains

    recursive subroutine solve (army1, rooklike11, rooklike12, &
         &                      army2, rooklike21, rooklike22, index)
      integer(kind = board_kind), value :: army1
      integer, value :: rooklike11, rooklike12
      integer(kind = board_kind), value :: army2
      integer, value :: rooklike21, rooklike22
      integer, value :: index

      integer :: num_queens1
      integer :: num_queens2
      integer(kind = board_kind) :: new_army
      integer(kind = board_kind) :: new_army_reversed
      integer :: bit1, bit2
      logical :: skip

      num_queens1 = popcnt (army1) 
      num_queens2 = popcnt (army2)

      if (num_queens1 + num_queens2 == 2 * m) then
         if (.not. is_a_duplicate (army1, army2, num_solutions, armies1, armies2)) then
            call save_a_solution (army1, army2, num_solutions, armies1, armies2)
            write (unit, '("Solution ", I0)') num_solutions
            call write_board (unit, army1, army2)
            write (unit, '()')
            write (unit, '()')
            call optionally_write_equivalents
         end if
      else if (num_queens1 - num_queens2 == 0) then
         ! It is time to add a queen to army1.
         do while (num_solutions < max_solutions .and. index /= n**2)
            skip = .false.
            new_army = ior (army1, ishft (one, index))
            if (new_army == army1) then
               skip = .true.
            else if (index < n) then
               new_army_reversed = board_reflect1 (new_army)
               if (new_army_reversed < new_army) then
                  ! Skip a bunch of board_reflect1 equivalents.
                  skip = .true.
               end if
            end if
            if (skip) then
               index = index + 1
            else
               bit1 = ishft (1, index / n)
               bit2 = ishft (1, mod (index, n))
               if (iand (rooklike21, bit1) /= 0) then
                  index = round_up_to_multiple (index + 1, n)
               else if (iand (rooklike22, bit2) /= 0) then
                  index = index + 1
               else if (bishops_attack_check (new_army, army2)) then
                  index = index + 1
               else
                  call solve (new_army, &
                       &      ior (rooklike11, bit1), &
                       &      ior (rooklike12, bit2), &
                       &      army2, rooklike21, rooklike22, &
                       &      n)
                  index = index + 1
               end if
            end if
         end do
      else
         ! It is time to add a queen to army2.
         do while (num_solutions < max_solutions .and. index /= n**2)
            new_army = ior (army2, ishft (one, index))
            skip = (new_army == army2)
            if (skip) then
               index = index + 1
            else
               bit1 = ishft (1, index / n)
               bit2 = ishft (1, mod (index, n))
               if (iand (rooklike11, bit1) /= 0) then
                  index = round_up_to_multiple (index + 1, n)
               else if (iand (rooklike12, bit2) /= 0) then
                  index = index + 1
               else if (bishops_attack_check (army1, new_army)) then
                  index = index + 1
               else
                  call solve (army1, rooklike11, rooklike12, &
                       &      new_army, &
                       &      ior (rooklike21, bit1), &
                       &      ior (rooklike22, bit2), &
                       &      0)
                  index = index + 1
               end if
            end if
         end do
      end if
    end subroutine solve

    subroutine optionally_write_equivalents
      integer :: i

      if (show_equivalents) then
         write (unit, '(5X)', advance = 'no')
         write (unit, '("Equivalents")')

         write (unit, '(5X)', advance = 'no')
         call write_board (unit, armies2(1, num_solutions), armies1(1, num_solutions), 5)
         write (unit, '()')
         write (unit, '()')

         do i = 2, 5
            if (all ((armies1(i, num_solutions) /= armies1(1 : i - 1, num_solutions) .or. &
                 &    armies2(i, num_solutions) /= armies2(1 : i - 1, num_solutions)) .and. &
                 &   (armies2(i, num_solutions) /= armies1(1 : i - 1, num_solutions) .or. &
                 &    armies1(i, num_solutions) /= armies2(1 : i - 1, num_solutions)))) then
               write (unit, '(5X)', advance = 'no')
               call write_board (unit, armies1(i, num_solutions), armies2(i, num_solutions), 5)
               write (unit, '()')
               write (unit, '()')
               write (unit, '(5X)', advance = 'no')
               call write_board (unit, armies2(i, num_solutions), armies1(i, num_solutions), 5)
               write (unit, '()')
               write (unit, '()')
            end if
         end do
      end if
    end subroutine optionally_write_equivalents

  end subroutine solve_peaceful_queens

  elemental function round_up_to_multiple (x, n) result (y)
    integer, value :: x, n
    integer :: y

    y = x + mod (n - mod (x, n), n)
  end function round_up_to_multiple

  pure function is_a_duplicate (army1, army2, num_solutions, armies1, armies2) result (is_dup)
    integer(kind = board_kind), intent(in) :: army1, army2
    integer, intent(in) :: num_solutions
    integer(kind = board_kind), intent(in) :: armies1(1:8, 1:max_solutions)
    integer(kind = board_kind), intent(in) :: armies2(1:8, 1:max_solutions)
    logical :: is_dup

    is_dup = any ((army1 == armies1(:, 1:num_solutions) .and. &
         &         army2 == armies2(:, 1:num_solutions)) .or. &
         &        (army2 == armies1(:, 1:num_solutions) .and. &
         &         army1 == armies2(:, 1:num_solutions)))
  end function is_a_duplicate

end module peaceful_queens_solver

program peaceful_queens
  use, intrinsic :: iso_fortran_env, only: output_unit
  use, non_intrinsic :: peaceful_queens_elements
  use, non_intrinsic :: peaceful_queens_support
  use, non_intrinsic :: peaceful_queens_solver

  implicit none

  integer :: num_solutions
  logical :: show_equivalents
  integer(kind = board_kind) :: armies1(1:8, 1:max_solutions)
  integer(kind = board_kind) :: armies2(1:8, 1:max_solutions)

  integer :: arg_count
  character(len = 200) :: arg

  show_equivalents = .false.

  arg_count = command_argument_count ()
  if (1 <= arg_count) then
     call get_command_argument (1, arg)
     select case (trim (arg))
     case ('1', 't', 'T', 'true', 'y', 'Y', 'yes')
        show_equivalents = .true.
     end select
  end if

  call solve_peaceful_queens (output_unit, show_equivalents, &
       &                      num_solutions, armies1, armies2)

end program peaceful_queens

Here is the driver script:

#!/bin/sh
#
# Driver script for peaceful_queens in Fortran.
#

if test ${ZSH_VERSION+y} && (emulate sh) >/dev/null 2>&1; then
    emulate sh
fi

if test $# -ne 3 && test $# -ne 4; then
    echo "Usage: $0 M N MAX_SOLUTIONS [SHOW_EQUIVALENTS]"
    exit 1
fi

M=${1}
N=${2}
MAX_SOLUTIONS=${3}
SHOW_EQUIVALENTS=${4}

RM_GENERATED_SRC=yes
CHECK=no

case ${CHECK} in
    0 | f | F | false | N | n | no) FCCHECK="" ;;
    1 | t | T | true | Y | y | yes) FCCHECK="-fcheck=all" ;;
    *) echo 'CHECK is set incorrectly';
       exit 1 ;;
esac

FC="gfortran"
FCFLAGS="-std=f2018 -g -O3 -march=native -fno-stack-protector -Wall -Wextra ${FCCHECK}"

# If you have the graphite optimizer, here are some marginally helpful
# flags. They barely make a difference, for me.
FCFLAGS="${FCFLAGS} -funroll-loops -floop-nest-optimize"

RUN_IT="yes"

${FC} -o peaceful_queens_elements_generator peaceful_queens_elements_generator.f90 &&
    ./peaceful_queens_elements_generator ${M} ${N} ${MAX_SOLUTIONS} > peaceful_queens_elements.f90 &&
    ${FC} ${FCFLAGS} -c peaceful_queens_elements.f90 &&
    if test x"${RM_GENERATED_SRC}" != xno; then rm -f peaceful_queens_elements.f90; fi &&
    ${FC} ${FCFLAGS} -c peaceful_queens.f90 &&
    ${FC} ${FCFLAGS} -o peaceful_queens peaceful_queens_elements.o peaceful_queens.o &&
    if test x"${RUN_IT}" = xyes; then time ./peaceful_queens ${SHOW_EQUIVALENTS}; else :; fi

Output:

$ ./peaceful_queens-fortran-driver.sh 4 5 1000 T

Solution 1
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+

     Equivalents
     +----+----+----+----+----+
     |  W |    |    |    |  W |
     +----+----+----+----+----+
     |    |    |  B |    |    |
     +----+----+----+----+----+
     |    |  B |    |  B |    |
     +----+----+----+----+----+
     |    |    |  B |    |    |
     +----+----+----+----+----+
     |  W |    |    |    |  W |
     +----+----+----+----+----+

Solution 2
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+

     Equivalents
     +----+----+----+----+----+
     |  W |    |    |    |  W |
     +----+----+----+----+----+
     |    |    |  B |    |    |
     +----+----+----+----+----+
     |  W |    |    |    |  W |
     +----+----+----+----+----+
     |    |    |  B |    |    |
     +----+----+----+----+----+
     |    |  B |    |  B |    |
     +----+----+----+----+----+

     +----+----+----+----+----+
     |  B |    |  B |    |    |
     +----+----+----+----+----+
     |    |    |    |    |  W |
     +----+----+----+----+----+
     |    |  W |    |  W |    |
     +----+----+----+----+----+
     |    |    |    |    |  W |
     +----+----+----+----+----+
     |  B |    |  B |    |    |
     +----+----+----+----+----+

     +----+----+----+----+----+
     |  W |    |  W |    |    |
     +----+----+----+----+----+
     |    |    |    |    |  B |
     +----+----+----+----+----+
     |    |  B |    |  B |    |
     +----+----+----+----+----+
     |    |    |    |    |  B |
     +----+----+----+----+----+
     |  W |    |  W |    |    |
     +----+----+----+----+----+

     +----+----+----+----+----+
     |    |  W |    |  W |    |
     +----+----+----+----+----+
     |    |    |  W |    |    |
     +----+----+----+----+----+
     |  B |    |    |    |  B |
     +----+----+----+----+----+
     |    |    |  W |    |    |
     +----+----+----+----+----+
     |  B |    |    |    |  B |
     +----+----+----+----+----+

     +----+----+----+----+----+
     |    |  B |    |  B |    |
     +----+----+----+----+----+
     |    |    |  B |    |    |
     +----+----+----+----+----+
     |  W |    |    |    |  W |
     +----+----+----+----+----+
     |    |    |  B |    |    |
     +----+----+----+----+----+
     |  W |    |    |    |  W |
     +----+----+----+----+----+

     +----+----+----+----+----+
     |    |    |  B |    |  B |
     +----+----+----+----+----+
     |  W |    |    |    |    |
     +----+----+----+----+----+
     |    |  W |    |  W |    |
     +----+----+----+----+----+
     |  W |    |    |    |    |
     +----+----+----+----+----+
     |    |    |  B |    |  B |
     +----+----+----+----+----+

     +----+----+----+----+----+
     |    |    |  W |    |  W |
     +----+----+----+----+----+
     |  B |    |    |    |    |
     +----+----+----+----+----+
     |    |  B |    |  B |    |
     +----+----+----+----+----+
     |  B |    |    |    |    |
     +----+----+----+----+----+
     |    |    |  W |    |  W |
     +----+----+----+----+----+

Solution 3
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+

     Equivalents
     +----+----+----+----+----+
     |  W |    |  W |    |    |
     +----+----+----+----+----+
     |    |    |    |    |  B |
     +----+----+----+----+----+
     |  W |    |  W |    |    |
     +----+----+----+----+----+
     |    |    |    |    |  B |
     +----+----+----+----+----+
     |    |  B |    |  B |    |
     +----+----+----+----+----+

     +----+----+----+----+----+
     |    |  W |    |  W |    |
     +----+----+----+----+----+
     |    |    |    |    |  W |
     +----+----+----+----+----+
     |  B |    |  B |    |    |
     +----+----+----+----+----+
     |    |    |    |    |  W |
     +----+----+----+----+----+
     |  B |    |  B |    |    |
     +----+----+----+----+----+

     +----+----+----+----+----+
     |    |  B |    |  B |    |
     +----+----+----+----+----+
     |    |    |    |    |  B |
     +----+----+----+----+----+
     |  W |    |  W |    |    |
     +----+----+----+----+----+
     |    |    |    |    |  B |
     +----+----+----+----+----+
     |  W |    |  W |    |    |
     +----+----+----+----+----+

     +----+----+----+----+----+
     |    |  W |    |  W |    |
     +----+----+----+----+----+
     |  W |    |    |    |    |
     +----+----+----+----+----+
     |    |    |  B |    |  B |
     +----+----+----+----+----+
     |  W |    |    |    |    |
     +----+----+----+----+----+
     |    |    |  B |    |  B |
     +----+----+----+----+----+

     +----+----+----+----+----+
     |    |  B |    |  B |    |
     +----+----+----+----+----+
     |  B |    |    |    |    |
     +----+----+----+----+----+
     |    |    |  W |    |  W |
     +----+----+----+----+----+
     |  B |    |    |    |    |
     +----+----+----+----+----+
     |    |    |  W |    |  W |
     +----+----+----+----+----+

     +----+----+----+----+----+
     |    |    |  B |    |  B |
     +----+----+----+----+----+
     |  W |    |    |    |    |
     +----+----+----+----+----+
     |    |    |  B |    |  B |
     +----+----+----+----+----+
     |  W |    |    |    |    |
     +----+----+----+----+----+
     |    |  W |    |  W |    |
     +----+----+----+----+----+

     +----+----+----+----+----+
     |    |    |  W |    |  W |
     +----+----+----+----+----+
     |  B |    |    |    |    |
     +----+----+----+----+----+
     |    |    |  W |    |  W |
     +----+----+----+----+----+
     |  B |    |    |    |    |
     +----+----+----+----+----+
     |    |  B |    |  B |    |
     +----+----+----+----+----+

On my computer, the program can find all the solutions of m=5, n=6, and eliminate any other possibilities, in under 5 seconds. The m=7, n=7 case took about 4.25 hours, mostly eliminating other possibilities. The next thing to try would be m=9, n=8, but probably a faster program is called for, there.

