# Ramsey's theorem

Ramsey's theorem is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Find a graph with 17 Nodes such that any 4 Nodes are neither totally connected nor totally unconnected, so demonstrating Ramsey's theorem.

A specially-nominated solution may be used, but if so it must be checked to see if if there are any sub-graphs that are totally connected or totally unconnected.

## 11l

Translation of: Python
```V a = [[‘0’] * 17] * 17
V idx = [0] * 4

F find_group(mark, min_n, max_n, depth = 1)
I depth == 4
V prefix = I mark == ‘1’ {‘’} E ‘un’
print(‘Fail, found totally #.connected group:’.format(prefix))
L(i) 4
print(:idx[i])
R 1B

L(i) min_n .< max_n
V n = 0
L n < depth
I :a[:idx[n]][i] != mark
L.break
n++

I n == depth
:idx[n] = i
I find_group(mark, 1, max_n, depth + 1)
R 1B
R 0B

L(i) 17
a[i][i] = ‘-’
L(k) 4
L(i) 17
V j = (i + pow(2, k)) % 17
a[i][j] = a[j][i] = ‘1’

L(row) a
print(row.join(‘ ’))

L(i) 17
idx[0] = i
I find_group(‘1’, i + 1, 17) | find_group(‘0’, i + 1, 17)
print(‘no good’)
L.break
L.was_no_break
print(‘all good’)```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
all good
```

## 360 Assembly

Translation of: C
```*        Ramsey's theorem          19/03/2017
RAMSEY   CSECT
USING  RAMSEY,R13         base register
B      72(R15)            skip savearea
DC     17F'0'             savearea
STM    R14,R12,12(R13)    save previous context
LA     R6,1               i=1
DO WHILE=(C,R6,LE,NN)       do i=1 to nn
LR     R1,R6                i
MH     R1,=AL2(N)           *n
LR     R0,R6                i
AR     R1,R0                i*i+i
SLA    R1,1                 *2
LA     R0,2                 2
STH    R0,A-36(R1)          a(i,i)=2
LA     R6,1(R6)             i++
ENDDO    ,                  enddo i
LA     R6,1               i=1
DO WHILE=(C,R6,LE,=F'8')    do while i<=8
LA     R7,1                 j=1
DO WHILE=(C,R7,LE,NN)         do j=1 to nn
LR     R8,R7                  j
AR     R8,R6                  +i
BCTR   R8,0                   -1
SRDA   R8,32                  ~
D      R8,NN                  /nn
LA     R8,1(R8)               k=((j+i-1) mod nn)+1
LR     R1,R7                  j
MH     R1,=AL2(N)             *n
LR     R0,R8                  k
AR     R1,R0                  j*n+ki
SLA    R1,1                   *2
LA     R0,1                   1
STH    R0,A-36(R1)            a(j,k)=1
LR     R1,R8                  k
MH     R1,=AL2(N)             *n
LR     R0,R7                  j
AR     R1,R0                  k*n+j
SLA    R1,1                   *2
LA     R0,1                   1
STH    R0,A-36(R1)            a(k,j)=1
LA     R7,1(R7)               j++
ENDDO    ,                    enddo j
AR     R6,R6                i=i+i
ENDDO    ,                  enddo i
LA     R6,1               i=1
DO WHILE=(C,R6,LE,NN)       do i=1 to nn
LA     R7,1                 j=1
LA     R10,PG               pgi=0
DO WHILE=(C,R7,LE,NN)         do j=1 to nn
LR     R1,R6                  i
MH     R1,=AL2(N)             *n
LR     R0,R7                  j
AR     R1,R0                  i*n+j
SLA    R1,1                   *2
LH     R4,A-36(R1)            a(i,j)
IF CH,R4,EQ,=H'2' THEN          if a(i,j)=2 then
MVC    0(2,R10),=C' -'          output '-'
ELSE     ,                      else
XDECO  R4,XDEC                  edit a(i,j)
MVC    0(2,R10),XDEC+10         output a(i,j)
ENDIF    ,                      endif
LA     R10,2(R10)             pgi+=2
LA     R7,1(R7)               j++
ENDDO    ,                    enddo j
XPRNT  PG,L'PG              print buffer
LA     R6,1(R6)             i++
ENDDO    ,                  enddo i
LA     R6,1               i=1
DO WHILE=(C,R6,LE,NN)       do i=1 to nn
SR     R0,R0                0
STH    R0,BH                bh=0
STH    R0,BV                bv=0
LA     R7,1                 j=1
DO WHILE=(C,R7,LE,NN)         do j=1 to nn
LR     R1,R6                  i
MH     R1,=AL2(N)             *n
LR     R0,R7                  j
AR     R1,R0                  i*n+j
SLA    R1,1                   *2
LH     R2,A-36(R1)            a(i,j)
IF CH,R2,EQ,=H'1' THEN          if a(i,j)=1 then
LH     R2,BH                    bh
LA     R2,1(R2)                 +1
STH    R2,BH                    bh=bh+1
ENDIF    ,                      endif
LR     R1,R7                  j
MH     R1,=AL2(N)             *n
LR     R0,R6                  i
AR     R1,R0                  j*n+i
SLA    R1,1                   *2
LH     R2,A-36(R1)            a(j,i)
IF CH,R2,EQ,=H'1' THEN          if a(j,i)=1 then
LH     R2,BV                    bv
LA     R2,1(R2)                 +1
STH    R2,BV                    bv=bv+1
ENDIF    ,                      endif
LA     R7,1(R7)               j++
ENDDO    ,                    enddo j
L      R2,NN                nn
SRA    R2,1                 /2
MVI    XX,X'01'             xx=true
IF CH,R2,NE,BH THEN           if bh<>nn/2 then
MVI    XX,X'00'               xx=false
ENDIF    ,                    endif
NC     OKH,XX               okh=okh and (bh=nn/2)
L      R2,NN                nn
SRA    R2,1                 /2
MVI    XX,X'01'             xx=true
IF CH,R2,NE,BV THEN           if bv<>nn/2 then
MVI    XX,X'00'               xx=false
ENDIF    ,                    endif
NC     OKV,XX               okv=okv and (bv=nn/2)
LA     R6,1(R6)             i++
ENDDO    ,                  enddo i
MVC    XX,OKH             xx=okh
NC     XX(1),OKV          xx=okh and okv
IF CLI,XX,EQ,X'01' THEN     if okh and okv then
MVC    WOK,=CL4'yes'        wok='yes'
ELSE     ,                  else
MVC    WOK,=CL4'no'         wok='no'
ENDIF    ,                  endif
MVC    PG,=CL80'check='   output 'check='
MVC    PG+6(L'WOK),WOK    output wok
XPRNT  PG,L'PG            print buffer
L      R13,4(0,R13)       restore previous savearea pointer
LM     R14,R12,12(R13)    restore previous context
XR     R15,R15            return_code=0
BR     R14                exit
N        EQU    17                 n=17
NN       DC     A(N)               nn=n
A        DC     (N*N)H'0'          table a(n,n) halfword init 0
BH       DS     H                  count horizontal
BV       DS     H                  count vertical
OKH      DC     X'01'              check horizontal
OKV      DC     X'01'              check vertical
WOK      DS     CL4                temp ok
XX       DS     X                  temp logical
PG       DC     CL80' '            buffer
XDEC     DS     CL12               temp xdeco
YREGS
END    RAMSEY```
Output:
``` - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
check=yes
```

## AWK

