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Thanks for posting this inspiring problem. Similar to what tybalt89 has posted, one can significantly reduce the search space by checking whether for a given number in a given position the remaining numbers would still fit. Below some code to do that based on positions counting from 0 to 5 and each can be vertical or horizontal. Given the output it is nearly trivial to solve the puzzle manually.

use strict; use warnings; my @numbers = qw( 113443 143132 241131 321422 323132 331222 341114 412433 414422 431331 443112 444313 ); # find possible positions my %positions; for my $n (@numbers) { $positions{$n} = []; # frequency of digits in current number my @nfreq = (0) x 5; $nfreq[$_]++ for split //, $n; # check which position is possible for my $p (0..5) { # frequency of digits in current position w/o current number my @freq = (0) x 5; $freq[substr( $_, $p, 1 )]++ for @numbers; $freq[substr( $n, $p, 1 )]--; # check if position is feasible # ie enough of each digit available my $possible = 1; $freq[$_]<$nfreq[$_] and $possible = 0 for 1..4; push @{$positions{$n}}, $p if $possible; } } for my $n (sort { scalar(@{$positions{$a}}) <=> scalar(@{$positions{$b +}}) } @numbers) { print "Number $n can be at positions @{$positions{$n}}.\n"; }

In reply to Re: Number Grid Fillin by hdb
in thread Number Grid Fillin by QM

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