It would be instructive to save and examine the generated peaceful_queens_elements.f90 files. I leave that as an exercise for the reader. :)

FreeBASIC

Type posicion
    x As Integer
    y As Integer
End Type

Type pieza
    empty As Integer
    black As Integer
    white As Integer
End Type

Function isAttacking(q As posicion, posic As posicion) As Integer
    Return (q.x = posic.x Or q.y = posic.y Or Abs(q.x - posic.x) = Abs(q.y - posic.y))
End Function

Sub place(m As Integer, n As Integer, blackQueens() As posicion, whiteQueens() As posicion, Byref result As Integer)
    If m = 0 Then 
        result = -1
        Exit Sub
    End If
    Dim As Integer placingBlack = -1
    Dim As Integer i, j, k, equalposicion
    Dim As Boolean inner
    
    For i = 0 To n-1
        For j = 0 To n-1
            Dim As posicion posic = Type<posicion>(i, j)
            inner = False
            For k = Lbound(blackQueens) To Ubound(blackQueens)
                equalposicion = (blackQueens(k).x = posic.x And blackQueens(k).y = posic.y)
                If equalposicion Or (Not placingBlack And isAttacking(blackQueens(k), posic)) Then
                    inner = True
                    Exit For
                End If
            Next
            If Not inner Then
                For k = Lbound(whiteQueens) To Ubound(whiteQueens)
                    equalposicion = (whiteQueens(k).x = posic.x And whiteQueens(k).y = posic.y)
                    If equalposicion Or (placingBlack And isAttacking(whiteQueens(k), posic)) Then
                        inner = True
                        Exit For
                    End If
                Next
                If Not inner Then
                    If placingBlack Then
                        Redim Preserve blackQueens(Ubound(blackQueens) + 1)
                        blackQueens(Ubound(blackQueens)) = posic
                        placingBlack = 0
                    Else
                        Redim Preserve whiteQueens(Ubound(whiteQueens) + 1)
                        whiteQueens(Ubound(whiteQueens)) = posic
                        place(m-1, n, blackQueens(), whiteQueens(), result)
                        If result Then Exit Sub
                        Redim Preserve blackQueens(Ubound(blackQueens) - 1)
                        Redim Preserve whiteQueens(Ubound(whiteQueens) - 1)
                        placingBlack = -1
                    End If
                End If
            End If
        Next
    Next
    If Not placingBlack Then Redim Preserve blackQueens(Ubound(blackQueens) - 1)
    result = 0
End Sub

Sub printBoard(n As Integer, blackQueens() As posicion, whiteQueens() As posicion)
    Dim As Integer board(n * n)
    Dim As Integer i, j, k
    
    For i = Lbound(blackQueens) To Ubound(blackQueens)
        board(blackQueens(i).x * n + blackQueens(i).y) = 1
    Next
    For i = Lbound(whiteQueens) To Ubound(whiteQueens)
        board(whiteQueens(i).x * n + whiteQueens(i).y) = 2
    Next
    For i = 0 To n*n-1
        If i Mod n = 0 And i <> 0 Then Print
        Select Case board(i)
        Case 1
            Print "B ";
        Case 2
            Print "W ";
        Case Else
            j = i \ n
            k = i - j * n
            If j Mod 2 = k Mod 2 Then
                Print Chr(253); " ";
            Else
                Print Chr(252); " "; 
            End If
        End Select
    Next i
    Print
End Sub

Dim As posicion nms(23) = { _
Type<posicion>(2, 1), Type<posicion>(3, 1), Type<posicion>(3, 2), Type<posicion>(4, 1), Type<posicion>(4, 2), Type<posicion>(4, 3), _
Type<posicion>(5, 1), Type<posicion>(5, 2), Type<posicion>(5, 3), Type<posicion>(5, 4), Type<posicion>(5, 5), _
Type<posicion>(6, 1), Type<posicion>(6, 2), Type<posicion>(6, 3), Type<posicion>(6, 4), Type<posicion>(6, 5), Type<posicion>(6, 6), _
Type<posicion>(7, 1), Type<posicion>(7, 2), Type<posicion>(7, 3), Type<posicion>(7, 4), Type<posicion>(7, 5), Type<posicion>(7, 6), Type<posicion>(7, 7) }

For i As Integer = Lbound(nms) To Ubound(nms)
    Print Chr(10); nms(i).y; " black and "; nms(i).y; " white queens on a "; nms(i).x; " x "; nms(i).x; " board:"
    Dim As posicion blackQueens(0)
    Dim As posicion whiteQueens(0)
    Dim As Integer result
    place(nms(i).y, nms(i).x, blackQueens(), whiteQueens(), result)
    If result Then
        printBoard(nms(i).x, blackQueens(), whiteQueens())
    Else
        Print "No solution exists."
    End If
Next i

Sleep

Output:

 1 black and  1 white queens on a  2 x  2 board:
No solution exists.

 1 black and  1 white queens on a  3 x  3 board:
² ³ ²
³ ² B
W ³ ²

 2 black and  2 white queens on a  3 x  3 board:
² B ²
³ ² ³
² ³ W

 1 black and  1 white queens on a  4 x  4 board:
² ³ ² ³
³ ² B ²
W ³ ² ³
³ ² ³ ²

 2 black and  2 white queens on a  4 x  4 board:
² B ² ³
³ ² ³ W
² ³ ² ³
³ ² ³ ²

 3 black and  3 white queens on a  4 x  4 board:
B ³ ² ³
³ ² W ²
² ³ ² ³
³ ² ³ ²

 1 black and  1 white queens on a  5 x  5 board:
² ³ ² ³ ²
³ ² B ² ³
W ³ ² ³ ²
³ ² ³ ² ³
² ³ ² ³ ²

 2 black and  2 white queens on a  5 x  5 board:
² B ² ³ ²
³ ² ³ W ³
² ³ ² ³ ²
³ ² ³ ² ³
² ³ ² ³ ²

 3 black and  3 white queens on a  5 x  5 board:
B ³ ² ³ ²
³ ² W ² ³
² ³ ² ³ ²
³ ² ³ ² ³
² ³ ² ³ ²

 4 black and  4 white queens on a  5 x  5 board:
² ³ ² ³ B
W ² ³ ² ³
² ³ ² ³ ²
³ ² ³ ² ³
² ³ ² ³ ²

 5 black and  5 white queens on a  5 x  5 board:
² ³ B ³ ²
³ ² ³ ² W
² ³ ² ³ ²
³ ² ³ ² ³
² ³ ² ³ ²

 1 black and  1 white queens on a  6 x  6 board:
² ³ ² ³ ² ³
³ ² B ² ³ ²
W ³ ² ³ ² ³
³ ² ³ ² ³ ²
² ³ ² ³ ² ³
³ ² ³ ² ³ ²

 2 black and  2 white queens on a  6 x  6 board:
² B ² ³ ² ³
³ ² ³ W ³ ²
² ³ ² ³ ² ³
³ ² ³ ² ³ ²
² ³ ² ³ ² ³
³ ² ³ ² ³ ²

 3 black and  3 white queens on a  6 x  6 board:
B ³ ² ³ ² ³
³ ² W ² ³ ²
² ³ ² ³ ² ³
³ ² ³ ² ³ ²
² ³ ² ³ ² ³
³ ² ³ ² ³ ²

 4 black and  4 white queens on a  6 x  6 board:
² ³ ² ³ B ³
W ² ³ ² ³ ²
² ³ ² ³ ² ³
³ ² ³ ² ³ ²
² ³ ² ³ ² ³
³ ² ³ ² ³ ²

 5 black and  5 white queens on a  6 x  6 board:
² ³ B ³ ² ³
³ ² ³ ² W ²
² ³ ² ³ ² ³
³ ² ³ ² ³ ²
² ³ ² ³ ² ³
³ ² ³ ² ³ ²

 6 black and  6 white queens on a  6 x  6 board:
B ³ ² ³ ² ³
³ ² W ² ³ ²
² ³ ² ³ ² ³
³ ² ³ ² ³ ²
² ³ ² ³ ² ³
³ ² ³ ² ³ ²

 1 black and  1 white queens on a  7 x  7 board:
² ³ ² ³ ² ³ ²
³ ² B ² ³ ² ³
W ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²

 2 black and  2 white queens on a  7 x  7 board:
² B ² ³ ² ³ ²
³ ² ³ W ³ ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²

 3 black and  3 white queens on a  7 x  7 board:
B ³ ² ³ ² ³ ²
³ ² W ² ³ ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²

 4 black and  4 white queens on a  7 x  7 board:
² ³ ² ³ B ³ ²
W ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²

 5 black and  5 white queens on a  7 x  7 board:
² ³ B ³ ² ³ ²
³ ² ³ ² W ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²

 6 black and  6 white queens on a  7 x  7 board:
B ³ ² ³ ² ³ ²
³ ² W ² ³ ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²

 7 black and  7 white queens on a  7 x  7 board:
² ³ ² ³ B ³ ²
W ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²
³ ² ³ ² ³ ² ³
² ³ ² ³ ² ³ ²

Go

This is based on the C# code here.

Textual rather than HTML output. Whilst the unicode symbols for the black and white queens are recognized by the Ubuntu 16.04 terminal, I found it hard to visually distinguish between them so I've used 'B' and 'W' instead.

package main

import "fmt"

const (
    empty = iota
    black
    white
)

const (
    bqueen  = 'B'
    wqueen  = 'W'
    bbullet = '•'
    wbullet = '◦'
)

type position struct{ i, j int }

func iabs(i int) int {
    if i < 0 {
        return -i
    }
    return i
}

func place(m, n int, pBlackQueens, pWhiteQueens *[]position) bool {
    if m == 0 {
        return true
    }
    placingBlack := true
    for i := 0; i < n; i++ {
    inner:
        for j := 0; j < n; j++ {
            pos := position{i, j}
            for _, queen := range *pBlackQueens {
                if queen == pos || !placingBlack && isAttacking(queen, pos) {
                    continue inner
                }
            }
            for _, queen := range *pWhiteQueens {
                if queen == pos || placingBlack && isAttacking(queen, pos) {
                    continue inner
                }
            }
            if placingBlack {
                *pBlackQueens = append(*pBlackQueens, pos)
                placingBlack = false
            } else {
                *pWhiteQueens = append(*pWhiteQueens, pos)
                if place(m-1, n, pBlackQueens, pWhiteQueens) {
                    return true
                }
                *pBlackQueens = (*pBlackQueens)[0 : len(*pBlackQueens)-1]
                *pWhiteQueens = (*pWhiteQueens)[0 : len(*pWhiteQueens)-1]
                placingBlack = true
            }
        }
    }
    if !placingBlack {
        *pBlackQueens = (*pBlackQueens)[0 : len(*pBlackQueens)-1]
    }
    return false
}

func isAttacking(queen, pos position) bool {
    if queen.i == pos.i {
        return true
    }
    if queen.j == pos.j {
        return true
    }
    if iabs(queen.i-pos.i) == iabs(queen.j-pos.j) {
        return true
    }
    return false
}

func printBoard(n int, blackQueens, whiteQueens []position) {
    board := make([]int, n*n)
    for _, queen := range blackQueens {
        board[queen.i*n+queen.j] = black
    }
    for _, queen := range whiteQueens {
        board[queen.i*n+queen.j] = white
    }

    for i, b := range board {
        if i != 0 && i%n == 0 {
            fmt.Println()
        }
        switch b {
        case black:
            fmt.Printf("%c ", bqueen)
        case white:
            fmt.Printf("%c ", wqueen)
        case empty:
            if i%2 == 0 {
                fmt.Printf("%c ", bbullet)
            } else {
                fmt.Printf("%c ", wbullet)
            }
        }
    }
    fmt.Println("\n")
}

func main() {
    nms := [][2]int{
        {2, 1}, {3, 1}, {3, 2}, {4, 1}, {4, 2}, {4, 3},
        {5, 1}, {5, 2}, {5, 3}, {5, 4}, {5, 5},
        {6, 1}, {6, 2}, {6, 3}, {6, 4}, {6, 5}, {6, 6},
        {7, 1}, {7, 2}, {7, 3}, {7, 4}, {7, 5}, {7, 6}, {7, 7},
    }
    for _, nm := range nms {
        n, m := nm[0], nm[1]
        fmt.Printf("%d black and %d white queens on a %d x %d board:\n", m, m, n, n)
        var blackQueens, whiteQueens []position
        if place(m, n, &blackQueens, &whiteQueens) {
            printBoard(n, blackQueens, whiteQueens)
        } else {
            fmt.Println("No solution exists.\n")
        }
    }
}

Output:

1 black and 1 white queens on a 2 x 2 board:
No solution exists.

1 black and 1 white queens on a 3 x 3 board:
B ◦ • 
◦ • W 
• ◦ • 

2 black and 2 white queens on a 3 x 3 board:
No solution exists.

1 black and 1 white queens on a 4 x 4 board:
B ◦ • ◦ 
• ◦ W ◦ 
• ◦ • ◦ 
• ◦ • ◦ 

2 black and 2 white queens on a 4 x 4 board:
B ◦ • ◦ 
• ◦ W ◦ 
B ◦ • ◦ 
• ◦ W ◦ 

3 black and 3 white queens on a 4 x 4 board:
No solution exists.

1 black and 1 white queens on a 5 x 5 board:
B ◦ • ◦ • 
◦ • W • ◦ 
• ◦ • ◦ • 
◦ • ◦ • ◦ 
• ◦ • ◦ • 

2 black and 2 white queens on a 5 x 5 board:
B ◦ • ◦ B 
◦ • W • ◦ 
• W • ◦ • 
◦ • ◦ • ◦ 
• ◦ • ◦ • 

3 black and 3 white queens on a 5 x 5 board:
B ◦ • ◦ B 
◦ • W • ◦ 
• W • ◦ • 
◦ • ◦ B ◦ 
• W • ◦ • 

4 black and 4 white queens on a 5 x 5 board:
• B • B • 
◦ • ◦ • B 
W ◦ W ◦ • 
◦ • ◦ • B 
W ◦ W ◦ • 

5 black and 5 white queens on a 5 x 5 board:
No solution exists.