```# syntax: GAWK -f RAMSEYS_THEOREM.AWK
# converted from Ring
BEGIN {
for (i=1; i<=17; i++) {
arr[i,i] = -1
}
k = 1
while (k <= 8) {
for (i=1; i<=17; i++) {
j = (i + k) % 17
if (j != 0) {
arr[i,j] = 1
arr[j,i] = 1
}
}
k = k * 2
}
for (i=1; i<=17; i++) {
for (j=1; j<=17; j++) {
printf("%s",arr[i,j]+0)
}
printf("\n")
}
exit(0)
}
```
Output:
```-11101000110001011
1-1110100011000101
11-111010001100010
011-11101000110001
1011-1110100011000
01011-111010001100
001011-11101000110
0001011-1110100011
10001011-111010000
110001011-11101000
0110001011-1110100
00110001011-111010
000110001011-11100
1000110001011-1110
01000110001011-110
101000110001011-10
1101000100000000-1
```

## BASIC256

Translation of: FreeBASIC
```global k, a, idx
k = 1
dim a(18,18)
dim idx(5)
for i = 0 to 17
a[i,i] = 2 #-1
next i

while k <= 8
for i = 1 to 17
j = (i + k) mod 17
if j <> 0 then
a[i,j] = 1 : a[j,i] = 1
end if
next i
k *= 2
end while
for i = 1 to 17
for j = 1 to 17
if a[i,j] = 2 then
print "- ";
else
print int(a[i,j]) & " ";
end if
next j
print
next i

# Es simétrico, por lo que solo necesita probar grupos que contengan el nodo 0.
for i = 0 to 17
idx[0] = i
if EncontrarGrupo(1, i+1, 17, 1) or EncontrarGrupo(0, i+1, 17, 1) then
print chr(10) & "No satisfecho."
exit for
end if
next i
print chr(10) & "Satisface el teorema de Ramsey."
end

function EncontrarGrupo(tipo, min, max, fondo)
if fondo = 0 then
c = ""
if tipo = 0 then c = "des"
print "Grupo totalmente "; c; "conectado:";
for i = 0 to 4
print " " & idx[i]
next i
print
return true
end if

for i = min to max
k = 0
for j = k to fondo
if a[idx[k],i] <> tipo then exit for
next j

if k = fondo then
idx[k] = i
if EncontrarGrupo(tipo, 1, max, fondo+1) then return true
end if
next i
return false
end function```
Output:
`Same as FreeBASIC entry.`

## C

For 17 nodes, (4,4) happens to have a special solution: arrange nodes on a circle, and connect all pairs with distances 1, 2, 4, and 8. It's easier to prove it on paper and just show the result than let a computer find it (you can call it optimization).

No issue with the code or the output, there seems to be a bug with Rosettacode's tag handlers. - aamrun

```#include <stdio.h>

int a[17][17], idx[4];

int find_group(int type, int min_n, int max_n, int depth)
{
int i, n;
if (depth == 4) {
printf("totally %sconnected group:", type ? "" : "un");
for (i = 0; i < 4; i++) printf(" %d", idx[i]);
putchar('\n');
return 1;
}

for (i = min_n; i < max_n; i++) {
for (n = 0; n < depth; n++)
if (a[idx[n]][i] != type) break;

if (n == depth) {
idx[n] = i;
if (find_group(type, 1, max_n, depth + 1))
return 1;
}
}
return 0;
}

int main()
{
int i, j, k;
const char *mark = "01-";

for (i = 0; i < 17; i++)
a[i][i] = 2;

for (k = 1; k <= 8; k <<= 1) {
for (i = 0; i < 17; i++) {
j = (i + k) % 17;
a[i][j] = a[j][i] = 1;
}
}

for (i = 0; i < 17; i++) {
for (j = 0; j < 17; j++)
printf("%c ", mark[a[i][j]]);
putchar('\n');
}

// testcase breakage
// a[2][1] = a[1][2] = 0;

// it's symmetric, so only need to test groups containing node 0
for (i = 0; i < 17; i++) {
idx[0] = i;
if (find_group(1, i+1, 17, 1) || find_group(0, i+1, 17, 1)) {
puts("no good");
return 0;
}
}
puts("all good");
return 0;
}
```
Output:

(17 x 17 connectivity matrix)

```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
all good
```

