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Talk:Peaceful chess queen armies (view source)

Revision as of 10:08, 27 March 2019

24,188 bytes added ,  5 years ago
→‎Original Python exhaustive search
Line 1:
==SimplifiedOriginal Python exhaustive search==
I was experimenting with various things when doing the Python.
This is itthe simplifiedoriginal:
 
Exhaustive search.
<lang python>from itertools import combinations, product, count
<lang python>from itertools import combinations, count
from functools import lru_cache, reduce
 
 
# n-by-n board
n = 5
 
def _2d(n=n):
for i in range(n):
print(' '.join(f'{i},{j}' for j in range(n)))
 
def _1d(n=n):
for i in range(0, n*n, n):
print(', '.join(f'{i+j:2}' for j in range(n)))
 
_bbullet, _wbullet = '\u2022\u25E6'
#_bqueen, _wqueen = 'BW'
_bqueen, _wqueen = '\u265B\u2655'
_bqueenh, _wqueenh = '&#x265b;', '<font color="green">&#x2655;</font>'
_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
# 2-D Board as 1-D array: 2D(x, y) == 1D(t%n, t//n)
board = set(range(n*n))
 
#placements = list(combinations(board, m))
placements = {frozenset(c) for c in combinations(board, m)}
for blacks in placements:
Line 18 ⟶ 38:
(queen_attacks_from(pos, n) for pos in blacks),
set())
#for whites in {frozenset(c) # Never on blsck attacking squaresplacements:
for whites in {frozenset(c) for c in combinations(board - black_attacks, m)}:
if not black_attacks & whites:
return blacks, whites
Line 25 ⟶ 45:
 
@lru_cache(maxsize=None)
def queen_attacks_from(pos, n=n):
x0, y0 = pos
a = set([pos]) # Its position
a.update(range(xpos//n*n, y0) for x in range(pos//n*n+n)) # Its row
a.update(range(x0pos%n, yn*n, n)) for y in range(n)) # Its column
# Diagonals
x0, y0 = pos%n, pos//n
for x1 in range(n):
# l-to-r diag
y1 = y0 -x0 +x1
if 0 <= y1 < n:
a.add((x1, + y1) * n)
# r-to-l diag
y1 = y0 +x0 -x1
if 0 <= y1 < n:
a.add((x1, + y1) * n)
return a
 
def pboard(black_white=None, n=n):
"Print board"
if black_white is None:
blk, wht = set(), set()
Line 50 ⟶ 69:
print(f"## {len(blk)} black and {len(wht)} white queens "
f"on a {n}-by-{n} board:", end='')
for x, yxy in product(range(n), repeat=2*n):
if yxy %n == 0:
print()
xy = (x, y)
ch = ('?' if xy in blk and xy in wht
else 'B'_bqueen if xy in blk
else 'W'_wqueen if xy in wht
else _bbullet if (xxy%n + yxy//n)%2 else _wbullet)
print('%s' % ch, end='')
print()
 
def hboard(black_white=None, n=n):
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>\n "
tbl = ''
for xy in range(n*n):
if xy %n == 0:
tbl += '</tr>\n <tr>\n'
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 (xy%n + xy//n)%2 else ' bgcolor="silver"'
tbl += f' <td style="width:16pt; height:16pt;"{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()
queen_attacks_from.cache_clear() # memoization cache
#
for m in count(1):
ans = place(m, n)
if ans[0]:
pboard(ans, n)
html += hboard(ans, n)
else:
printcomment = (f"# Can't place {m}+ queens on a {n}-by-{n} board")
print (comment)
html += f"<b>{comment}</b><br><br>\n\n"
break
#
print('\n')
html += '<br>\n'
#
m, n = 5, 7
queen_attacks_from.cache_clear()
ans = place(m, n)
pboard(ans, n)</lang>
html += hboard(ans, n)
with open('peaceful_queen_armies.htm', 'w') as f:
f.write(html)</lang>
 
{{out}}
The console output Unicode queen characters display wider than other characters in monospace font so the alternative HTML output is shown below.
<pre># Can't place 1+ queens on a 2-by-2 board
 
<div style="overflow:scroll; height:250px;">
## 1 black and 1 white queens on a 3-by-3 board:
<b># Can't place 1+ queens on a 2-by-2 board</b><br><br>
◦•◦
B◦•
◦•W
# Can't place 2+ queens on a 3-by-3 board
 
<br><b>## 1 black and 1 white queens on a 43-by-43 board:</b><br>
<table>
◦•W•
<tr>
B◦•◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
◦•◦•
<td style="width:16pt; height:16pt;"></td>
•◦•◦
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
## 2 black and 2 white queens on a 4-by-4 board:
</tr>
◦B◦•
<tr>
•B•◦
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
◦•◦•
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
W◦W◦
<td style="width:16pt; height:16pt;"></td>
# Can't place 3+ queens on a 4-by-4 board
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
</table>
<br>
<b># Can't place 2+ queens on a 3-by-3 board</b><br><br>
 