1 black and 1 white queens on a 6 x 6 board:
B ◦ • ◦ • ◦ 
• ◦ W ◦ • ◦ 
• ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ 

2 black and 2 white queens on a 6 x 6 board:
B ◦ • ◦ B ◦ 
• ◦ W ◦ • ◦ 
• W • ◦ • ◦ 
• ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ 

3 black and 3 white queens on a 6 x 6 board:
B ◦ • ◦ B B 
• ◦ W ◦ • ◦ 
• W • ◦ • ◦ 
• ◦ • ◦ • ◦ 
• ◦ W ◦ • ◦ 
• ◦ • ◦ • ◦ 

4 black and 4 white queens on a 6 x 6 board:
B ◦ • ◦ B B 
• ◦ W ◦ • ◦ 
• W • ◦ • ◦ 
• ◦ • ◦ • B 
• ◦ W W • ◦ 
• ◦ • ◦ • ◦ 

5 black and 5 white queens on a 6 x 6 board:
• B • ◦ B ◦ 
• ◦ • B • B 
W ◦ • ◦ • ◦ 
W ◦ W ◦ • ◦ 
• ◦ • ◦ • B 
W ◦ W ◦ • ◦ 

6 black and 6 white queens on a 6 x 6 board:
No solution exists.

1 black and 1 white queens on a 7 x 7 board:
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

2 black and 2 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

3 black and 3 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

4 black and 4 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

5 black and 5 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

6 black and 6 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 

7 black and 7 white queens on a 7 x 7 board:
• B • ◦ • B • 
◦ B ◦ • B • ◦ 
• B • ◦ • B • 
◦ • ◦ • B • ◦ 
W ◦ W ◦ • ◦ W 
◦ • ◦ W ◦ • ◦ 
W ◦ W W • ◦ • 

Java

Translation of: Kotlin

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class Peaceful {
    enum Piece {
        Empty,
        Black,
        White,
    }

    public static class Position {
        public int x, y;

        public Position(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj instanceof Position) {
                Position pos = (Position) obj;
                return pos.x == x && pos.y == y;
            }
            return false;
        }
    }

    private static boolean place(int m, int n, List<Position> pBlackQueens, List<Position> pWhiteQueens) {
        if (m == 0) {
            return true;
        }
        boolean placingBlack = true;
        for (int i = 0; i < n; ++i) {
            inner:
            for (int j = 0; j < n; ++j) {
                Position pos = new Position(i, j);
                for (Position queen : pBlackQueens) {
                    if (pos.equals(queen) || !placingBlack && isAttacking(queen, pos)) {
                        continue inner;
                    }
                }
                for (Position queen : pWhiteQueens) {
                    if (pos.equals(queen) || placingBlack && isAttacking(queen, pos)) {
                        continue inner;
                    }
                }
                if (placingBlack) {
                    pBlackQueens.add(pos);
                    placingBlack = false;
                } else {
                    pWhiteQueens.add(pos);
                    if (place(m - 1, n, pBlackQueens, pWhiteQueens)) {
                        return true;
                    }
                    pBlackQueens.remove(pBlackQueens.size() - 1);
                    pWhiteQueens.remove(pWhiteQueens.size() - 1);
                    placingBlack = true;
                }
            }
        }
        if (!placingBlack) {
            pBlackQueens.remove(pBlackQueens.size() - 1);
        }
        return false;
    }

    private static boolean isAttacking(Position queen, Position pos) {
        return queen.x == pos.x
            || queen.y == pos.y
            || Math.abs(queen.x - pos.x) == Math.abs(queen.y - pos.y);
    }

    private static void printBoard(int n, List<Position> blackQueens, List<Position> whiteQueens) {
        Piece[] board = new Piece[n * n];
        Arrays.fill(board, Piece.Empty);

        for (Position queen : blackQueens) {
            board[queen.x + n * queen.y] = Piece.Black;
        }
        for (Position queen : whiteQueens) {
            board[queen.x + n * queen.y] = Piece.White;
        }
        for (int i = 0; i < board.length; ++i) {
            if ((i != 0) && i % n == 0) {
                System.out.println();
            }

            Piece b = board[i];
            if (b == Piece.Black) {
                System.out.print("B ");
            } else if (b == Piece.White) {
                System.out.print("W ");
            } else {
                int j = i / n;
                int k = i - j * n;
                if (j % 2 == k % 2) {
                    System.out.print("• ");
                } else {
                    System.out.print("◦ ");
                }
            }
        }
        System.out.println('\n');
    }

    public static void main(String[] args) {
        List<Position> nms = List.of(
            new Position(2, 1),
            new Position(3, 1),
            new Position(3, 2),
            new Position(4, 1),
            new Position(4, 2),
            new Position(4, 3),
            new Position(5, 1),
            new Position(5, 2),
            new Position(5, 3),
            new Position(5, 4),
            new Position(5, 5),
            new Position(6, 1),
            new Position(6, 2),
            new Position(6, 3),
            new Position(6, 4),
            new Position(6, 5),
            new Position(6, 6),
            new Position(7, 1),
            new Position(7, 2),
            new Position(7, 3),
            new Position(7, 4),
            new Position(7, 5),
            new Position(7, 6),
            new Position(7, 7)
        );
        for (Position nm : nms) {
            int m = nm.y;
            int n = nm.x;
            System.out.printf("%d black and %d white queens on a %d x %d board:\n", m, m, n, n);
            List<Position> blackQueens = new ArrayList<>();
            List<Position> whiteQueens = new ArrayList<>();
            if (place(m, n, blackQueens, whiteQueens)) {
                printBoard(n, blackQueens, whiteQueens);
            } else {
                System.out.println("No solution exists.\n");
            }
        }
    }
}

Output:

1 black and 1 white queens on a 2 x 2 board:
No solution exists.

1 black and 1 white queens on a 3 x 3 board:
B ◦ • 
◦ • ◦ 
• W • 

2 black and 2 white queens on a 3 x 3 board:
No solution exists.

1 black and 1 white queens on a 4 x 4 board:
B ◦ • ◦ 
◦ • ◦ • 
• W • ◦ 
◦ • ◦ • 

2 black and 2 white queens on a 4 x 4 board:
B ◦ B ◦ 
◦ • ◦ • 
• W • W 
◦ • ◦ • 

3 black and 3 white queens on a 4 x 4 board:
No solution exists.

1 black and 1 white queens on a 5 x 5 board:
B ◦ • ◦ • 
◦ • ◦ • ◦ 
• W • ◦ • 
◦ • ◦ • ◦ 
• ◦ • ◦ • 

2 black and 2 white queens on a 5 x 5 board:
B ◦ • ◦ • 
◦ • W • ◦ 
• W • ◦ • 
◦ • ◦ • ◦ 
B ◦ • ◦ • 

3 black and 3 white queens on a 5 x 5 board:
B ◦ • ◦ • 
◦ • W • W 
• W • ◦ • 
◦ • ◦ B ◦ 
B ◦ • ◦ • 

4 black and 4 white queens on a 5 x 5 board:
• ◦ W ◦ W 
B • ◦ • ◦ 
• ◦ W ◦ W 
B • ◦ • ◦ 
• B • B • 

5 black and 5 white queens on a 5 x 5 board:
No solution exists.

1 black and 1 white queens on a 6 x 6 board:
B ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 

2 black and 2 white queens on a 6 x 6 board:
B ◦ • ◦ • ◦ 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ • 
B ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 

3 black and 3 white queens on a 6 x 6 board:
B ◦ • ◦ • ◦ 
◦ • W • ◦ • 
• W • ◦ W ◦ 
◦ • ◦ • ◦ • 
B ◦ • ◦ • ◦ 
B • ◦ • ◦ • 

4 black and 4 white queens on a 6 x 6 board:
B ◦ • ◦ • ◦ 
◦ • W • ◦ • 
• W • ◦ W ◦ 
◦ • ◦ • W • 
B ◦ • ◦ • ◦ 
B • ◦ B ◦ • 

5 black and 5 white queens on a 6 x 6 board:
• ◦ W W • W 
B • ◦ • ◦ • 
• ◦ • W • W 
◦ B ◦ • ◦ • 
B ◦ • ◦ • ◦ 
◦ B ◦ • B • 

6 black and 6 white queens on a 6 x 6 board:
No solution exists.

1 black and 1 white queens on a 7 x 7 board:
B ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• W • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

2 black and 2 white queens on a 7 x 7 board:
B ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• W • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
B ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• W • ◦ • ◦ • 

3 black and 3 white queens on a 7 x 7 board:
B ◦ B ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• W • W • ◦ • 
◦ • ◦ • ◦ • ◦ 
B ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• W • ◦ • ◦ • 

4 black and 4 white queens on a 7 x 7 board:
B ◦ B ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• W • W • ◦ • 
◦ • ◦ • ◦ • ◦ 
B ◦ B ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• W • W • ◦ • 

5 black and 5 white queens on a 7 x 7 board:
B ◦ B ◦ B ◦ • 
◦ • ◦ • ◦ • ◦ 
• W • W • W • 
◦ • ◦ • ◦ • ◦ 
B ◦ B ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• W • W • ◦ • 

6 black and 6 white queens on a 7 x 7 board:
B ◦ B ◦ B ◦ • 
◦ • ◦ • ◦ • ◦ 
• W • W • W • 
◦ • ◦ • ◦ • ◦ 
B ◦ B ◦ B ◦ • 
◦ • ◦ • ◦ • ◦ 
• W • W • W • 

7 black and 7 white queens on a 7 x 7 board:
• ◦ • ◦ W ◦ W 
B B B • ◦ • ◦ 
• ◦ • ◦ W ◦ W 
◦ • ◦ • ◦ W W 
• B • B • ◦ • 
B • B • ◦ • ◦ 
• ◦ • ◦ W ◦ • 

jq

Adapted from Wren

Works with jq, the C implementation of jq

Works with gojq, the Go implementation of jq

In the following, positions on the chessboard are represented by {x,y} objects.

# Is the queen at position . attacking the position $pos ?
def isAttacking($pos):
   .x == $pos.x or
   .y == $pos.y or
   (((.x - $pos.x)|length) == ((.y - $pos.y)|length)); # i.e. abs

# Place $q black and $q white queens on an $n*$n board,
# where .blackQueens holds the positions of existing black Queens,
# and similarly for .whiteQueens.
# input: {blackQueens, whiteQueens}
# output: updated input on success, otherwise null.
def place($queens; $n):
  def place($q):
    if $q == 0 then .ok = true
    else .placingBlack = true
    | first(
       foreach range(0; $n) as $i (.;
        foreach range(0; $n) as $j (.;
           {x:$i, y:$j} as $pos
           | .placingBlack as $placingBlack
           | if any( .blackQueens[], .whiteQueens[];
                      ((.x == $pos.x) and (.y == $pos.y)))
             then . # failure
             elif .placingBlack
             then if any( .whiteQueens[]; isAttacking($pos) )
                  then .
                  else .blackQueens += [$pos]
                  | .placingBlack = false
                  end
             elif any( .blackQueens[]; isAttacking($pos) )
             then .
             else .whiteQueens += [$pos]
             | place($q-1) as $place
             | if $place then $place  # success
               else .blackQueens |= .[:-1]
               | .whiteQueens |= .[:-1]
               | .placingBlack = true
               end
             end
           | if $i == $n-1 and $j == $n-1 then .ok = false end );
        select(.ok) )
      ) // null
    end;
  {blackQueens: [], whiteQueens: [] } | place($queens);

# Input {blackQueens, whiteQueens}
def printBoard($n):
  [range(0; $n) | 0] as $row
  | .board = [range(0; $n) | $row]
  | reduce .blackQueens[] as $queen (.; .board[$queen.x][$queen.y] = "B ")
  | reduce .whiteQueens[] as $queen (.; .board[$queen.x][$queen.y] = "W ")
  | foreach range(0; $n) as $i (.;
      reduce range(0; $n) as $j (.row="";
        .board[$i][$j] as $b
        | .row +=
             (if $b != 0 then $b
              elif $i%2 == $j%2
              then "• "
              else "◦ "
              end) ) )
  | .row;

# Use an object {squares, queens} to record the task:
# $squares is the number of squares on each side of the board,
# and $queens is the number of queens of each color.
def Task($squares; $queens): {$squares, $queens};

def tasks: [
    Task(2; 1), Task(3; 1), Task(3; 2), Task(4; 1), Task(4; 2), Task(4; 3),
    Task(5; 1), Task(5; 2), Task(5; 3), Task(5; 4), Task(5; 5),
    Task(6; 1), Task(6; 2), Task(6; 3), Task(6; 4), Task(6; 5), Task(6; 6),
    Task(7; 1), Task(7; 2), Task(7; 3), Task(7; 4), Task(7; 5), Task(7; 6), Task(7; 7)
];

tasks[] as $t
| "\($t.queens) black and \($t.queens) white queens on a \($t.squares) x \($t.squares) board:",
  ((place($t.queens; $t.squares)
   | select(.)
   | printBoard($t.squares))
   // "No solution exists."),
   ""

Output:

See Wren.