## D

Translation of: Tcl
```import std.stdio, std.string, std.algorithm, std.range;

/// Generate the connectivity matrix.
immutable(char)[][] generateMatrix() {
immutable r = format("-%b", 53643);
return r.length.iota.map!(i => r[\$-i .. \$] ~ r[0 .. \$-i]).array;
}

/**Check that every clique of four has at least one pair connected
and one pair unconnected. It requires a symmetric matrix.*/
string ramseyCheck(in char[][] mat) pure @safe
in {
foreach (immutable r, const row; mat) {
assert(row.length == mat.length);
foreach (immutable c, immutable x; row)
assert(x == mat[c][r]);
}
} body {
immutable N = mat.length;
char[6] connectivity = '-';

foreach (immutable a; 0 .. N) {
foreach (immutable b; 0 .. N) {
if (a == b) continue;
connectivity[0] = mat[a][b];
foreach (immutable c; 0 .. N) {
if (a == c || b == c) continue;
connectivity[1] = mat[a][c];
connectivity[2] = mat[b][c];
foreach (immutable d; 0 .. N) {
if (a == d || b == d || c == d) continue;
connectivity[3] = mat[a][d];
connectivity[4] = mat[b][d];
connectivity[5] = mat[c][d];

// We've extracted a meaningful subgraph,
// check its connectivity.
if (!connectivity[].canFind('0'))
return format("Fail, found wholly connected: ",
a, " ", b," ", c, " ", d);
else if (!connectivity[].canFind('1'))
return format("Fail, found wholly " ~
"unconnected: ",
a, " ", b," ", c, " ", d);
}
}
}
}

return "Satisfies Ramsey condition.";
}

void main() {
const mat = generateMatrix;
writefln("%-(%(%c %)\n%)", mat);
mat.ramseyCheck.writeln;
}
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
Satisfies Ramsey condition.```

## Elixir

Translation of: Erlang
```defmodule Ramsey do
def main(n\\17) do
vertices = Enum.to_list(0 .. n-1)
g = create_graph(n,vertices)
edges = for v1 <- :digraph.vertices(g), v2 <- :digraph.out_neighbours(g, v1), do: {v1,v2}
print_graph(vertices,edges)
case ramsey_check(vertices,edges) do
true           -> "Satisfies Ramsey condition."
{false,reason} -> "Not satisfies Ramsey condition:\n#{inspect reason}"
end
|> IO.puts
end

def create_graph(n,vertices) do
g = :digraph.new([:cyclic])
for v <- vertices, do: :digraph.add_vertex(g,v)
for i <- vertices, k <- [1,2,4,8] do
j = rem(i + k, n)
end
g
end

def print_graph(vertices,edges) do
Enum.each(vertices, fn j ->
Enum.map_join(vertices, " ", fn i ->
cond do
i==j           -> "-"
{i,j} in edges -> "1"
true           -> "0"
end
end)
|> IO.puts
end)
end

def ramsey_check(vertices,edges) do
listconditions =
for v1 <- vertices, v2 <- vertices, v3 <- vertices, v4 <- vertices,
v1 != v2, v1 != v3, v1 != v4, v2 != v3, v2 != v4, v3 != v4
do
all_cases = [ {v1,v2} in edges, {v1,v3} in edges, {v1,v4} in edges,
{v2,v3} in edges, {v2,v4} in edges, {v3,v4} in edges ]
{v1, v2, v3, v4, Enum.any?(all_cases), not(Enum.all?(all_cases))}
end
if Enum.all?(listconditions, fn {_,_,_,_,c1,c2} -> c1 and c2 end) do
true
else
{false, (for {v1,v2,v3,v4,false,_} <- listconditions, do: {:wholly_unconnected,v1,v2,v3,v4})
++ (for {v1,v2,v3,v4,_,false} <- listconditions, do: {:wholly_connected,v1,v2,v3,v4}) }
end
end
end

Ramsey.main
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
Satisfies Ramsey condition.
```

## Erlang

Translation of: C
```-module(ramsey_theorem).
-export([main/0]).

main() ->
Vertices = lists:seq(0,16),
G = create_graph(Vertices),
String_ramsey =
case ramsey_check(G,Vertices) of
true ->
"Satisfies Ramsey condition.";
{false,Reason} ->
"Not satisfies Ramsey condition:\n"
++ io_lib:format("~p\n",[Reason])
end,
io:format("~s\n~s\n",[print_graph(G,Vertices),String_ramsey]).

create_graph(Vertices) ->
G = digraph:new([cyclic]),
[begin
J = ((I + K) rem 17),
end || I <- Vertices, K <- [1,2,4,8]],
G.

print_graph(G,Vertices) ->
Edges =
[{V1,V2} ||
V1 <- digraph:vertices(G),
V2 <- digraph:out_neighbours(G, V1)],
lists:flatten(
[[
[case I of
J ->
\$-;
_ ->
case lists:member({I,J},Edges) of
true -> \$1;
false -> \$0
end
end,\$ ]
|| I <- Vertices] ++ [\$\n] || J <- Vertices]).

ramsey_check(G,Vertices) ->
Edges =
[{V1,V2} ||
V1 <- digraph:vertices(G),
V2 <- digraph:out_neighbours(G, V1)],
ListConditions =
[begin
All_cases =
[lists:member({V1,V2},Edges),
lists:member({V1,V3},Edges),
lists:member({V1,V4},Edges),
lists:member({V2,V3},Edges),
lists:member({V2,V4},Edges),
lists:member({V3,V4},Edges)],
{V1,V2,V3,V4,
lists:any(fun(X) -> X end, All_cases),
not(lists:all(fun(X) -> X end, All_cases))}
end
|| V1 <- Vertices, V2 <- Vertices, V3 <- Vertices, V4 <- Vertices,
V1/=V2,V1/=V3,V1/=V4,V2/=V3,V2/=V4,V3/=V4],
case lists:all(fun({_,_,_,_,C1,C2}) -> C1 and C2 end,ListConditions) of
true -> true;
false ->
{false,
[{wholly_unconnected,V1,V2,V3,V4}
|| {V1,V2,V3,V4,false,_} <- ListConditions]
++ [{wholly_connected,V1,V2,V3,V4}
|| {V1,V2,V3,V4,_,false} <- ListConditions]}
end.
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -

