C:\test>215606
No 2-column solutions found
There are 1956 3-column solutions

C:\test>

##</code><code>##

#! perl -slw
use strict;
my @cols=(0x15);

while (<DATA>) {
	my @c = split' ';
	$cols[$_] |= ($c[$_]<<($.-1)) for 0..$#c;
}

my $test = 0;
$test |= $_ for @cols;

print "There is no solution\n" and exit if $test != 32767;

my @found;
# look for 2 column solutions...
for my $first (0..$#cols) {
	for my $second (0..$#cols) {
		next if $first == $second;
			push @found, [$first,$second]
		# and print "Columns $first & $second is a solution"
			if	(($cols[$first] | $cols[$second]) == 32767);
	}
}
if (@found) {
	print 'There are ', scalar @found, ' 2-column solutions';
	exit;
} else {
	print 'No 2-column solutions found';
}

# look for 3 column solutions...
for my $first (0..$#cols) {
	for my $second (0..$#cols) {
		for my $third (0..$#cols) {
			next if $first == $second or $first == $third or $second == $third;
			my $route = $cols[$first] | $cols[$second] | $cols[$third];
				push @found, [$first, $second, $third]
			# and print "Columns $first & $second & $third is a solution"
				if	$route == 32767;
		}
	}
}

if (@found) {
	print 'There are ', scalar @found, ' 3-column solutions';
	exit;
} else {
	print 'No 3-column solutions found\n';
}
__DATA__
1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0
0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1
1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0
1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 1
1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1
0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 1 0
0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1
0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1
1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1
1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1
1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0
0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1
1 1 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1
1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 0 0