Julia

GUI version, uses the Gtk library. The place! function is condensed from the C# example.

using Gtk

struct Position
    row::Int
    col::Int
end

function place!(numeach, bsize, bqueens, wqueens)
    isattack(q, pos) = (q.row == pos.row || q.col == pos.col ||
                        abs(q.row - pos.row) == abs(q.col - pos.col))
    noattack(qs, pos) = !any(x -> isattack(x, pos), qs)
    positionopen(bqs, wqs, p) = !any(x -> x == p, bqs) && !any(x -> x == p, wqs)

    placingbqueens = true
    if numeach < 1
        return true
    end
    for i in 1:bsize, j in 1:bsize
        bpos = Position(i, j)
        if positionopen(bqueens, wqueens, bpos)
            if placingbqueens && noattack(wqueens, bpos)
                push!(bqueens, bpos)
                placingbqueens = false
            elseif !placingbqueens && noattack(bqueens, bpos)
                push!(wqueens, bpos)
                if place!(numeach - 1, bsize, bqueens, wqueens)
                    return true
                end
                pop!(bqueens)
                pop!(wqueens)
                placingbqueens = true
            end
        end
    end
    if !placingbqueens
        pop!(bqueens)
    end
    false
end

function peacefulqueenapp()
    win = GtkWindow("Peaceful Chess Queen Armies", 800, 800) |> (GtkFrame() |> (box = GtkBox(:v)))
    boardsize = 5
    numqueenseach = 4
    hbox = GtkBox(:h)
    boardscale = GtkScale(false, 2:16)
    set_gtk_property!(boardscale, :hexpand, true)
    blabel = GtkLabel("Choose Board Size")
    nqueenscale = GtkScale(false, 1:24)
    set_gtk_property!(nqueenscale, :hexpand, true)
    qlabel = GtkLabel("Choose Number of Queens Per Side")
    solveit = GtkButton("Solve")
    set_gtk_property!(solveit, :label, "   Solve   ")
    solvequeens(wid) = (boardsize = Int(GAccessor.value(boardscale));
        numqueenseach = Int(GAccessor.value(nqueenscale)); update!())
    signal_connect(solvequeens, solveit, :clicked)
    map(w->push!(hbox, w),[blabel, boardscale, qlabel, nqueenscale, solveit])
    scrwin = GtkScrolledWindow()
    grid = GtkGrid()
    push!(scrwin, grid)
    map(w -> push!(box, w),[hbox, scrwin])
    piece = (white = "\u2655", black = "\u265B", blank = "   ")
    stylist = GtkStyleProvider(Gtk.CssProviderLeaf(data="""
        label {background-image: image(cornsilk); font-size: 48px;}
        button {background-image: image(tan); font-size: 48px;}"""))

    function update!()
        bqueens, wqueens = Vector{Position}(), Vector{Position}()
        place!(numqueenseach, boardsize, bqueens, wqueens)
        if length(bqueens) == 0
            warn_dialog("No solution for board size $boardsize and $numqueenseach queens each.", win)
            return
        end
        empty!(grid)
        labels = Array{Gtk.GtkLabelLeaf, 2}(undef, (boardsize, boardsize))
        buttons = Array{GtkButtonLeaf, 2}(undef, (boardsize, boardsize))
        for i in 1:boardsize, j in 1:boardsize
            if isodd(i + j)
                grid[i, j] = buttons[i, j] = GtkButton(piece.blank)
                set_gtk_property!(buttons[i, j], :expand, true)
                push!(Gtk.GAccessor.style_context(buttons[i, j]), stylist, 600)
            else
                grid[i, j] = labels[i, j] = GtkLabel(piece.blank)
                set_gtk_property!(labels[i, j], :expand, true)
                push!(Gtk.GAccessor.style_context(labels[i, j]), stylist, 600)
            end
            pos = Position(i, j)
            if pos in bqueens
                set_gtk_property!(grid[i, j], :label, piece.black)
            elseif pos in wqueens
                set_gtk_property!(grid[i, j], :label, piece.white)
            end
        end
        showall(win)
    end

    update!()
    cond = Condition()
    endit(w) = notify(cond)
    signal_connect(endit, win, :destroy)
    showall(win)
    wait(cond)
end

peacefulqueenapp()

Kotlin

Translation of: D

import kotlin.math.abs

enum class Piece {
    Empty,
    Black,
    White,
}

typealias Position = Pair<Int, Int>

fun place(m: Int, n: Int, pBlackQueens: MutableList<Position>, pWhiteQueens: MutableList<Position>): Boolean {
    if (m == 0) {
        return true
    }
    var placingBlack = true
    for (i in 0 until n) {
        inner@
        for (j in 0 until n) {
            val pos = Position(i, j)
            for (queen in pBlackQueens) {
                if (queen == pos || !placingBlack && isAttacking(queen, pos)) {
                    continue@inner
                }
            }
            for (queen in pWhiteQueens) {
                if (queen == pos || placingBlack && isAttacking(queen, pos)) {
                    continue@inner
                }
            }
            placingBlack = if (placingBlack) {
                pBlackQueens.add(pos)
                false
            } else {
                pWhiteQueens.add(pos)
                if (place(m - 1, n, pBlackQueens, pWhiteQueens)) {
                    return true
                }
                pBlackQueens.removeAt(pBlackQueens.lastIndex)
                pWhiteQueens.removeAt(pWhiteQueens.lastIndex)
                true
            }
        }
    }
    if (!placingBlack) {
        pBlackQueens.removeAt(pBlackQueens.lastIndex)
    }
    return false
}

fun isAttacking(queen: Position, pos: Position): Boolean {
    return queen.first == pos.first
            || queen.second == pos.second
            || abs(queen.first - pos.first) == abs(queen.second - pos.second)
}

fun printBoard(n: Int, blackQueens: List<Position>, whiteQueens: List<Position>) {
    val board = MutableList(n * n) { Piece.Empty }

    for (queen in blackQueens) {
        board[queen.first * n + queen.second] = Piece.Black
    }
    for (queen in whiteQueens) {
        board[queen.first * n + queen.second] = Piece.White
    }
    for ((i, b) in board.withIndex()) {
        if (i != 0 && i % n == 0) {
            println()
        }
        if (b == Piece.Black) {
            print("B ")
        } else if (b == Piece.White) {
            print("W ")
        } else {
            val j = i / n
            val k = i - j * n
            if (j % 2 == k % 2) {
                print("• ")
            } else {
                print("◦ ")
            }
        }
    }
    println('\n')
}

fun main() {
    val nms = listOf(
        Pair(2, 1), Pair(3, 1), Pair(3, 2), Pair(4, 1), Pair(4, 2), Pair(4, 3),
        Pair(5, 1), Pair(5, 2), Pair(5, 3), Pair(5, 4), Pair(5, 5),
        Pair(6, 1), Pair(6, 2), Pair(6, 3), Pair(6, 4), Pair(6, 5), Pair(6, 6),
        Pair(7, 1), Pair(7, 2), Pair(7, 3), Pair(7, 4), Pair(7, 5), Pair(7, 6), Pair(7, 7)
    )
    for ((n, m) in nms) {
        println("$m black and $m white queens on a $n x $n board:")
        val blackQueens = mutableListOf<Position>()
        val whiteQueens = mutableListOf<Position>()
        if (place(m, n, blackQueens, whiteQueens)) {
            printBoard(n, blackQueens, whiteQueens)
        } else {
            println("No solution exists.\n")
        }
    }
}

Output:

1 black and 1 white queens on a 2 x 2 board:
No solution exists.

1 black and 1 white queens on a 3 x 3 board:
B ◦ • 
◦ • W 
• ◦ • 

2 black and 2 white queens on a 3 x 3 board:
No solution exists.

1 black and 1 white queens on a 4 x 4 board:
B ◦ • ◦ 
◦ • W • 
• ◦ • ◦ 
◦ • ◦ • 

2 black and 2 white queens on a 4 x 4 board:
B ◦ • ◦ 
◦ • W • 
B ◦ • ◦ 
◦ • W • 

3 black and 3 white queens on a 4 x 4 board:
No solution exists.

1 black and 1 white queens on a 5 x 5 board:
B ◦ • ◦ • 
◦ • W • ◦ 
• ◦ • ◦ • 
◦ • ◦ • ◦ 
• ◦ • ◦ • 

2 black and 2 white queens on a 5 x 5 board:
B ◦ • ◦ B 
◦ • W • ◦ 
• W • ◦ • 
◦ • ◦ • ◦ 
• ◦ • ◦ • 

3 black and 3 white queens on a 5 x 5 board:
B ◦ • ◦ B 
◦ • W • ◦ 
• W • ◦ • 
◦ • ◦ B ◦ 
• W • ◦ • 

4 black and 4 white queens on a 5 x 5 board:
• B • B • 
◦ • ◦ • B 
W ◦ W ◦ • 
◦ • ◦ • B 
W ◦ W ◦ • 

5 black and 5 white queens on a 5 x 5 board:
No solution exists.

1 black and 1 white queens on a 6 x 6 board:
B ◦ • ◦ • ◦ 
◦ • W • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 

2 black and 2 white queens on a 6 x 6 board:
B ◦ • ◦ B ◦ 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 

3 black and 3 white queens on a 6 x 6 board:
B ◦ • ◦ B B 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ W ◦ • ◦ 
◦ • ◦ • ◦ • 

4 black and 4 white queens on a 6 x 6 board:
B ◦ • ◦ B B 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ B 
• ◦ W W • ◦ 
◦ • ◦ • ◦ • 

5 black and 5 white queens on a 6 x 6 board:
• B • ◦ B ◦ 
◦ • ◦ B ◦ B 
W ◦ • ◦ • ◦ 
W • W • ◦ • 
• ◦ • ◦ • B 
W • W • ◦ • 

6 black and 6 white queens on a 6 x 6 board:
No solution exists.

1 black and 1 white queens on a 7 x 7 board:
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

2 black and 2 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

3 black and 3 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

4 black and 4 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

5 black and 5 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

6 black and 6 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 

7 black and 7 white queens on a 7 x 7 board:
• B • ◦ • B • 
◦ B ◦ • B • ◦ 
• B • ◦ • B • 
◦ • ◦ • B • ◦ 
W ◦ W ◦ • ◦ W 
◦ • ◦ W ◦ • ◦ 
W ◦ W W • ◦ • 

Mathematica /Wolfram Language

ClearAll[ValidSpots, VisibleByQueen, SolveQueen, GetSolution]
VisualizeState[state_] := Module[{q, cells},
  q = MapIndexed[If[#["q"] == -1, {}, Text[Style[#["q"], 24], #2]] &, state, {2}];
  cells = MapIndexed[{If[OddQ[Total[#2]], FaceForm[], 
       FaceForm[GrayLevel[0.8]]], EdgeForm[Black], 
      Rectangle[#2 - 0.5, #2 + 0.5]} &, state, {2}];
  Graphics[{cells, q}]
 ]
ValidSpots[state_, tp_Integer] := Module[{vals},
  vals = Catenate@MapIndexed[If[#1["q"] == -1 \[And] DeleteCases[#1["v"], tp] == {}, #2, Missing[]] &, state, {2}];
  DeleteMissing[vals]
 ]
VisibleByQueen[{i_, j_}, {a_, b_}] := i == a \[Or] j == b \[Or] i + j == a + b \[Or] i - j == a - b
PlaceQueen[state_, pos : {i_Integer, j_Integer}, tp_Integer] := Module[{vals, out},
  out = state;
  out[[i, j]] = Association[out[[i, j]], "q" -> tp];
  out = MapIndexed[If[VisibleByQueen[{i, j}, #2], <|#1, "v" -> Append[#1["v"], tp]|>, #1] &, out, {2}];
  out
  ]
SolveQueen[state_, toplace_List] := 
 Module[{len = Length[toplace], next, valid, newstate},
  If[len == 0,
   Print[VisualizeState@state];
   Print[StringRiffle[StringJoin /@ Map[ToString, state[[All, All, "q"]] /. -1 -> ".", {2}], "\n"]];
   Abort[];
   ,
   next = First[toplace];
   valid = ValidSpots[state, next];
   Do[
    newstate = PlaceQueen[state, v, next];
    SolveQueen[newstate, Rest[toplace]]
    ,
    {v, valid}
    ]
   ]
  ]
GetSolution[n_Integer?Positive, m_Integer?Positive, numcol_ : 2] := 
 Module[{state, tp},
  state = ConstantArray[<|"q" -> -1, "v" -> {}|>, {n, n}];
  tp = Flatten[Transpose[ConstantArray[#, m] & /@ Range[numcol]]];
  SolveQueen[state, tp]
  ]
GetSolution[8, 4, 3](* Solves placing 3 armies of each 4 queens on an 8*8 board*)
GetSolution[5, 4, 2](* Solves placing 2 armies of each 4 queens on an 5*5 board*)

Output:

[Graphical object]
1....1..
..2....2
....3...
.3....3.
...1....
1.......
..2....2
....3...

[Graphical object]
1...1
..2..
.2.2.
..2..
1...1

Nim

Translation of: Kotlin

Almost a direct translation except for "printBoard" where we have chosen to use a sequence of sequences to simplify the code.

import sequtils, strformat

type

  Piece {.pure.} = enum Empty, Black, White
  Position = tuple[x, y: int]


func isAttacking(queen, pos: Position): bool =
  queen.x == pos.x or queen.y == pos.y or abs(queen.x - pos.x) == abs(queen.y - pos.y)


func place(m, n: int; blackQueens, whiteQueens: var seq[Position]): bool =

  if m == 0: return true

  var placingBlack = true
  for i in 0..<n:
    for j in 0..<n:

      block inner:
        let pos: Position = (i, j)
        for queen in blackQueens:
          if queen == pos or not placingBlack and queen.isAttacking(pos):
            break inner
        for queen in whiteQueens:
          if queen == pos or placingBlack and queen.isAttacking(pos):
            break inner

        if placingBlack:
          blackQueens.add pos
        else:
          whiteQueens.add pos
          if place(m - 1, n, blackQueens, whiteQueens): return true
          discard blackQueens.pop()
          discard whiteQueens.pop()
        placingBlack = not placingBlack

  if not placingBlack:
    discard blackQueens.pop()


proc printBoard(n: int; blackQueens, whiteQueens: seq[Position]) =

  var board = newSeqWith(n, newSeq[Piece](n))   # Initialized to Empty.

  for queen in blackQueens:
    board[queen.x][queen.y] = Black
  for queen in whiteQueens:
    board[queen.x][queen.y] = White

  for i in 0..<n:
    for j in 0..<n:
      stdout.write case board[i][j]
                   of Black: "B "
                   of White: "W "
                   of Empty: (if (i and 1) == (j and 1): "• " else: "◦ ")
    stdout.write '\n'

  echo ""


const Nms = [(2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3),
             (5, 1), (5, 2), (5, 3), (5, 4), (5, 5),
             (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),
             (7, 1), (7, 2), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7)]

for (n, m) in Nms:
  echo &"{m} black and {m} white queens on a {n} x {n} board:"
  var blackQueens, whiteQueens: seq[Position]
  if place(m, n, blackQueens, whiteQueens):
    printBoard(n, blackQueens, whiteQueens)
  else:
    echo "No solution exists.\n"

Output:

1 black and 1 white queens on a 2 x 2 board:
No solution exists.

1 black and 1 white queens on a 3 x 3 board:
B ◦ • 
◦ • W 
• ◦ • 

2 black and 2 white queens on a 3 x 3 board:
No solution exists.

1 black and 1 white queens on a 4 x 4 board:
B ◦ • ◦ 
◦ • W • 
• ◦ • ◦ 
◦ • ◦ • 

2 black and 2 white queens on a 4 x 4 board:
B ◦ • ◦ 
◦ • W • 
B ◦ • ◦ 
◦ • W • 

3 black and 3 white queens on a 4 x 4 board:
No solution exists.