Satisfies Ramsey condition.```

## FreeBASIC

Translation of: Ring
Translation of: Go
```Dim Shared As Integer i, j, k = 1
Dim Shared As Integer a(17,17), idx(4)
For i = 0 To 17
a(i,i) = 2
Next i

Function EncontrarGrupo(tipo As Integer, min As Integer, max As Integer, fondo As Integer) As Boolean
If fondo = 0 Then
Dim As String c = ""
If tipo = 0 Then c = "des"
Print Using "Grupo totalmente &conectado:"; c
For i = 0 To 4
Print " " & idx(i)
Next i
Print
Return true
End If

For i = min To max
k = 0
For j = k To fondo
If a(idx(k),i) <> tipo Then Exit For
Next j

If k = fondo Then
idx(k) = i
If EncontrarGrupo(tipo, 1, max, fondo+1) Then Return true
End If
Next i
Return false
End Function

While k <= 8
For i = 1 To 17
j = (i + k) Mod 17
If j <> 0 Then
a(i,j) = 1 : a(j,i) = 1
End If
Next i
k *= 2
Wend
For i = 1 To 17
For j = 1 To 17
If a(i,j) = 2 Then
Print "- ";
Else
Print a(i,j) & " ";
End If
Next j
Print
Next i

' Es simétrico, por lo que solo necesita probar grupos que contengan el nodo 0.
For i = 0 To 17
idx(0) = i
If EncontrarGrupo(1, i+1, 17, 1) Or EncontrarGrupo(0, i+1, 17, 1) Then
Print Chr(10) & "No satisfecho."
Exit For
End If
Next i
Print Chr(10) & "Satisface el teorema de Ramsey."
End```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 0
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 -

Satisface el teorema de Ramsey.
```

## Go

Translation of: C
```package main

import "fmt"

var (
a   [17][17]int
idx [4]int
)

func findGroup(ctype, min, max, depth int) bool {
if depth == 4 {
cs := ""
if ctype == 0 {
cs = "un"
}
fmt.Printf("Totally %sconnected group:", cs)
for i := 0; i < 4; i++ {
fmt.Printf(" %d", idx[i])
}
fmt.Println()
return true
}

for i := min; i < max; i++ {
n := 0
for ; n < depth; n++ {
if a[idx[n]][i] != ctype {
break
}
}

if n == depth {
idx[n] = i
if findGroup(ctype, 1, max, depth+1) {
return true
}
}
}
return false
}

func main() {
const mark = "01-"

for i := 0; i < 17; i++ {
a[i][i] = 2
}

for k := 1; k <= 8; k <<= 1 {
for i := 0; i < 17; i++ {
j := (i + k) % 17
a[i][j], a[j][i] = 1, 1
}
}

for i := 0; i < 17; i++ {
for j := 0; j < 17; j++ {
fmt.Printf("%c ", mark[a[i][j]])
}
fmt.Println()
}

// Test case breakage
// a[2][1] = a[1][2] = 0

// It's symmetric, so only need to test groups containing node 0.
for i := 0; i < 17; i++ {
idx[0] = i
if findGroup(1, i+1, 17, 1) || findGroup(0, i+1, 17, 1) {
fmt.Println("No good.")
return
}
}
fmt.Println("All good.")
}
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
All good.
```

## J

Interpreting this task as "reproduce the output of all the other examples", then here's a stroll to the goal through the J interpreter:

```   i.@<.&.(2&^.) N =: 17                                           NB.  Count to N by powers of 2
1 2 4 8
1 #~ 1 j. 0 _1:} i.@<.&.(2&^.) N =: 17                          NB.  Turn indices into bit mask
1 0 1 0 0 1 0 0 0 0 1
(, |.) 1 #~ 1 j. 0 _1:} i.@<.&.(2&^.) N =: 17                   NB.  Cat the bitmask with its own reflection
1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1
_1 |.^:(<N) _ , (, |.) 1 #~ 1 j. 0 _1:} <: i.@<.&.(2&^.) N=:17  NB.  Then rotate N times to produce the array
_ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 _ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 _ 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 _

NB. Packaged up as a re-usable function
ramsey =: _1&|.^:((<@])`(_ , [: (, |.) 1 #~ 1 j. 0 _1:} [: <: i.@<.&.(2&^.)@]))

ramsey 17
_ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 _ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 _ 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 _
```

To test if all combinations of 4 rows and columns contain both a 0 and a 1

```   comb=: 4 : 0 M.   NB. All size x combinations of i.y
if. (x>:y)+.0=x do. i.(x<:y),x else. (0,.x comb&.<: y),1+x comb y-1 end.
)

NB. returns 1 iff the subbmatrix of y consisting of the columns and rows labelled x contains both 1 and 0
checkRow =. 4 : 0 "1 _
*./ 0 1 e. ,x{"1 x{y
)

*./ (4 comb 17) checkRow ramsey 17
1
```

## Java

Translation of Tcl via D

Works with: Java version 8
```import java.util.Arrays;
import java.util.stream.IntStream;

public class RamseysTheorem {

static char[][] createMatrix() {
String r = "-" + Integer.toBinaryString(53643);
int len = r.length();
return IntStream.range(0, len)
.mapToObj(i -> r.substring(len - i) + r.substring(0, len - i))
.map(String::toCharArray)
.toArray(char[][]::new);
}

/**
* Check that every clique of four has at least one pair connected and one
* pair unconnected. It requires a symmetric matrix.
*/
static String ramseyCheck(char[][] mat) {
int len = mat.length;
char[] connectivity = "------".toCharArray();

for (int a = 0; a < len; a++) {
for (int b = 0; b < len; b++) {
if (a == b)
continue;
connectivity[0] = mat[a][b];
for (int c = 0; c < len; c++) {
if (a == c || b == c)
continue;
connectivity[1] = mat[a][c];
connectivity[2] = mat[b][c];
for (int d = 0; d < len; d++) {
if (a == d || b == d || c == d)
continue;
connectivity[3] = mat[a][d];
connectivity[4] = mat[b][d];
connectivity[5] = mat[c][d];

// We've extracted a meaningful subgraph,
// check its connectivity.
String conn = new String(connectivity);
if (conn.indexOf('0') == -1)
return String.format("Fail, found wholly connected: "
+ "%d %d %d %d", a, b, c, d);
else if (conn.indexOf('1') == -1)
return String.format("Fail, found wholly unconnected: "
+ "%d %d %d %d", a, b, c, d);
}
}
}
}
return "Satisfies Ramsey condition.";
}

public static void main(String[] a) {
char[][] mat = createMatrix();
for (char[] s : mat)
System.out.println(Arrays.toString(s));
System.out.println(ramseyCheck(mat));
}
}
```
```[-, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1]
[1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1]
[1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0]
[0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1]
[1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0]
[0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0]
[0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0]
[0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1]
[1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1]
[1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0]
[0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0]
[0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0]
[0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1]
[1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0]
[0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1]
[1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1]
[1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -]
Satisfies Ramsey condition.```

## jq

Works with: jq

Also works with gojq, the Go implementation of jq.

With a minor tweak of the line using string interpolation, the following program also works with jaq (as of April 13, 2023), the Rust implementation of jq.

In the following, if a is a connectivity matrix and if \$i != \$j, then a[\$i][\$j] is either 0 or 1 depending on whether the nodes are unconnected or connected respectively.

