Anonymous user
Talk:Peaceful chess queen armies: Difference between revisions
→Error in solution?: Maximim not asked for in task description.
m (→Simplified Python exhaustive search: Sig.) |
(→Error in solution?: Maximim not asked for in task description.) |
||
(2 intermediate revisions by 2 users not shown) | |||
Line 1:
==
I was experimenting with various things when doing the Python.
This is
Exhaustive search.
<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 = '♛', '<font color="green">♕</font>'
_or = set.__or__
def place(m, n):
"Place m black and white queens, peacefully, on an n-by-n board"
# 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
for whites in
if not black_attacks & whites:
return blacks, whites
Line 25 ⟶ 45:
@lru_cache(maxsize=None)
def queen_attacks_from(pos, n=n):
a = set([pos]) # Its position
a.update(range(
a.update(range(
# 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
# r-to-l diag
y1 = y0 +x0 -x1
if 0 <= y1 < n:
a.add
return a
def pboard(black_white=None, n=n):
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
if
print()
ch = ('?' if xy in blk and xy in wht
else
else
else _bbullet if (
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:
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)
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.
<div style="overflow:scroll; height:250px;">
<b># Can't place 1+ queens on a 2-by-2 board</b><br><br>
<br><b>## 1 black and 1 white queens on a 3-by-3 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>
</tr>
<tr>
<td style="width:16pt; height:16pt;"><font color="green">♕</font></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>
</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 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">♛</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>
</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;"><font color="green">♕</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>
</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">♛</td>
<td style="width:16pt; height:16pt;">♛</td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"><font color="green">♕</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">♕</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 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;"></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"></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;"><font color="green">♕</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</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">♛</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;"><font color="green">♕</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">♕</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">♕</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">♕</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">♛</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">♕</font></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>
</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">♕</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
<td style="width:16pt; height:16pt;"><font color="green">♕</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">♕</font></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>
</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">♕</font></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>
</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">♕</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;">♛</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">♛</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">♕</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">♕</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;">♛</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">♛</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">♕</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;">♛</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;"><font color="green">♕</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">♕</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">♕</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">♕</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;">♛</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">♕</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">♕</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;">♛</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>
</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">♛</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;"><font color="green">♕</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">♕</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">♕</font></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;"></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">♕</font></td>
<td style="width:16pt; height:16pt;"><font color="green">♕</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>
<br><b>## 5 black and 5 white queens on a 7-by-7 board:</b><br>
<table>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">♕</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">♕</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;">♛</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>
<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;">♛</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>
<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;"></td>
</tr>
<tr>
<td style="width:16pt; height:16pt;" bgcolor="silver"><font color="green">♕</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">♕</font></td>
<td style="width:16pt; height:16pt;"><font color="green">♕</font></td>
<td style="width:16pt; height:16pt;" bgcolor="silver"></td>
</tr>
</table>
<br>
</div>
--[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 10:08, 27 March 2019 (UTC)
== Error in solution? ==
No solutions for {8,9},{10,14} and some other boards. For {9, 12} correctly:
B * x * B * x * B
* x W x * x W x *
B * x * B * x * B
* x W x * x W x *
B * x * B * x * B
* x W x * x W x *
B * x * B * x * B
* x W x * x W x *
x W x W x W x W x
I checked C and C++ codes and compare results from https://oeis.org/A250000
Hi, Please sign your contribution bove, thanks. --[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 10:58, 19 January 2020 (UTC)
:If you carefully check the wording of the task, it doesn't ask for ''maximum'' numbers of armies.
:Language implementations might well have implied this though which may need individual mods.
:Thanks for spotting it. --[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 10:58, 19 January 2020 (UTC)
|