1 black and 1 white queens on a 5 x 5 board:
B ◦ • ◦ • 
◦ • W • ◦ 
• ◦ • ◦ • 
◦ • ◦ • ◦ 
• ◦ • ◦ • 

2 black and 2 white queens on a 5 x 5 board:
B ◦ • ◦ B 
◦ • W • ◦ 
• W • ◦ • 
◦ • ◦ • ◦ 
• ◦ • ◦ • 

3 black and 3 white queens on a 5 x 5 board:
B ◦ • ◦ B 
◦ • W • ◦ 
• W • ◦ • 
◦ • ◦ B ◦ 
• W • ◦ • 

4 black and 4 white queens on a 5 x 5 board:
• B • B • 
◦ • ◦ • B 
W ◦ W ◦ • 
◦ • ◦ • B 
W ◦ W ◦ • 

5 black and 5 white queens on a 5 x 5 board:
No solution exists.

1 black and 1 white queens on a 6 x 6 board:
B ◦ • ◦ • ◦ 
◦ • W • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 

2 black and 2 white queens on a 6 x 6 board:
B ◦ • ◦ B ◦ 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 

3 black and 3 white queens on a 6 x 6 board:
B ◦ • ◦ B B 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ W ◦ • ◦ 
◦ • ◦ • ◦ • 

4 black and 4 white queens on a 6 x 6 board:
B ◦ • ◦ B B 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ B 
• ◦ W W • ◦ 
◦ • ◦ • ◦ • 

5 black and 5 white queens on a 6 x 6 board:
• B • ◦ B ◦ 
◦ • ◦ B ◦ B 
W ◦ • ◦ • ◦ 
W • W • ◦ • 
• ◦ • ◦ • B 
W • W • ◦ • 

6 black and 6 white queens on a 6 x 6 board:
No solution exists.

1 black and 1 white queens on a 7 x 7 board:
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

2 black and 2 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

3 black and 3 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

4 black and 4 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

5 black and 5 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

6 black and 6 white queens on a 7 x 7 board:
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 

7 black and 7 white queens on a 7 x 7 board:
• B • ◦ • B • 
◦ B ◦ • B • ◦ 
• B • ◦ • B • 
◦ • ◦ • B • ◦ 
W ◦ W ◦ • ◦ W 
◦ • ◦ W ◦ • ◦ 
W ◦ W W • ◦ • 

Perl

Terse

use strict;
use warnings;

my $m = shift // 4;
my $n = shift // 5;
my %seen;
my $gaps = join '|', qr/-*/, map qr/.{$_}(?:-.{$_})*/s, $n-1, $n, $n+1;
my $attack = qr/(\w)(?:$gaps)(?!\1)\w/;

place( scalar ('-' x $n . "\n") x $n );
print "No solution to $m $n\n";

sub place
  {
  local $_ = shift;
  $seen{$_}++ || /$attack/ and return; # previously or attack
  (my $have = tr/WB//) < $m * 2 or exit !print "Solution to $m $n\n\n$_";
  place( s/-\G/ qw(W B)[$have % 2] /er ) while /-/g; # place next queen
  }

Output:

Solution to 4 5

W---W
--B--
-B-B-
--B--
W---W

Verbose

A refactored version of the same code, with fancier output.

use strict;
use warnings;
use feature 'say';
use feature 'state';
use utf8;
binmode(STDOUT, ':utf8');

# recursively place the next queen
sub place {
    my($board, $n, $m, $empty_square) = @_;
    state(%seen,$attack,$solution);

    # logic of 'attack' regex: queen ( ... paths between queens containing only empty squares ... ) queen of other color
    unless ($attack) {
      $attack =
        '([WB])' .      # 1st queen
        '(?:' .
            join('|',
                "[$empty_square]*",
                map {
                    "(?^s:.{$_}(?:[$empty_square].{$_})*)"
                } $n-1, $n, $n+1
            ) .
        ')' .
        '(?!\1)[WB]';   # 2nd queen
    }

    # pass first result found back up the stack (omit this line to get last result found)
    return $solution if $solution;

    # bail out if seen this configuration previously, or attack detected
    return if $seen{$board}++ or $board =~ /$attack/;

    # success if queen count is m×2
    $solution = $board and return if $m * 2 == (my $have = $board =~ tr/WB//);

    # place the next queen (alternating colors each time)
    place(   $board =~ s/[$empty_square]\G/ qw<W B>[$have % 2] /er, $n, $m, $empty_square ) 
       while $board =~  /[$empty_square]/g;

    return $solution
}

my($m, $n) = $#ARGV == 1 ? @ARGV : (4, 5);
my $empty_square = '◦•';
my $board = join "\n", map { substr $empty_square x $n, $_%2, $n } 1..$n;

my $solution = place $board, $n, $m, $empty_square;

say $solution
    ? sprintf "Solution to $m $n\n\n%s", map { s/(.)/$1 /gm; s/B /♛/gm; s/W /♕/gmr } $solution
    : "No solution to $m $n";

Output:

Solution to 4 5

♕◦ • ◦ ♕
◦ • ♛• ◦
• ♛• ♛•
◦ • ♛• ◦
♕◦ • ◦ ♕

Phix

Translation of: Go

Translation of: Python

You can run this online here.

--
-- demo\rosetta\Queen_Armies.exw
-- =============================
--
with javascript_semantics
requires("1.0.2") -- (puts(fn,x,false) for p2js.js)
string html = ""
constant as_html = true
constant queens = {``,
                   `♛`, 
                   `<font color="green">♕</font>`,
                   `<span style="color:red">?</span>`}

procedure showboard(integer n, sequence blackqueens, whitequeens)
    sequence board = repeat(repeat('-',n),n)
    for i=1 to length(blackqueens) do
        integer {qi,qj} = blackqueens[i]
        board[qi,qj] = 'B'
        {qi,qj} = whitequeens[i]
        board[qi,qj] = 'W'
    end for
    if as_html then
        string out = sprintf("<br><b>## %d black and %d white queens on a %d-by-%d board</b><br>\n",
                             {length(blackqueens),length(whitequeens),n,n}),
               tbl = ""
        out &= "<table style=\"font-weight:bold\">\n  "
        for x=1 to n do
            for y=1 to n do
                if y=1 then tbl &= "  </tr>\n  <tr valign=\"middle\" align=\"center\">\n" end if
                integer xw = find({x,y},blackqueens)!=0,
                        xb = find({x,y},whitequeens)!=0,
                        dx = xw+xb*2+1
                string ch = queens[dx],
                       bg = iff(mod(x+y,2)?"":` bgcolor="silver"`)
                tbl &= sprintf("    <td style=\"width:14pt; height:14pt;\"%s>%s</td>\n",{bg,ch})
            end for
        end for
        out &= tbl[11..$]
        out &= "  </tr>\n</table>\n<br>\n"
        html &= out
    else
        integer b = length(blackqueens),
                w = length(whitequeens)
        printf(1,"%d black and %d white queens on a %d x %d board:\n", {b, w, n, n})
        puts(1,join(board,"\n")&"\n")
--      ?{n,blackqueens, whitequeens}
    end if
end procedure 

function isAttacking(sequence queen, pos)
    integer {qi,qj} = queen, {pi,pj} = pos
    return qi=pi or qj=pj or abs(qi-pi)=abs(qj-pj)
end function

function place(integer m, n, sequence blackqueens = {}, whitequeens = {})
    if m == 0 then showboard(n,blackqueens,whitequeens) return true end if
    bool placingBlack := true
    for i=1 to n do
        for j=1 to n do
            sequence pos := {i, j}
            for q=1 to length(blackqueens) do
                sequence queen := blackqueens[q]
                if queen == pos or ((not placingBlack) and isAttacking(queen, pos)) then
                    pos = {}
                    exit
                end if
            end for
            if pos!={} then
                for q=1 to length(whitequeens) do
                    sequence queen := whitequeens[q]
                    if queen == pos or (placingBlack and isAttacking(queen, pos)) then
                        pos = {}
                        exit
                    end if
                end for
                if pos!={} then
                    if placingBlack then
                        blackqueens = append(deep_copy(blackqueens), pos)
                        placingBlack = false
                    else
                        whitequeens = append(deep_copy(whitequeens), pos)
                        if place(m-1, n, blackqueens, whitequeens) then return true end if
                        blackqueens = blackqueens[1..$-1]
                        whitequeens = whitequeens[1..$-1]
                        placingBlack = true
                    end if
                end if
            end if
        end for
    end for
    return false
end function

for n=2 to 7 do
    for m=1 to n-(n<5) do
        if not place(m,n) then
            string no = sprintf("Cannot place %d+ queen armies on a %d-by-%d board",{m,n,n})
            if as_html then
                html &= sprintf("<b># %s</b><br><br>\n\n",{no})
            else
                printf(1,"%s.\n", {no})
            end if
        end if
    end for
end for

constant html_header = """
<!DOCTYPE html>
<html lang="en">
 <head>
  <meta charset="utf-8" />
  <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
  <title>Queen Armies</title>
 </head>
 <body>
  <h2>queen armies</h2>
""", -- or <div style="overflow:scroll; height:250px;">
         html_footer = """
 </body>
</html>
""" -- or </div>

if as_html then
    if platform()=JS then
        puts(1,html,false)
    else
        integer fn = open("queen_armies.html","w")
        puts(fn,html_header)
        puts(fn,html)
        puts(fn,html_footer)
        close(fn)
        printf(1,"See queen_armies.html\n")
    end if
end if

?"done"
{} = wait_key()

Output:

with as_html = false

Cannot place 1+ queen armies on a 2-by-2 board.
1 black and 1 white queens on a 3 x 3 board:
B--
--W
---
Cannot place 2+ queen armies on a 3-by-3 board.
<snip>
7 black and 7 white queens on a 7 x 7 board:
-B---B-
-B--B--
-B---B-
----B--
W-W---W
---W---
W-WW---

Output:

with as_html = true

# Cannot place 1+ queen armies on a 2-by-2 board

## 1 black and 1 white queens on a 3-by-3 board

♛
		♕

# Cannot place 2+ queen armies on a 3-by-3 board

<snip>

## 7 black and 7 white queens on a 7-by-7 board

	♛				♛
	♛			♛
	♛				♛
				♛
♕		♕				♕
			♕
♕		♕	♕

Python

Python: Textual output

from itertools import combinations, product, count
from functools import lru_cache, reduce


_bbullet, _wbullet = '\u2022\u25E6'
_or = set.__or__

def place(m, n):
    "Place m black and white queens, peacefully, on an n-by-n board"
    board = set(product(range(n), repeat=2))  # (x, y) tuples
    placements = {frozenset(c) for c in combinations(board, m)}
    for blacks in placements:
        black_attacks = reduce(_or, 
                               (queen_attacks_from(pos, n) for pos in blacks), 
                               set())
        for whites in {frozenset(c)     # Never on blsck attacking squares
                       for c in combinations(board - black_attacks, m)}:
            if not black_attacks & whites:
                return blacks, whites
    return set(), set()

@lru_cache(maxsize=None)
def queen_attacks_from(pos, n):
    x0, y0 = pos
    a = set([pos])    # Its position
    a.update((x, y0) for x in range(n))    # Its row
    a.update((x0, y) for y in range(n))    # Its column
    # Diagonals
    for x1 in range(n):
        # l-to-r diag
        y1 = y0 -x0 +x1
        if 0 <= y1 < n: 
            a.add((x1, y1))
        # r-to-l diag
        y1 = y0 +x0 -x1
        if 0 <= y1 < n: 
            a.add((x1, y1))
    return a

def pboard(black_white, n):
    "Print board"
    if black_white is None: 
        blk, wht = set(), set()
    else:
        blk, wht = black_white
    print(f"## {len(blk)} black and {len(wht)} white queens "
          f"on a {n}-by-{n} board:", end='')
    for x, y in product(range(n), repeat=2):
        if y == 0:
            print()
        xy = (x, y)
        ch = ('?' if xy in blk and xy in wht 
              else 'B' if xy in blk
              else 'W' if xy in wht
              else _bbullet if (x + y)%2 else _wbullet)
        print('%s' % ch, end='')
    print()

if __name__ == '__main__':
    n=2
    for n in range(2, 7):
        print()
        for m in count(1):
            ans = place(m, n)
            if ans[0]:
                pboard(ans, n)
            else:
                print (f"# Can't place {m} queens on a {n}-by-{n} board")
                break
    #
    print('\n')
    m, n = 5, 7
    ans = place(m, n)
    pboard(ans, n)

Output:

# Can't place 1 queens on a 2-by-2 board

## 1 black and 1 white queens on a 3-by-3 board:
◦•◦
B◦•
◦•W
# Can't place 2 queens on a 3-by-3 board

## 1 black and 1 white queens on a 4-by-4 board:
◦•W•
B◦•◦
◦•◦•
•◦•◦
## 2 black and 2 white queens on a 4-by-4 board:
◦B◦•
•B•◦
◦•◦•
W◦W◦
# Can't place 3 queens on a 4-by-4 board

## 1 black and 1 white queens on a 5-by-5 board:
◦•◦•◦
W◦•◦•
◦•◦•◦
•◦•◦B
◦•◦•◦
## 2 black and 2 white queens on a 5-by-5 board:
◦•◦•W
•◦B◦•
◦•◦•◦
•◦•B•
◦W◦•◦
## 3 black and 3 white queens on a 5-by-5 board:
◦W◦•◦
•◦•◦W
B•B•◦
B◦•◦•
◦•◦W◦
## 4 black and 4 white queens on a 5-by-5 board:
◦•B•B
W◦•◦•
◦W◦W◦
W◦•◦•
◦•B•B
# Can't place 5 queens on a 5-by-5 board

## 1 black and 1 white queens on a 6-by-6 board:
◦•◦•◦•
W◦•◦•◦
◦•◦•◦•
•◦•◦B◦
◦•◦•◦•
•◦•◦•◦
## 2 black and 2 white queens on a 6-by-6 board:
◦•◦•◦•
•◦B◦•◦
◦•◦•◦•
•◦•B•◦
◦•◦•◦•
W◦•◦W◦
## 3 black and 3 white queens on a 6-by-6 board:
◦•B•◦•
•B•◦•◦
◦•◦W◦W
•◦•◦•◦
W•◦•◦•
•◦•◦B◦
## 4 black and 4 white queens on a 6-by-6 board:
WW◦•W•
•W•◦•◦
◦•◦•◦B
•◦B◦•◦
◦•◦B◦•
•◦•B•◦
## 5 black and 5 white queens on a 6-by-6 board:
◦•W•W•
B◦•◦•◦
◦•W•◦W
B◦•◦•◦
◦•◦•◦W
BB•B•◦
# Can't place 6 queens on a 6-by-6 board