```# Input: {a, idx} where .a is a connectivity matrix and
#   .idx is an array with length equal to the size of the group of interest.
# Assuming .idx[0] is 0, then depending on the value of \$ctype,
# findGroup(\$ctype; 1; 1) will either find
# a completely connected or a uncompletely unconnected
# group of size `.idx|length` in .a, if it exists, or emit false.
# Set \$ctype to 0 to find a completely unconnected group.
def findGroup(\$ctype; \$min; \$depth):
. as \$in
| (.a|length) as \$max
| (.idx|length) as \$size
| if \$depth == \$size
then (if \$ctype == 0 then "un" else "" end) as \$cs
| "Totally \(\$cs)connected group: " + (.idx | map(tostring) | join(" "))
else .i = \$min
| until (.i >= \$max or .emit;
.n = 0
| until (.n >= \$depth or .a[.idx[.n]][.i] != \$ctype;
.n += 1)
| if .n == \$depth
then .idx[.n] = .i
| .emit = findGroup(\$ctype; 1; \$depth+1)
else .
end
| .i += 1 )
| .emit // false
end ;

# Output: {a, idx}
def init:
def a:
[range(0;17) | 0] as \$zero
| [range(0;17) | \$zero]
| reduce range(0;17) as \$i (.; .[\$i][\$i] = 2);
def idx: [range(0;4)|0];

{a: a, idx: idx, k: 1}
| until (.k > 8;
reduce range(0;17) as \$i (.;
((\$i + .k) % 17) as \$j
| .a[\$i][\$j] = 1
| .a[\$j][\$i] = 1)
| .k *= 2 )
| del(.k);

# input: {a}
def printout:
def mark(n): "01-"[n:n+1];
.a as \$a
| range(0; \$a|length) as \$i
| reduce range(0; \$a|length) as \$j (""; . + mark(\$a[\$i][\$j]) + " ") ;

# input: {a, idx}
def check:
first( range(0; .a|length) as \$i
| .idx[0] = \$i
| findGroup(1; \$i+1; 1) // findGroup(0; \$i+1; 1) // empty
|  . + "\nNo good.")
// "All good." ;

init
| printout, check, "",
# Test case breakage
(  .a[2][1] = 0
| .a[1][2] = 0
| printout, check )```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
All good.

- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 0 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
Totally unconnected group: 1 2 7 12
No good.
```

## Julia

Translation of: C
```const a, idx = zeros(Int, 17, 17), zeros(Int, 4)

function findgroup(typ, nmin, nmax, depth)
if depth == 4
print("Totally ", typ > 0 ? "" : "un", "connected group:")
for i in 1:4
print(" ", idx[i], i == 4 ? "\n" : "")
end
return true
end
for i in nmin:nmax-1
for i in nmin:nmax-1
m = 0
for n in 0:depth-1
if a[idx[n + 1] + 1, i + 1] != typ
break
end
m = n +1
end
if m == depth
idx[m + 1] = i
if findgroup(typ, 1, nmax, depth + 1)
return true
end
end
end
end
return false
end

function testnodes()
mark = "01-"
for i in 1:17
a[i, i] = 2
end
for k in [1, 2, 4, 8], i in 0:16
j = (i + k) % 17
a[i + 1, j + 1] = a[j + 1, i + 1] = 1
end
for i in 1:17, j in 1:17
print(mark[a[i, j] + 1], j == 17 ? "\n" : " ")
end

# testcase breakage
# a[2][1] = a[1][2] = 0
# it's symmetric, so only need to test groups containing node 0
for i in 1:17
idx[1] = i
if findgroup(1, i + 1, 17, 1) || findgroup(0, i + 1, 17, 1)
println("Test with \$i is no good.")
return
end
end
println("All tests are OK.")
end

testnodes()
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
All tests are OK.
```

## Kotlin

Translation of: C
```// version 1.1.0

val a = Array(17) { IntArray(17) }
val idx = IntArray(4)

fun findGroup(type: Int, minN: Int, maxN: Int, depth: Int): Boolean {
if (depth == 4) {
print("\nTotally \${if (type != 0) "" else "un"}connected group:")
for (i in 0 until 4) print(" \${idx[i]}")
println()
return true
}

for (i in minN until maxN) {
var n = depth
for (m in 0 until depth) if (a[idx[m]][i] != type) {
n = m
break
}
if (n == depth) {
idx[n] = i
if (findGroup(type, 1, maxN, depth + 1)) return true
}
}
return false
}

fun main(args: Array<String>) {
for (i in 0 until 17) a[i][i] = 2
var j: Int
var k = 1
while (k <= 8) {
for (i in 0 until 17) {
j = (i + k) % 17
a[i][j] = 1
a[j][i] = 1
}
k = k shl 1
}
val mark = "01-"
for (i in 0 until 17) {
for (m in 0 until 17) print("\${mark[a[i][m]]} ")
println()
}
for (i in 0 until 17) {
idx[0] = i
if (findGroup(1, i + 1, 17, 1) || findGroup(0, i + 1, 17, 1)) {
println("\nRamsey condition not satisfied.")
return
}
}
println("\nRamsey condition satisfied.")
}
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -

Ramsey condition satisfied.
```

## Mathematica/Wolfram Language

```g = CirculantGraph[17, {1, 2, 4, 8}]
vl = VertexList[g];
ss = Subsets[vl, {4}];
NoneTrue[ss, CompleteGraphQ[Subgraph[g, #]] &]
NoneTrue[ss, Length[ConnectedComponents[Subgraph[g, #]]] == 4 &]
```
Output:

```True
True```

## Mathprog

 Some lines in this example are too long (more than 80 characters). Please fix the code if it's possible and remove this message.
```/*Ramsey 4 4 17

This model finds a graph with 17 Nodes such that no clique of 4 Nodes is either fully
connected, nor fully disconnected

Nigel_Galloway
January 18th., 2012
*/
param Nodes := 17;
var Arc{1..Nodes, 1..Nodes}, binary;

clique{a in 1..(Nodes-3), b in (a+1)..(Nodes-2), c in (b+1)..(Nodes-1), d in (c+1)..Nodes} : 1 <= Arc[a,b] + Arc[a,c] + Arc[a,d] + Arc[b,c] + Arc[b,d] + Arc[c,d] <= 5;

end;
```

This may be run with:

```glpsol --minisat --math R_4_4_17.mprog --output R_4_4_17.sol
```

The solution may be viewed on this page. In the solution file, the first section identifies the number of nodes connected in this clique. In the second part of the solution, the status of each arc in the graph (connected=1, unconnected=0) is shown.

## Nim

Translation of: Kotlin
```var a: array[17, array[17, int]]
var idx: array[4, int]

proc findGroup(kind, minN, maxN, depth: int): bool =

if depth == 4:
echo "\nTotally ", if kind != 0: "" else: "un", "connected group:"
for i in 0..3:
stdout.write idx[i], if i == 3: '\n' else: ' '
return true

for i in minN..<maxN:
var n = depth
for m in 0..<depth:
if a[idx[m]][i] != kind:
n = m
break
if n == depth:
idx[n] = i
if findGroup(kind, 1, maxN, depth + 1):
return true

for i in 0..16: a[i][i] = 2
var j: int
var k = 1
while k <= 8:
for i in 0..16:
j = (i + k) mod 17
a[i][j] = 1
a[j][i] = 1
k = k shl 1

const Mark = "01-"
for i in 0..16:
for m in 0..16:
stdout.write Mark[a[i][m]], if m == 16: '\n' else: ' '

for i in 0..16:
idx[0] = i
if findGroup(1, i + 1, 17, 1) or findGroup(0, i + 1, 17, 1):
quit "\nRamsey condition not satisfied.", QuitFailure

echo "\nRamsey condition satisfied."
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -

Ramsey condition satisfied.```

## PARI/GP

This takes the C solution to its logical extreme.

```check(M)={
my(n=#M);
for(a=1,n-3,
for(b=a+1,n-2,
my(goal=!M[a,b]);
for(c=b+1,n-1,
if(M[a,c]==goal || M[b,c]==goal, next(2));
for(d=c+1,n,
if(M[a,d]==goal || M[b,d]==goal || M[c,d]==goal, next(3));
)
);
print(a" "b);
return(0)
)
);
1
};

M=matrix(17,17,x,y,my(t=abs(x-y)%17);t==2^min(valuation(t,2),3))
check(M)```

## Perl

Translation of: Raku
Library: ntheory
```use ntheory qw(forcomb);
use Math::Cartesian::Product;

\$n = 17;
push @a, [(0) x \$n] for 0..\$n-1;
\$a[\$_][\$_] = '-' for 0..\$n-1;

for \$x (cartesian {@_} [(0..\$n-1)], [(1,2,4,8)]) {
\$i = @\$x[0];
\$k = @\$x[1];
\$j = (\$i + \$k) % \$n;
\$a[\$i][\$j] = \$a[\$j][\$i] = 1;
}

forcomb {
my \$l = 0;
@i = @_;
forcomb { \$l += \$a[ \$i[\$_[0]] ][ \$i[\$_[1]] ]; } (4,2);
die "Bogus!" unless 0 < \$l and \$l < 6;
} (\$n,4);

print join(' ' ,@\$_) . "\n" for @a;
print 'OK'
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
OK```

## Phix

Translation of: Go
```with javascript_semantics
sequence a = repeat(repeat('0',17),17),
idx = repeat(0,4)

function findGroup(integer ch, lo, hi, depth)
if depth == 4 then
string cs = iff(ch='1'?"":"un")
printf(1,"Totally %sconnected group:%s\n", {cs,sprint(idx)})
return true
end if

for i=lo to hi do
bool all_same = true
for n=1 to depth do
if a[idx[n]][i] != ch then
all_same = false
exit
end if
end for
if all_same then
idx[depth+1] = i
if findGroup(ch, 1, hi, depth+1) then
return true
end if
end if
end for
return false
end function

for i=1 to 17 do
a[i][i] = '-'
end for

integer k = 1
while k<=8 do
for i=1 to 17 do
integer j = mod(i-1+k,17)+1
a[i][j] = '1'
a[j][i] = '1'
end for
k *= 2
end while

-- Test case breakage
--a[2][1]='0'; a[1][2]='0'

puts(1,join(a,'\n')&"\n\n")

bool all_good = true
for i=1 to 17 do
idx[1] = i
if findGroup('1', i+1, 17, 1)
or findGroup('0', i+1, 17, 1) then
all_good = false
exit
end if
end for
printf(1,iff(all_good?"Satisfies Ramsey condition.\n":"No good.\n"))
```
Output:
```-1101000110001011
1-110100011000101
11-11010001100010
011-1101000110001
1011-110100011000
01011-11010001100
001011-1101000110
0001011-110100011
10001011-11010001
110001011-1101000
0110001011-110100
00110001011-11010
000110001011-1101
1000110001011-110
01000110001011-11
101000110001011-1
1101000110001011-

Satisfies Ramsey condition.
```

## Python

Works with: Python version 3.4.1
Translation of: C
```range17 = range(17)
a = [['0'] * 17 for i in range17]
idx = [0] * 4

def find_group(mark, min_n, max_n, depth=1):
if (depth == 4):
prefix = "" if (mark == '1') else "un"
print("Fail, found totally {}connected group:".format(prefix))
for i in range(4):
print(idx[i])
return True

for i in range(min_n, max_n):
n = 0
while (n < depth):
if (a[idx[n]][i] != mark):
break
n += 1

if (n == depth):
idx[n] = i
if (find_group(mark, 1, max_n, depth + 1)):
return True

return False

if __name__ == '__main__':
for i in range17:
a[i][i] = '-'
for k in range(4):
for i in range17:
j = (i + pow(2, k)) % 17
a[i][j] = a[j][i] = '1'