<br><b>## 1 black and 1 white queens on a 54-by-54 board:</b><br>
<table>
◦•◦•◦
<tr>
W◦•◦•
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
◦•◦•◦
<td style="width:16pt; height:16pt;"></td>
•◦•◦B
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
◦•◦•◦
<td style="width:16pt; height:16pt;"></td>
## 2 black and 2 white queens on a 5-by-5 board:
</tr>
◦•◦•W
<tr>
•◦B◦•
<td style="width:16pt; height:16pt;"></td>
◦•◦•◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
•◦•B•
<td style="width:16pt; height:16pt;"></td>
◦W◦•◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
## 3 black and 3 white queens on a 5-by-5 board:
</tr>
◦W◦•◦
<tr>
•◦•◦W
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
B•B•◦
<td style="width:16pt; height:16pt;"></td>
B◦•◦•
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
◦•◦W◦
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
## 4 black and 4 white queens on a 5-by-5 board:
</tr>
◦•B•B
<tr>
W◦•◦•
<td style="width:16pt; height:16pt;"></td>
◦W◦W◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
W◦•◦•
<td style="width:16pt; height:16pt;"></td>
◦•B•B
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
# Can't place 5+ queens on a 5-by-5 board
</tr>
</table>
<br>
<br><b>## 2 black and 2 white queens on a 4-by-4 board:</b><br>
<table>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
</table>
<br>
<b># Can't place 3+ queens on a 4-by-4 board</b><br><br>
 
<br><b>## 1 black and 1 white queens on a 65-by-65 board:</b><br>
<table>
◦•◦•◦•
<tr>
W◦•◦•◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
◦•◦•◦•
<td style="width:16pt; height:16pt;"></td>
•◦•◦B◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
◦•◦•◦•
<td style="width:16pt; height:16pt;"></td>
•◦•◦•◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
## 2 black and 2 white queens on a 6-by-6 board:
</tr>
◦•◦•◦•
<tr>
•◦B◦•◦
<td style="width:16pt; height:16pt;"></td>
◦•◦•◦•
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
•◦•B•◦
<td style="width:16pt; height:16pt;"></td>
◦•◦•◦•
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
W◦•◦W◦
<td style="width:16pt; height:16pt;"></td>
## 3 black and 3 white queens on a 6-by-6 board:
</tr>
◦•B•◦•
<tr>
•B•◦•◦
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
◦•◦W◦W
<td style="width:16pt; height:16pt;"></td>
•◦•◦•◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
W•◦•◦•
<td style="width:16pt; height:16pt;"></td>
•◦•◦B◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
## 4 black and 4 white queens on a 6-by-6 board:
</tr>
WW◦•W•
<tr>
•W•◦•◦
<td style="width:16pt; height:16pt;"></td>
◦•◦•◦B
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
•◦B◦•◦
<td style="width:16pt; height:16pt;"></td>
◦•◦B◦•
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
•◦•B•◦
<td style="width:16pt; height:16pt;"></td>
## 5 black and 5 white queens on a 6-by-6 board:
</tr>
◦•W•W•
<tr>
B◦•◦•◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
◦•W•◦W
<td style="width:16pt; height:16pt;"></td>
B◦•◦•◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
◦•◦•◦W
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
BB•B•◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
# Can't place 6+ queens on a 6-by-6 board
</tr>
</table>
<br>
<br><b>## 2 black and 2 white queens on a 5-by-5 board:</b><br>
<table>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
</tr>
</table>
<br>
<br><b>## 3 black and 3 white queens on a 5-by-5 board:</b><br>
<table>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
</table>
<br>
<br><b>## 4 black and 4 white queens on a 5-by-5 board:</b><br>
<table>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
</table>
<br>
<b># Can't place 5+ queens on a 5-by-5 board</b><br><br>
 
<br><b>## 1 black and 1 white queens on a 6-by-6 board:</b><br>
<table>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
</table>
<br>
<br><b>## 2 black and 2 white queens on a 6-by-6 board:</b><br>
<table>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
</table>
<br>
<br><b>## 3 black and 3 white queens on a 6-by-6 board:</b><br>
<table>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
</table>
<br>
<br><b>## 4 black and 4 white queens on a 6-by-6 board:</b><br>
<table>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
</table>
<br>
<br><b>## 5 black and 5 white queens on a 6-by-6 board:</b><br>
<table>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver">&#x265b;</td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
</table>
<br>
<b># Can't place 6+ queens on a 6-by-6 board</b><br><br>
 
<br>
## 5 black and 5 white queens on a 7-by-7 board:
<br><b>## 5 black and 5 white queens on a 7-by-7 board:</b><br>
◦•◦•B•◦
<table>
•W•◦•◦W
<tr>
◦•◦•B•◦
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
B◦•◦•◦•
<td style="width:16pt; height:16pt;"></td>
◦•B•◦•◦
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
•◦•B•◦•
<td style="width:16pt; height:16pt;"></td>
◦W◦•◦WW</pre>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;">&#x265b;</td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;"><font color="green">&#x2655;</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
</table>
<br>
</div>
 
--[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 1910:1908, 2627 March 2019 (UTC)
Anonymous user
Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/289361"