## 5 black and 5 white queens on a 7-by-7 board:
◦•◦•B•◦
•W•◦•◦W
◦•◦•B•◦
B◦•◦•◦•
◦•B•◦•◦
•◦•B•◦•
◦W◦•◦WW

Python: HTML output

Uses the solver function place from the above textual output case.

from peaceful_queen_armies_simpler import place
from itertools import product, count

_bqueenh, _wqueenh = '&#x265b;', '<font color="green">&#x2655;</font>'

def hboard(black_white, n):
    "HTML board generator"
    if black_white is None: 
        blk, wht = set(), set()
    else:
        blk, wht = black_white
    out = (f"<br><b>## {len(blk)} black and {len(wht)} white queens "
           f"on a {n}-by-{n} board</b><br>\n")
    out += '<table style="font-weight:bold">\n  '
    tbl = ''
    for x, y in product(range(n), repeat=2):
        if y == 0:
            tbl += '  </tr>\n  <tr valign="middle" align="center">\n'
        xy = (x, y)
        ch = ('<span style="color:red">?</span>' if xy in blk and xy in wht 
              else _bqueenh if xy in blk
              else _wqueenh if xy in wht
              else "")
        bg = "" if (x + y)%2 else ' bgcolor="silver"'
        tbl += f'    <td style="width:14pt; height:14pt;"{bg}>{ch}</td>\n'
    out += tbl[7:]
    out += '  </tr>\n</table>\n<br>\n'
    return out

if __name__ == '__main__':
    n=2
    html = ''
    for n in range(2, 7):
        print()
        for m in count(1):
            ans = place(m, n)
            if ans[0]:
                html += hboard(ans, n)
            else:
                html += (f"<b># Can't place {m} queen armies on a "
                         f"{n}-by-{n} board</b><br><br>\n\n" )
                break
    #
    html += '<br>\n'
    m, n = 6, 7
    ans = place(m, n)
    html += hboard(ans, n)
    with open('peaceful_queen_armies.htm', 'w') as f:
        f.write(html)

Output:

# Can't place 1 queen armies on a 2-by-2 board

## 1 black and 1 white queens on a 3-by-3 board

♛
		♕

# Can't place 2 queen armies on a 3-by-3 board

## 1 black and 1 white queens on a 4-by-4 board

		♕
♛

## 2 black and 2 white queens on a 4-by-4 board

	♛
	♛
♕		♕

# Can't place 3 queen armies on a 4-by-4 board

## 1 black and 1 white queens on a 5-by-5 board

♕
				♛

## 2 black and 2 white queens on a 5-by-5 board

				♕
		♛
			♛
	♕

## 3 black and 3 white queens on a 5-by-5 board

	♕
				♕
♛		♛
♛
			♕

## 4 black and 4 white queens on a 5-by-5 board

		♛		♛
♕
	♕		♕
♕
		♛		♛

# Can't place 5 queen armies on a 5-by-5 board

## 1 black and 1 white queens on a 6-by-6 board

♕
				♛

## 2 black and 2 white queens on a 6-by-6 board

		♛
			♛
♕				♕

## 3 black and 3 white queens on a 6-by-6 board

		♛
	♛
			♕		♕
♕
				♛

## 4 black and 4 white queens on a 6-by-6 board

♕	♕			♕
	♕
					♛
		♛
			♛
			♛

## 5 black and 5 white queens on a 6-by-6 board

		♕		♕
♛
		♕			♕
♛
					♕
♛	♛		♛

# Can't place 6 queen armies on a 6-by-6 board

## 6 black and 6 white queens on a 7-by-7 board

		♛		♛
						♕
	♕		♕		♕
						♕
		♛		♛
						♕
♛				♛

Raku

(formerly Perl 6)

Translation of: Perl

# recursively place the next queen
sub place ($board, $n, $m, $empty-square) {
    my $cnt;
    state (%seen,$attack);
    state $solution = False;

    # logic of regex: queen ( ... paths between queens containing only empty squares ... ) queen of other color
    once {
      my %Q = 'WBBW'.comb; # return the queen of alternate color
      my $re =
        '(<[WB]>)' ~                # 1st queen
        '[' ~
          join(' |',
            qq/<[$empty-square]>*/,
            map {
              qq/ . ** {$_}[<[$empty-square]> . ** {$_}]*/
            }, $n-1, $n, $n+1
          ) ~
        ']' ~
        '<{%Q{$0}}>';               # 2nd queen
      $attack = "rx/$re/".EVAL;
    }

    # return first result found (omit this line to get last result found)
    return $solution if $solution;

    # bail out if seen this configuration previously, or attack detected
    return if %seen{$board}++ or $board ~~ $attack;

    # success if queen count is m×2, set state variable and return from recursion
    $solution = $board and return if $m * 2 == my $queens = $board.comb.Bag{<W B>}.sum;

    # place the next queen (alternating colors each time)
    place( $board.subst( /<[◦•]>/, {<W B>[$queens % 2]}, :nth($cnt) ), $n, $m, $empty-square )
        while $board ~~ m:nth(++$cnt)/<[◦•]>/;

    return $solution
}

my ($m, $n) = @*ARGS == 2 ?? @*ARGS !! (4, 5);
my $empty-square = '◦•';
my $board = ($empty-square x $n**2).comb.rotor($n)>>.join[^$n].join: "\n";

my $solution = place $board, $n, $m, $empty-square;

say $solution
    ?? "Solution to $m $n\n\n{S:g/(\N)/$0 / with $solution}"
    !! "No solution to $m $n";

Output:

W • ◦ • W
• ◦ B ◦ •
◦ B ◦ B ◦
• ◦ B ◦ •
W • ◦ • W

Ruby

Translation of: Java

class Position
    attr_reader :x, :y

    def initialize(x, y)
        @x = x
        @y = y
    end

    def ==(other)
        self.x == other.x &&
        self.y == other.y
    end

    def to_s
        '(%d, %d)' % [@x, @y]
    end

    def to_str
        to_s
    end
end

def isAttacking(queen, pos)
    return queen.x == pos.x ||
           queen.y == pos.y ||
           (queen.x - pos.x).abs() == (queen.y - pos.y).abs()
end

def place(m, n, blackQueens, whiteQueens)
    if m == 0 then
        return true
    end
    placingBlack = true
    for i in 0 .. n-1
        for j in 0 .. n-1
            catch :inner do
                pos = Position.new(i, j)
                for queen in blackQueens
                    if pos == queen || !placingBlack && isAttacking(queen, pos) then
                        throw :inner
                    end
                end
                for queen in whiteQueens
                    if pos == queen || placingBlack && isAttacking(queen, pos) then
                        throw :inner
                    end
                end
                if placingBlack then
                    blackQueens << pos
                    placingBlack = false
                else
                    whiteQueens << pos
                    if place(m - 1, n, blackQueens, whiteQueens) then
                        return true
                    end
                    blackQueens.pop
                    whiteQueens.pop
                    placingBlack = true
                end
            end
        end
    end
    if !placingBlack then
        blackQueens.pop
    end
    return false
end

def printBoard(n, blackQueens, whiteQueens)
    # initialize the board
    board = Array.new(n) { Array.new(n) { ' ' } }
    for i in 0 .. n-1
        for j in 0 .. n-1
            if i % 2 == j % 2 then
                board[i][j] = '•'
            else
                board[i][j] = '◦'
            end
        end
    end

    # insert the queens
    for queen in blackQueens
        board[queen.y][queen.x] = 'B'
    end
    for queen in whiteQueens
        board[queen.y][queen.x] = 'W'
    end

    # print the board
    for row in board
        for cell in row
            print cell, ' '
        end
        print "\n"
    end
    print "\n"
end

nms = [
    [2, 1],
    [3, 1], [3, 2],
    [4, 1], [4, 2], [4, 3],
    [5, 1], [5, 2], [5, 3], [5, 4], [5, 5],
    [6, 1], [6, 2], [6, 3], [6, 4], [6, 5], [6, 6],
    [7, 1], [7, 2], [7, 3], [7, 4], [7, 5], [7, 6], [7, 7]
]
for nm in nms
    m = nm[1]
    n = nm[0]
    print "%d black and %d white queens on a %d x %d board:\n" % [m, m, n, n]

    blackQueens = []
    whiteQueens = []
    if place(m, n, blackQueens, whiteQueens) then
        printBoard(n, blackQueens, whiteQueens)
    else
        print "No solution exists.\n\n"
    end
end

Output:

1 black and 1 white queens on a 2 x 2 board:
No solution exists.

1 black and 1 white queens on a 3 x 3 board:
B ◦ •
◦ • ◦
• W •

2 black and 2 white queens on a 3 x 3 board:
No solution exists.

1 black and 1 white queens on a 4 x 4 board:
B ◦ • ◦
◦ • ◦ •
• W • ◦
◦ • ◦ •

2 black and 2 white queens on a 4 x 4 board:
B ◦ B ◦
◦ • ◦ •
• W • W
◦ • ◦ •

3 black and 3 white queens on a 4 x 4 board:
No solution exists.

1 black and 1 white queens on a 5 x 5 board:
B ◦ • ◦ •
◦ • ◦ • ◦ 
• W • ◦ •
◦ • ◦ • ◦
• ◦ • ◦ •

2 black and 2 white queens on a 5 x 5 board:
B ◦ • ◦ •
◦ • W • ◦
• W • ◦ •
◦ • ◦ • ◦
B ◦ • ◦ •

3 black and 3 white queens on a 5 x 5 board:
B ◦ • ◦ •
◦ • W • W
• W • ◦ •
◦ • ◦ B ◦
B ◦ • ◦ •

4 black and 4 white queens on a 5 x 5 board:
• ◦ W ◦ W 
B • ◦ • ◦
• ◦ W ◦ W
B • ◦ • ◦
• B • B •

5 black and 5 white queens on a 5 x 5 board:
No solution exists.

1 black and 1 white queens on a 6 x 6 board:
B ◦ • ◦ • ◦
◦ • ◦ • ◦ •
• W • ◦ • ◦
◦ • ◦ • ◦ •
• ◦ • ◦ • ◦
◦ • ◦ • ◦ •

2 black and 2 white queens on a 6 x 6 board:
B ◦ • ◦ • ◦
◦ • W • ◦ •
• W • ◦ • ◦ 
◦ • ◦ • ◦ •
B ◦ • ◦ • ◦
◦ • ◦ • ◦ •

3 black and 3 white queens on a 6 x 6 board:
B ◦ • ◦ • ◦
◦ • W • ◦ •
• W • ◦ W ◦
◦ • ◦ • ◦ •
B ◦ • ◦ • ◦
B • ◦ • ◦ •

4 black and 4 white queens on a 6 x 6 board:
B ◦ • ◦ • ◦
◦ • W • ◦ •
• W • ◦ W ◦
◦ • ◦ • W •
B ◦ • ◦ • ◦
B • ◦ B ◦ •

5 black and 5 white queens on a 6 x 6 board:
• ◦ W W • W 
B • ◦ • ◦ •
• ◦ • W • W
◦ B ◦ • ◦ •
B ◦ • ◦ • ◦
◦ B ◦ • B •

6 black and 6 white queens on a 6 x 6 board:
No solution exists.

1 black and 1 white queens on a 7 x 7 board:
B ◦ • ◦ • ◦ •
◦ • ◦ • ◦ • ◦
• W • ◦ • ◦ •
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ •
◦ • ◦ • ◦ • ◦
• ◦ • ◦ • ◦ •

2 black and 2 white queens on a 7 x 7 board:
B ◦ • ◦ • ◦ •
◦ • ◦ • ◦ • ◦
• W • ◦ • ◦ •
◦ • ◦ • ◦ • ◦
B ◦ • ◦ • ◦ •
◦ • ◦ • ◦ • ◦
• W • ◦ • ◦ •

3 black and 3 white queens on a 7 x 7 board:
B ◦ B ◦ • ◦ •
◦ • ◦ • ◦ • ◦
• W • W • ◦ •
◦ • ◦ • ◦ • ◦
B ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦
• W • ◦ • ◦ •

4 black and 4 white queens on a 7 x 7 board:
B ◦ B ◦ • ◦ •
◦ • ◦ • ◦ • ◦
• W • W • ◦ •
◦ • ◦ • ◦ • ◦
B ◦ B ◦ • ◦ •
◦ • ◦ • ◦ • ◦
• W • W • ◦ •

5 black and 5 white queens on a 7 x 7 board:
B ◦ B ◦ B ◦ •
◦ • ◦ • ◦ • ◦
• W • W • W • 
◦ • ◦ • ◦ • ◦
B ◦ B ◦ • ◦ •
◦ • ◦ • ◦ • ◦
• W • W • ◦ •

6 black and 6 white queens on a 7 x 7 board:
B ◦ B ◦ B ◦ •
◦ • ◦ • ◦ • ◦
• W • W • W •
◦ • ◦ • ◦ • ◦
B ◦ B ◦ B ◦ •
◦ • ◦ • ◦ • ◦
• W • W • W •

7 black and 7 white queens on a 7 x 7 board:
• ◦ • ◦ W ◦ W 
B B B • ◦ • ◦
• ◦ • ◦ W ◦ W
◦ • ◦ • ◦ W W
• B • B • ◦ •
B • B • ◦ • ◦
• ◦ • ◦ W ◦ •

Scheme

All solutions

Works with: CHICKEN version 5.3.0

Library: srfi-132

;;;
;;; Solutions to the Peaceful Chess Queen Armies puzzle, in R7RS
;;; Scheme (using also SRFI-132).
;;;
;;; https://rosettacode.org/wiki/Peaceful_chess_queen_armies
;;;

(cond-expand
  (r7rs)
  (chicken (import (r7rs))))

(import (scheme process-context))
(import (only (srfi 132) list-sort))

(define-record-type <&fail>
  (make-the-one-unique-&fail-that-you-must-not-make-twice)
  do-not-use-this:&fail?)