# testcase breakage
# a[2][1] = a[1][2] = '0'

for row in a:
print(' '.join(row))

for i in range17:
idx[0] = i
if (find_group('1', i + 1, 17) or find_group('0', i + 1, 17)):
print("no good")
exit()

print("all good")
```
Output same as C:

## Racket

 This example does not show the output mentioned in the task description on this page (or a page linked to from here). Please ensure that it meets all task requirements and remove this message. Note that phrases in task descriptions such as "print and display" and "print and show" for example, indicate that (reasonable length) output be a part of a language's solution.

 This example is incorrect. Please fix the code and remove this message.Details: The task has been changed to also require demonstrating that the graph is a solution.

Kind of a translation of C (ie, reducing this problem to generating a printout of a specific matrix).

```#lang racket

(define N 17)

(define (dist i j)
(define d (abs (- i j)))
(if (<= d (quotient N 2)) d (- N d)))

(define v
(build-vector N
(λ(i) (build-vector N
(λ(j) (case (dist i j) [(0) '-] [(1 2 4 8) 1] [else 0]))))))

(for ([row v]) (displayln row))
```

## Raku

(formerly Perl 6)

Works with: rakudo version 2018.08
```my \$n = 17;
my @a = [ 0 xx \$n ] xx \$n;
@a[\$_;\$_] = '-' for ^\$n;

for flat ^\$n X 1,2,4,8 -> \$i, \$k {
my \$j = (\$i + \$k) % \$n;
@a[\$i;\$j] = @a[\$j;\$i] = 1;
}
.say for @a;

for combinations(\$n,4) -> \$quartet {
my \$links = [+] \$quartet.combinations(2).map: -> \$i,\$j { @a[\$i;\$j] }
die "Bogus!" unless 0 < \$links < 6;
}
say "OK";
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
OK```

## REXX

Mainline programming was borrowed from   C.

```/*REXX program finds & displays a 17 node graph such that any four nodes are neither ···*/
/*────────────────────────────────────────── totally connected nor totally unconnected. */
@.=0;             #=17                           /*initialize the node graph to zero.   */
do d=0  for #;            @.d.d= 2         /*set the diagonal elements to 2 (two).*/
end   /*d*/

do k=1  by 0  while k<=8                   /*K  is doubled each time through loop.*/
do i=0  for #;  j= (i+k) // #    /*set a  row,column  and  column,row.  */
@.i.j= 1;       @.j.i= 1         /*set two array elements to unity (1). */
end   /*i*/
k= k + k                                   /*double the value of K for each loop. */
end             /*k*/
/* [↓]  display a connection grid.     */
do r=0  for #;  _=;       do c=0  for #    /*build rows;  build column by column. */
_= _  @.r.c      /*add  (append)  the column to the row.*/
end   /*c*/

say left('', 9)     translate(_, "─", 2)   /*display  (indented)  constructed row.*/
end   /*r*/
!.= 0                                            /*verify the sub─graphs connections.   */
ok= 1                                            /*Ramsey's connections;   OK  (so far).*/
do   v=0  for #                            /*check the sub─graphs # of connections*/
do h=0  for #                            /*check column connections to the rows.*/
if @.v.h==1  then !._v.v= !._v.v + 1     /*if connected,  then bump the counter.*/
end   /*h*/                              /* [↑]  Note:  we're counting each ··· */
ok= ok  &  !._v.v==# % 2                   /*      connection twice,  so      ··· */
end     /*v*/                              /*      divide the total by two.       */
/* [↓]  check col. with row connections*/
do   h=0  for #                            /*check the sub─graphs # of connections*/
do v=0  for #                            /*check the row connection to a column.*/
if @.h.v==1  then !._h.h= !._h.h + 1     /*if connected,  then bump the counter.*/
end   /*v*/                              /* [↑]  Note:  we're counting each ··· */
ok= ok  &  !._h.h==# % 2                   /*      connection twice,  so      ··· */
end     /*h*/                              /*      divide the total by two.       */
say                                              /*stick a fork in it,  we're all done. */
say  space("Ramsey's condition is"word("'nt", 1+ok) 'satisfied.')     /*show yea─or─nay.*/
```
output   (17x17 connectivity matrix):
```           ─ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 ─ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 ─ 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 ─ 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 ─ 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 ─ 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 ─ 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 ─ 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 ─ 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 ─ 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 ─ 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 ─ 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 ─ 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 ─ 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 ─ 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 ─ 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 ─

Ramsey's condition is satisfied.
```

## Ring

```# Project : Ramsey's theorem

a = newlist(17,17)
for i = 1 to 17
a[i][i] = -1
next
k = 1
while k <= 8
for i = 1 to 17
j = (i + k) % 17
if j != 0
a[i][j] = 1
a[j][i] = 1
ok
next
k = k * 2
end
for i = 1 to 17
for j = 1 to 17
see a[i][j] + " "
next
see nl
next```

Output:

```-11101000110001011
1-1110100011000101
11-111010001100010
011-11101000110001
1011-1110100011000
01011-111010001100
001011-11101000110
0001011-1110100011
10001011-111010000
110001011-11101000
0110001011-1110100
00110001011-111010
000110001011-11100
1000110001011-1110
01000110001011-110
101000110001011-10
1101000100000000-1
```

## Ruby

