# Large algorithm issue -- 5x5 grid, need to fit 5 queens plus some squares

Tim Roberts timr at probo.com
Fri Mar 17 09:03:01 CET 2006

```"totalgeekdom at gmail.com" <totalgeekdom at gmail.com> wrote:

>Background:
>The problem I'm trying to solve is.
>There is a 5x5 grid.
>You need to fit 5 queens on the board such that when placed there are
>three spots left that are not threatened by the queen.

I know this wasn't a contest, but here's my solution.  This finds 8
solutions, which are all reflections and rotations of each other:

rows = (
(  1,  2,  3,  4,  5 ),
(  6,  7,  8,  9, 10 ),
( 11, 12, 13, 14, 15 ),
( 16, 17, 18, 19, 20 ),
( 21, 22, 23, 24, 25 ),
( 1, 6, 11, 16, 21 ),
( 2, 7, 12, 17, 22 ),
( 3, 8, 13, 18, 23 ),
( 4, 9, 14, 19, 24 ),
( 5, 10, 15, 20, 25 ),
( 16, 22 ),
( 11, 17, 23 ),
( 6, 12, 18, 24 ),
( 1, 7, 13, 19, 25 ),
( 2, 8, 14, 20 ),
( 3, 9, 15 ),
( 4, 10 ),
( 2, 6 ),
( 3, 7, 11 ),
( 4, 8, 12, 16 ),
( 5, 9, 13, 17, 21 ),
( 10, 14, 18, 22 ),
( 15, 19, 23 ),
( 20, 24 )
)

zeros = [ 0 ] * 25

def printme( cells ):
for i,j in enumerate(cells):
print "%2d" % j,
if i % 5 == 4:
print

def check( queens ):
cells = zeros[:]
for q in queens:
for row in rows:
if q in row:
for x in row:
cells[x-1] = 1
nils = len( [1 for k in cells if not k] )
if nils >= 3:
for i in queens:
cells[i-1] = 9
print queens
printme( cells )

for q1 in range(25):
for q2 in range(q1+1,25):
for q3 in range(q2+1,25):
for q4 in range(q3+1,25):
for q5 in range(q4+1,25):
check( [q1+1,q2+1,q3+1,q4+1,q5+1] )
--
- Tim Roberts, timr at probo.com
Providenza & Boekelheide, Inc.

```