(define &fail
  (make-the-one-unique-&fail-that-you-must-not-make-twice))

(define (failure? f)
  (eq? f &fail))

(define (success? f)
  (not (failure? f)))

(define *suspend*
  (make-parameter (lambda (x) x)))

(define (suspend v)
  ((*suspend*) v))

(define (fail-forever)
  (let loop ()
    (suspend &fail)
    (loop)))

(define (make-generator-procedure thunk)
  ;;
  ;; Make a suspendable procedure that takes no arguments. It is a
  ;; simple generator of values. (One can elaborate on this to have
  ;; the procedure accept an argument upon resumption, like an Icon
  ;; co-expression.)
  ;;
  (define (next-run return)
    (define (my-suspend v)
      (set! return
        (call/cc
         (lambda (resumption-point)
           (set! next-run resumption-point)
           (return v)))))
    (parameterize ((*suspend* my-suspend))
      (suspend (thunk))
      (fail-forever)))
  (lambda ()
    (call/cc next-run)))

(define BLACK 'B)
(define WHITE 'W)

(define (flip-color c)
  (if (eq? c BLACK) WHITE BLACK))

(define-record-type <queen>
  (make-queen color rank file)
  queen?
  (color queen-color)
  (rank queen-rank)
  (file queen-file))

(define (serialize-queen queen)
  (string-append (if (eq? (queen-color queen) BLACK) "B" "W")
                 "(" (number->string (queen-rank queen))
                 "," (number->string (queen-file queen)) ")"))

(define (serialize-queens queens)
  (apply string-append
         (list-sort string<? (map serialize-queen queens))))

(define (queens->string n queens)

  (define board
    (let ((board (make-vector (* n n) #f)))
      (do ((q queens (cdr q)))
          ((null? q))
        (let* ((color (queen-color (car q)))
               (i (queen-rank (car q)))
               (j (queen-file (car q))))
          (vector-set! board (ij->index n i j) color)))
      board))

  (define rule
    (let ((str "+"))
      (do ((j 1 (+ j 1)))
          ((= j (+ n 1)))
        (set! str (string-append str "----+")))
      str))

  (define str "")

  (when (< 0 n)
    (set! str rule)
    (do ((i n (- i 1)))
        ((= i 0))
      (set! str (string-append str "\n"))
      (do ((j 1 (+ j 1)))
          ((= j (+ n 1)))
        (let* ((color (vector-ref board (ij->index n i j)))
               (representation
                (cond ((eq? color #f) "    ")
                      ((eq? color BLACK) "  B ")
                      ((eq? color WHITE) "  W ")
                      (else " ?? "))))
          (set! str (string-append str "|" representation))))
      (set! str (string-append str "|\n" rule))))
  str)

(define (queen-fits-in? queen other-queens)
  (or (null? other-queens)
      (let ((other (car other-queens)))
        (let ((colorq (queen-color queen))
              (rankq (queen-rank queen))
              (fileq (queen-file queen))
              (coloro (queen-color other))
              (ranko (queen-rank other))
              (fileo (queen-file other)))
          (if (eq? colorq coloro)
              (and (or (not (= rankq ranko))
                       (not (= fileq fileo)))
                   (queen-fits-in? queen (cdr other-queens)))
              (and (not (= rankq ranko))
                   (not (= fileq fileo))
                   (not (= (+ rankq fileq) (+ ranko fileo)))
                   (not (= (- rankq fileq) (- ranko fileo)))
                   (queen-fits-in? queen (cdr other-queens))))))))

(define (latest-queen-fits-in? queens)
  (or (null? (cdr queens))
      (queen-fits-in? (car queens) (cdr queens))))

(define (make-peaceful-queens-generator m n)
  (make-generator-procedure
   (lambda ()
     (define solutions '())

     (let loop ((queens (list (make-queen BLACK 1 1)))
                (num-queens 1))

       (define (add-another-queen)
         (let ((color (flip-color (queen-color (car queens)))))
           (loop (cons (make-queen color 1 1) queens)
                 (+ num-queens 1))))

       (define (move-a-queen)
         (let drop-one ((queens queens)
                        (num-queens num-queens))
           (if (zero? num-queens)
               (loop '() 0)
               (let* ((latest (car queens))
                      (color (queen-color latest))
                      (rank (queen-rank latest))
                      (file (queen-file latest)))
                 (if (and (= rank n) (= file n))
                     (drop-one (cdr queens) (- num-queens 1))
                     (let-values (((rank^ file^)
                                   (advance-ij n rank file)))
                       (loop (cons (make-queen color rank^ file^)
                                   (cdr queens))
                             num-queens)))))))

       (cond ((zero? num-queens)
              ;; There are no more solutions.
              &fail)

             ((latest-queen-fits-in? queens)
              (if (= num-queens (* 2 m))
                  (let ((str (serialize-queens queens)))
                    ;; The current "queens" is a solution.
                    (unless (member str solutions)
                      ;; The current "queens" is a *new* solution.
                      (set! solutions (cons str solutions))
                      (suspend queens))
                    (move-a-queen))
                  (add-another-queen)))

             (else
              (move-a-queen)))))))

(define (ij->index n i j)
  (let ((i1 (- i 1))
        (j1 (- j 1)))
    (+ i1 (* n j1))))

(define (index->ij n index)
  (let-values (((q r) (floor/ index n)))
    (values (+ r 1) (+ q 1))))

(define (advance-ij n i j)
  (index->ij n (+ (ij->index n i j) 1)))

(define args (command-line))
(unless (or (= (length args) 3)
            (= (length args) 4))
  (display "Usage: ")
  (display (list-ref args 0))
  (display " M N [MAX_SOLUTIONS]")
  (newline)
  (exit 1))
(define m (string->number (list-ref args 1)))
(define n (string->number (list-ref args 2)))
(define max-solutions
  (if (= (length args) 4)
      (string->number (list-ref args 3))
      +inf.0))

(define generate-peaceful-queens
  (make-peaceful-queens-generator m n))

(let loop ((next-solution-number 1))
  (when (<= next-solution-number max-solutions)
    (let ((solution (generate-peaceful-queens)))
      (when (success? solution)
        (display "Solution ")
        (display next-solution-number)
        (newline)
        (display (queens->string n solution))
        (newline)
        (newline)
        (loop (+ next-solution-number 1))))))

Output:

$ csc -O3 peaceful_queens.scm && ./peaceful_queens 4 5

Solution 1
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+

Solution 2
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+

Solution 3
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+

Solution 4
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+

Solution 5
+----+----+----+----+----+
|    |  B |    |  B |    |
+----+----+----+----+----+
|  B |    |    |    |    |
+----+----+----+----+----+
|    |    |  W |    |  W |
+----+----+----+----+----+
|  B |    |    |    |    |
+----+----+----+----+----+
|    |    |  W |    |  W |
+----+----+----+----+----+

Solution 6
+----+----+----+----+----+
|    |    |  W |    |  W |
+----+----+----+----+----+
|  B |    |    |    |    |
+----+----+----+----+----+
|    |  B |    |  B |    |
+----+----+----+----+----+
|  B |    |    |    |    |
+----+----+----+----+----+
|    |    |  W |    |  W |
+----+----+----+----+----+

Solution 7
+----+----+----+----+----+
|    |    |  W |    |  W |
+----+----+----+----+----+
|  B |    |    |    |    |
+----+----+----+----+----+
|    |    |  W |    |  W |
+----+----+----+----+----+
|  B |    |    |    |    |
+----+----+----+----+----+
|    |  B |    |  B |    |
+----+----+----+----+----+

Solution 8
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+

Solution 9
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+

Solution 10
+----+----+----+----+----+
|  W |    |    |    |  W |
+----+----+----+----+----+
|    |    |  B |    |    |
+----+----+----+----+----+
|  W |    |    |    |  W |
+----+----+----+----+----+
|    |    |  B |    |    |
+----+----+----+----+----+
|    |  B |    |  B |    |
+----+----+----+----+----+

Solution 11
+----+----+----+----+----+
|  W |    |  W |    |    |
+----+----+----+----+----+
|    |    |    |    |  B |
+----+----+----+----+----+
|  W |    |  W |    |    |
+----+----+----+----+----+
|    |    |    |    |  B |
+----+----+----+----+----+
|    |  B |    |  B |    |
+----+----+----+----+----+

Solution 12
+----+----+----+----+----+
|  W |    |    |    |  W |
+----+----+----+----+----+
|    |    |  B |    |    |
+----+----+----+----+----+
|    |  B |    |  B |    |
+----+----+----+----+----+
|    |    |  B |    |    |
+----+----+----+----+----+
|  W |    |    |    |  W |
+----+----+----+----+----+

Solution 13
+----+----+----+----+----+
|  W |    |  W |    |    |
+----+----+----+----+----+
|    |    |    |    |  B |
+----+----+----+----+----+
|    |  B |    |  B |    |
+----+----+----+----+----+
|    |    |    |    |  B |
+----+----+----+----+----+
|  W |    |  W |    |    |
+----+----+----+----+----+

Solution 14
+----+----+----+----+----+
|    |  B |    |  B |    |
+----+----+----+----+----+
|    |    |  B |    |    |
+----+----+----+----+----+
|  W |    |    |    |  W |
+----+----+----+----+----+
|    |    |  B |    |    |
+----+----+----+----+----+
|  W |    |    |    |  W |
+----+----+----+----+----+

Solution 15
+----+----+----+----+----+
|    |  B |    |  B |    |
+----+----+----+----+----+
|    |    |    |    |  B |
+----+----+----+----+----+
|  W |    |  W |    |    |
+----+----+----+----+----+
|    |    |    |    |  B |
+----+----+----+----+----+
|  W |    |  W |    |    |
+----+----+----+----+----+

Solution 16
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|  W |    |    |    |    |
+----+----+----+----+----+
|    |    |  B |    |  B |
+----+----+----+----+----+
|  W |    |    |    |    |
+----+----+----+----+----+
|    |    |  B |    |  B |
+----+----+----+----+----+

Solution 17
+----+----+----+----+----+
|    |    |  B |    |  B |
+----+----+----+----+----+
|  W |    |    |    |    |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|  W |    |    |    |    |
+----+----+----+----+----+
|    |    |  B |    |  B |
+----+----+----+----+----+

Solution 18
+----+----+----+----+----+
|    |    |  B |    |  B |
+----+----+----+----+----+
|  W |    |    |    |    |
+----+----+----+----+----+
|    |    |  B |    |  B |
+----+----+----+----+----+
|  W |    |    |    |    |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+

All non-equivalent solutions

Works with: CHICKEN version 5.3.0

;;;
;;; Solutions to the Peaceful Chess Queen Armies puzzle, in R7RS
;;; Scheme. This implementation returns only one of each equivalent
;;; solution. See https://oeis.org/A260680
;;;
;;; I weed out equivalent solutions by comparing them tediously
;;; against solutions already found.
;;;
;;; (At least when compiled with CHICKEN 5.3.0, this program gets kind
;;; of slow for m=5, n=6, once you get past having found the 35
;;; non-equivalent solutions. There are still other, equivalent
;;; solutions to eliminate.)
;;;
;;; https://rosettacode.org/wiki/Peaceful_chess_queen_armies
;;;

(cond-expand
  (r7rs)
  (chicken (import (r7rs))))

(import (scheme process-context))

(define-record-type <&fail>
  (make-the-one-unique-&fail-that-you-must-not-make-twice)
  do-not-use-this:&fail?)

(define &fail
  (make-the-one-unique-&fail-that-you-must-not-make-twice))

(define (failure? f)
  (eq? f &fail))

(define (success? f)
  (not (failure? f)))

(define *suspend*
  (make-parameter (lambda (x) x)))

(define (suspend v)
  ((*suspend*) v))

(define (fail-forever)
  (let loop ()
    (suspend &fail)
    (loop)))

(define (make-generator-procedure thunk)
  ;;
  ;; Make a suspendable procedure that takes no arguments. It is a
  ;; simple generator of values. (One can elaborate on this to have
  ;; the procedure accept an argument upon resumption, like an Icon
  ;; co-expression.)
  ;;
  (define (next-run return)
    (define (my-suspend v)
      (set! return
        (call/cc
         (lambda (resumption-point)
           (set! next-run resumption-point)
           (return v)))))
    (parameterize ((*suspend* my-suspend))
      (suspend (thunk))
      (fail-forever)))
  (lambda ()
    (call/cc next-run)))

(define (isqrt m)
  ;; Integer Newton’s method. See
  ;; https://en.wikipedia.org/w/index.php?title=Integer_square_root&oldid=1074473475#Using_only_integer_division
  (let ((k (truncate-quotient m 2)))
    (if (zero? k)
        m
        (let loop ((k k)
                   (k^ (truncate-quotient
                        (+ k (truncate-quotient m k)) 2)))
          (if (< k^ k)
              (loop k^ (truncate-quotient
                        (+ k^ (truncate-quotient m k^)) 2))
              k)))))

(define (ij->index n i j)
  (let ((i1 (- i 1))
        (j1 (- j 1)))
    (+ i1 (* n j1))))

(define (index->ij n index)
  (let-values (((q r) (floor/ index n)))
    (values (+ r 1) (+ q 1))))

(define (advance-ij n i j)
  (index->ij n (+ (ij->index n i j) 1)))

(define (index-rotate90 n index)
  (let-values (((i j) (index->ij n index)))
    (ij->index n (- n j -1) i)))

(define (index-rotate180 n index)
  (let-values (((i j) (index->ij n index)))
    (ij->index n (- n i -1) (- n j -1))))

(define (index-rotate270 n index)
  (let-values (((i j) (index->ij n index)))
    (ij->index n j (- n i -1))))

(define (index-reflecti n index)
  (let-values (((i j) (index->ij n index)))
    (ij->index n (- n i -1) j)))

(define (index-reflectj n index)
  (let-values (((i j) (index->ij n index)))
    (ij->index n i (- n j -1))))

(define (index-reflect-diag-down n index)
  (let-values (((i j) (index->ij n index)))
    (ij->index n j i)))

(define (index-reflect-diag-up n index)
  (let-values (((i j) (index->ij n index)))
    (ij->index n (- n j -1) (- n i -1))))

(define BLACK 'B)
(define WHITE 'W)

(define (reverse-color c)
  (cond ((eq? c WHITE) BLACK)
        ((eq? c BLACK) WHITE)
        (else c)))

(define (pick-color-adjuster c)
  (if (eq? c WHITE)
      reverse-color
      (lambda (x) x)))