```a = Array.new(17){['0'] * 17}
17.times{|i| a[i][i] = '-'}
4.times do |k|
17.times do |i|
j = (i + 2 ** k) % 17
a[i][j] = a[j][i] = '1'
end
end
a.each {|row| puts row.join(' ')}
# check taken from Raku version
(0...17).to_a.combination(4) do |quartet|
end
puts "Ok"
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
Ok
```

## Run BASIC

 This example is incorrect. Please fix the code and remove this message.Details: The task has been changed to also require demonstrating that the graph is a solution.
```dim a(17,17)
for i = 1 to 17: a(i,i) = -1: next i
k = 1
while k <= 8
for i = 1 to 17
j = (i + k) mod 17
a(i,j) = 1
a(j,i) = 1
next i
k = k * 2
wend
for i = 1 to 17
for j = 1 to 17
print a(i,j);" ";
next j
print
next i```
```-1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 -1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 -1 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 -1 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 -1 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 -1 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 -1 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 -1 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 -1 1 1 0 1 0 0 0 0
1 1 0 0 0 1 0 1 1 -1 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 -1 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 -1 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 -1 1 1 0 0
1 0 0 0 1 1 0 0 0 1 0 1 1 -1 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 -1 1 0
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -1 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 -1```

## Sidef

Translation of: Ruby
```var a = 17.of { 17.of(0) }

17.times {|i| a[i][i] = '-' }
4.times { |k|
17.times { |i|
var j = ((i + 1<<k) % 17)
a[i][j] = (a[j][i] = 1)
}
}

a.each {|row| say row.join(' ') }

combinations(17, 4, { |*quartet|
var links = quartet.combinations(2).map{|p| a.dig(p...) }.sum
})
say "Ok"
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
Ok
```

## Tcl

Works with: Tcl version 8.6
```package require Tcl 8.6

# Generate the connectivity matrix
set init [split [format -%b 53643] ""]
set matrix {}
for {set r \$init} {\$r ni \$matrix} {set r [concat [lindex \$r end] [lrange \$r 0 end-1]]} {
lappend matrix \$r
}

# Check that every clique of four has at least *one* pair connected and one
# pair unconnected. ASSUMES that the graph is symmetric.
proc ramseyCheck4 {matrix} {
set N [llength \$matrix]
set connectivity [lrepeat 6 -]
for {set a 0} {\$a < \$N} {incr a} {
for {set b 0} {\$b < \$N} {incr b} {
if {\$a==\$b} continue
lset connectivity 0 [lindex \$matrix \$a \$b]
for {set c 0} {\$c < \$N} {incr c} {
if {\$a==\$c || \$b==\$c} continue
lset connectivity 1 [lindex \$matrix \$a \$c]
lset connectivity 2 [lindex \$matrix \$b \$c]
for {set d 0} {\$d < \$N} {incr d} {
if {\$a==\$d || \$b==\$d || \$c==\$d} continue
lset connectivity 3 [lindex \$matrix \$a \$d]
lset connectivity 4 [lindex \$matrix \$b \$d]
lset connectivity 5 [lindex \$matrix \$c \$d]

# We've extracted a meaningful subgraph; check its connectivity
if {0 ni \$connectivity} {
puts "FAIL! Found wholly connected: \$a \$b \$c \$d"
return
} elseif {1 ni \$connectivity} {
puts "FAIL! Found wholly unconnected: \$a \$b \$c \$d"
return
}
}
}
}
}
puts "Satisfies Ramsey condition"
}

puts [join \$matrix \n]
ramseyCheck4 \$matrix
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
Satisfies Ramsey condition
```

## Wren

Translation of: C
Library: Wren-fmt
```import "./fmt" for Fmt

var a = List.filled(17, null)
for (i in 0..16) a[i] = List.filled(17, 0)

var idx = List.filled(4, 0)

var findGroup // recursive
findGroup = Fn.new { |ctype, min, max, depth|
if (depth == 4) {
var cs = (ctype == 0) ? "un" : ""
System.write("Totally %(cs)connected group:")
for (i in 0..3) System.write(" %(idx[i])")
System.print()
return true
}

var i = min
while (i < max) {
var n = 0
while (n < depth) {
if (a[idx[n]][i] != ctype) break
n = n + 1
}
if (n == depth) {
idx[n] = i
if (findGroup.call(ctype, 1, max, depth+1)) return true
}
i = i + 1
}
return false
}

var mark = "01-"
for (i in 0..16) a[i][i] = 2
var k = 1
while (k <= 8) {
for (i in 0..16) {
var j = (i + k) % 17
a[i][j] = 1
a[j][i] = 1
}
k = k << 1
}
for (i in 0..16) {
for (j in 0..16) Fmt.write("\$s ", mark[a[i][j]])
System.print()
}

// Test case breakage
// a[2][1] = a[1][2] = 0

// It's symmetric, so only need to test groups containing node 0.
for (i in 0..16) {
idx[0] = i
if (findGroup.call(1, i+1, 17, 1) || findGroup.call(0, i+1, 17, 1)) {
System.print("No good.")
return
}
}
System.print("All good.")
```
Output:
```- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
All good.
```

## Yabasic

```// Rosetta Code problem: https://www.rosettacode.org/wiki/Ramsey%27s_theorem
// by Jjuanhdez, 06/2022

clear screen
k = 1
dim a(17,17), idx(4)
for i = 0 to 17
a(i,i) = 2 //-1
next i

sub EncontrarGrupo(tipo, mini, maxi, fondo)
if fondo = 0 then
c\$ = ""
if tipo = 0 then c\$ = "des" : fi
print "Grupo totalmente ", c, "conectado:"
for i = 0 to 4
print " ", idx(i)
next i
print
return true
end if

for i = mini to maxi
k = 0
for j = k to fondo
if a(idx(k),i) <> tipo then break : fi
next j

if k = fondo then
idx(k) = i
if EncontrarGrupo(tipo, 1, maxi, fondo+1) then return true : fi
end if
next i
return false
end sub

while k <= 8
for i = 1 to 17
j = mod((i + k), 17)
if j <> 0 then
a(i,j) = 1 : a(j,i) = 1
end if
next i
k = k * 2
wend
for i = 1 to 17
for j = 1 to 17
if a(i,j) = 2 then
print "- ";
else
print a(i,j), " ";
end if
next j
print
next i

// Es simétrico, por lo que solo necesita probar grupos que contengan el nodo 0.
for i = 0 to 17
idx(0) = i
if EncontrarGrupo(1, i+1, 17, 1) or EncontrarGrupo(0, i+1, 17, 1) then
print color("red") "\nNo satisfecho.\n"
break
end if
next i
print color("gre") "\nSatisface el teorema de Ramsey.\n"
end```
Output:
`Same as FreeBASIC entry.`