(define-record-type <queen>
  (make-queen color rank file)
  queen?
  (color queen-color)
  (rank queen-rank)
  (file queen-file))

(define (queens->board queens)
  (let ((board (make-vector (* n n) #f)))
    (do ((q queens (cdr q)))
        ((null? q))
      (let* ((color (queen-color (car q)))
             (i (queen-rank (car q)))
             (j (queen-file (car q))))
        (vector-set! board (ij->index n i j) color)))
    board))

(define-syntax board-partial-equiv?
  (syntax-rules ()
    ((_ board1 board2 n*n n reindex recolor)
     (let loop ((i 0))
       (or (= i n*n)
           (let ((color1 (vector-ref board1 i))
                 (color2 (recolor (vector-ref board2 (reindex n i)))))
             (and (eq? color1 color2)
                  (loop (+ i 1)))))))))

(define (board-equiv? board1 board2)
  (define (identity x) x)
  (define (2nd-argument n i) i)
  (let ((n*n (vector-length board1)))
    (or (board-partial-equiv? board1 board2 n*n #f
                              2nd-argument identity)
        (board-partial-equiv? board1 board2 n*n #f
                              2nd-argument reverse-color)
        (let ((n (isqrt n*n)))
          (or (board-partial-equiv? board1 board2 n*n n
                                    index-rotate90
                                    identity)
              (board-partial-equiv? board1 board2 n*n n
                                    index-rotate90
                                    reverse-color)
              (board-partial-equiv? board1 board2 n*n n
                                    index-rotate180
                                    identity)
              (board-partial-equiv? board1 board2 n*n n
                                    index-rotate180
                                    reverse-color)
              (board-partial-equiv? board1 board2 n*n n
                                    index-rotate270
                                    identity)
              (board-partial-equiv? board1 board2 n*n n
                                    index-rotate270
                                    reverse-color)
              (board-partial-equiv? board1 board2 n*n n
                                    index-reflecti
                                    identity)
              (board-partial-equiv? board1 board2 n*n n
                                    index-reflecti
                                    reverse-color)
              (board-partial-equiv? board1 board2 n*n n
                                    index-reflectj
                                    identity)
              (board-partial-equiv? board1 board2 n*n n
                                    index-reflectj
                                    reverse-color)
              (board-partial-equiv? board1 board2 n*n n
                                    index-reflect-diag-down
                                    identity)
              (board-partial-equiv? board1 board2 n*n n
                                    index-reflect-diag-down
                                    reverse-color)
              (board-partial-equiv? board1 board2 n*n n
                                    index-reflect-diag-up
                                    identity)
              (board-partial-equiv? board1 board2 n*n n
                                    index-reflect-diag-up
                                    reverse-color) )))))

(define (queens->string n queens)

  (define board (queens->board queens))

  (define rule
    (let ((str "+"))
      (do ((j 1 (+ j 1)))
          ((= j (+ n 1)))
        (set! str (string-append str "----+")))
      str))

  (define str "")

  (when (< 0 n)
    (set! str rule)
    (do ((i n (- i 1)))
        ((= i 0))
      (set! str (string-append str "\n"))
      (do ((j 1 (+ j 1)))
          ((= j (+ n 1)))
        (let* ((color (vector-ref board (ij->index n i j)))
               (representation
                (cond ((eq? color #f) "    ")
                      ((eq? color BLACK) "  B ")
                      ((eq? color WHITE) "  W ")
                      (else " ?? "))))
          (set! str (string-append str "|" representation))))
      (set! str (string-append str "|\n" rule))))
  str)

(define (queen-fits-in? queen other-queens)
  (or (null? other-queens)
      (let ((other (car other-queens)))
        (let ((colorq (queen-color queen))
              (rankq (queen-rank queen))
              (fileq (queen-file queen))
              (coloro (queen-color other))
              (ranko (queen-rank other))
              (fileo (queen-file other)))
          (if (eq? colorq coloro)
              (and (or (not (= rankq ranko))
                       (not (= fileq fileo)))
                   (queen-fits-in? queen (cdr other-queens)))
              (and (not (= rankq ranko))
                   (not (= fileq fileo))
                   (not (= (+ rankq fileq) (+ ranko fileo)))
                   (not (= (- rankq fileq) (- ranko fileo)))
                   (queen-fits-in? queen (cdr other-queens))))))))

(define (latest-queen-fits-in? queens)
  (or (null? (cdr queens))
      (queen-fits-in? (car queens) (cdr queens))))

(define (make-peaceful-queens-generator m n)
  (make-generator-procedure
   (lambda ()
     (define solutions '())

     (let loop ((queens (list (make-queen BLACK 1 1)))
                (num-queens 1))

       (define (add-another-queen)
         (let ((color (reverse-color (queen-color (car queens)))))
           (loop (cons (make-queen color 1 1) queens)
                 (+ num-queens 1))))

       (define (move-a-queen)
         (let drop-one ((queens queens)
                        (num-queens num-queens))
           (if (zero? num-queens)
               (loop '() 0)
               (let* ((latest (car queens))
                      (color (queen-color latest))
                      (rank (queen-rank latest))
                      (file (queen-file latest)))
                 (if (and (= rank n) (= file n))
                     (drop-one (cdr queens) (- num-queens 1))
                     (let-values (((rank^ file^)
                                   (advance-ij n rank file)))
                       (loop (cons (make-queen color rank^ file^)
                                   (cdr queens))
                             num-queens)))))))

       (cond ((zero? num-queens)
              ;; There are no more solutions.
              &fail)

             ((latest-queen-fits-in? queens)
              (if (= num-queens (* 2 m))
                  (let ((board (queens->board queens)))
                    ;; The current "queens" is a solution.
                    (unless (member board solutions board-equiv?)
                      ;; The current "queens" is a *new* solution.
                      (set! solutions (cons board solutions))
                      (suspend queens))
                    (move-a-queen))
                  (add-another-queen)))

             (else
              (move-a-queen)))))))

(define args (command-line))
(unless (or (= (length args) 3)
            (= (length args) 4))
  (display "Usage: ")
  (display (list-ref args 0))
  (display " M N [MAX_SOLUTIONS]")
  (newline)
  (exit 1))
(define m (string->number (list-ref args 1)))
(define n (string->number (list-ref args 2)))
(define max-solutions
  (if (= (length args) 4)
      (string->number (list-ref args 3))
      +inf.0))

(define generate-peaceful-queens
  (make-peaceful-queens-generator m n))

(let loop ((next-solution-number 1))
  (when (<= next-solution-number max-solutions)
    (let ((solution (generate-peaceful-queens)))
      (when (success? solution)
        (display "Solution ")
        (display next-solution-number)
        (newline)
        (display (queens->string n solution))
        (newline)
        (newline)
        (loop (+ next-solution-number 1))))))

Output:

$ csc -O5 peaceful_queens2.scm && ./peaceful_queens2 4 5

Solution 1
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|    |    |  W |    |    |
+----+----+----+----+----+
|  B |    |    |    |  B |
+----+----+----+----+----+

Solution 2
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+

Solution 3
+----+----+----+----+----+
|    |  W |    |  W |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+
|    |    |    |    |  W |
+----+----+----+----+----+
|  B |    |  B |    |    |
+----+----+----+----+----+

Swift

Translation of: Kotlin

enum Piece {
  case empty, black, white
}

typealias Position = (Int, Int)

func place(_ m: Int, _ n: Int, pBlackQueens: inout [Position], pWhiteQueens: inout [Position]) -> Bool {
  guard m != 0 else {
    return true
  }

  var placingBlack = true

  for i in 0..<n {
    inner: for j in 0..<n {
      let pos = (i, j)

      for queen in pBlackQueens where queen == pos || !placingBlack && isAttacking(queen, pos) {
        continue inner
      }

      for queen in pWhiteQueens where queen == pos || placingBlack && isAttacking(queen, pos) {
        continue inner
      }

      if placingBlack {
        pBlackQueens.append(pos)
        placingBlack = false
      } else {
        placingBlack = true

        pWhiteQueens.append(pos)

        if place(m - 1, n, pBlackQueens: &pBlackQueens, pWhiteQueens: &pWhiteQueens) {
          return true
        } else {
          pBlackQueens.removeLast()
          pWhiteQueens.removeLast()
        }
      }
    }
  }

  if !placingBlack {
    pBlackQueens.removeLast()
  }

  return false
}

func isAttacking(_ queen: Position, _ pos: Position) -> Bool {
  queen.0 == pos.0 || queen.1 == pos.1 || abs(queen.0 - pos.0) == abs(queen.1 - pos.1)
}

func printBoard(n: Int, pBlackQueens: [Position], pWhiteQueens: [Position]) {
  var board = Array(repeating: Piece.empty, count: n * n)

  for queen in pBlackQueens {
    board[queen.0 * n + queen.1] = .black
  }

  for queen in pWhiteQueens {
    board[queen.0 * n + queen.1] = .white
  }

  for (i, p) in board.enumerated() {
    if i != 0 && i % n == 0 {
      print()
    }

    switch p {
    case .black:
      print("B ", terminator: "")
    case .white:
      print("W ", terminator: "")
    case .empty:
      let j = i / n
      let k = i - j * n

      if j % 2 == k % 2 {
        print("• ", terminator: "")
      } else {
        print("◦ ", terminator: "")
      }
    }
  }

  print("\n")
}

let nms = [
  (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3),
  (5, 1), (5, 2), (5, 3), (5, 4), (5, 5),
  (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),
  (7, 1), (7, 2), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7)
]

for (n, m) in nms {
  print("\(m) black and white queens on \(n) x \(n) board")

  var blackQueens = [Position]()
  var whiteQueens = [Position]()

  if place(m, n, pBlackQueens: &blackQueens, pWhiteQueens: &whiteQueens) {
    printBoard(n: n, pBlackQueens: blackQueens, pWhiteQueens: whiteQueens)
  } else {
    print("No solution")
  }
}

Output:

1 black and white queens on 2 x 2 board
No solution
1 black and white queens on 3 x 3 board
B ◦ • 
◦ • W 
• ◦ • 

2 black and white queens on 3 x 3 board
No solution
1 black and white queens on 4 x 4 board
B ◦ • ◦ 
◦ • W • 
• ◦ • ◦ 
◦ • ◦ • 

2 black and white queens on 4 x 4 board
B ◦ • ◦ 
◦ • W • 
B ◦ • ◦ 
◦ • W • 

3 black and white queens on 4 x 4 board
No solution
1 black and white queens on 5 x 5 board
B ◦ • ◦ • 
◦ • W • ◦ 
• ◦ • ◦ • 
◦ • ◦ • ◦ 
• ◦ • ◦ • 

2 black and white queens on 5 x 5 board
B ◦ • ◦ B 
◦ • W • ◦ 
• W • ◦ • 
◦ • ◦ • ◦ 
• ◦ • ◦ • 

3 black and white queens on 5 x 5 board
B ◦ • ◦ B 
◦ • W • ◦ 
• W • ◦ • 
◦ • ◦ B ◦ 
• W • ◦ • 

4 black and white queens on 5 x 5 board
• B • B • 
◦ • ◦ • B 
W ◦ W ◦ • 
◦ • ◦ • B 
W ◦ W ◦ • 

5 black and white queens on 5 x 5 board
No solution
1 black and white queens on 6 x 6 board
B ◦ • ◦ • ◦ 
◦ • W • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 

2 black and white queens on 6 x 6 board
B ◦ • ◦ B ◦ 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ • ◦ • ◦ 
◦ • ◦ • ◦ • 

3 black and white queens on 6 x 6 board
B ◦ • ◦ B B 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ • 
• ◦ W ◦ • ◦ 
◦ • ◦ • ◦ • 

4 black and white queens on 6 x 6 board
B ◦ • ◦ B B 
◦ • W • ◦ • 
• W • ◦ • ◦ 
◦ • ◦ • ◦ B 
• ◦ W W • ◦ 
◦ • ◦ • ◦ • 

5 black and white queens on 6 x 6 board
• B • ◦ B ◦ 
◦ • ◦ B ◦ B 
W ◦ • ◦ • ◦ 
W • W • ◦ • 
• ◦ • ◦ • B 
W • W • ◦ • 

6 black and white queens on 6 x 6 board
No solution
1 black and white queens on 7 x 7 board
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

2 black and white queens on 7 x 7 board
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

3 black and white queens on 7 x 7 board
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

4 black and white queens on 7 x 7 board
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 
◦ • ◦ • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

5 black and white queens on 7 x 7 board
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ • ◦ • 
◦ • W • ◦ • ◦ 
• ◦ • ◦ • ◦ • 

6 black and white queens on 7 x 7 board
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
B ◦ • ◦ B ◦ • 
◦ • W • ◦ • W 
• ◦ • ◦ • ◦ • 

7 black and white queens on 7 x 7 board
• B • ◦ • B • 
◦ B ◦ • B • ◦ 
• B • ◦ • B • 
◦ • ◦ • B • ◦ 
W ◦ W ◦ • ◦ W 
◦ • ◦ W ◦ • ◦ 
W ◦ W W • ◦ •

Wren

Translation of: Kotlin

Library: Wren-dynamic

import "./dynamic" for Enum, Tuple

var Piece = Enum.create("Piece", ["empty", "black", "white"])

var Pos = Tuple.create("Pos", ["x", "y"])

var isAttacking = Fn.new { |q, pos|
    return q.x == pos.x || q.y == pos.y || (q.x - pos.x).abs == (q.y - pos.y).abs
}

var place // recursive
place = Fn.new { |m, n, blackQueens, whiteQueens|
    if (m == 0) return true
    var placingBlack = true
    for (i in 0...n) {        
        for (j in 0...n) {
            var pos = Pos.new(i, j)
            var inner = false
            for (queen in blackQueens) {
                var equalPos = queen.x == pos.x && queen.y == pos.y
                if (equalPos || !placingBlack && isAttacking.call(queen, pos)) {
                    inner = true
                    break
                }
            }
            if (!inner) {
                for (queen in whiteQueens) {
                    var equalPos = queen.x == pos.x && queen.y == pos.y
                    if (equalPos || placingBlack && isAttacking.call(queen, pos)) {
                        inner = true
                        break
                    }
                }
                if (!inner) {
                    if (placingBlack) {
                        blackQueens.add(pos)
                        placingBlack = false
<