#!/usr/bin/perl
use strict;
use warnings;
use Storable;

my $db = 'msquare_solutions.db';
if (! -e $db) {
    my %possible;
    for my $x (5 .. 22) {
        for my $y (grep {$_ != $x} 1 .. int((25 - $x) / 2)) {
            my $max = 26 - $x - 2 * $y;
            my $min = $x - 2 * $y - 1;
            for my $z (grep {$_ != $x && $_ != $y} 1 .. ($min < $max ? $min : $max)) {
                my @square = (
                    ($x + $y),          ($x + $z),  ($x - $y - $z),
                    ($x - 2 * $y - $z),   ($x),     ($x + 2 * $y + $z),
                    ($x + $y + $z),     ($x - $z),  ($x - $y) 
                );
                my @sol = map chr($_ + 64), @square;
                my $pow_iter = powerset(sort @sol);
                while (my @set = $pow_iter->()) {
                    my $key = join '', @set;
                    push @{$possible{$key}}, \@sol;
                }
            }
        }
    }    
    store(\%possible, $db);
}
my $possible = retrieve($db);

for (qw/PAUL JOHN MARTY SHEILA SMACK SUZY ELSA/) {
    my $key = join '', sort split //;
    if ($possible->{$key}) {
        for my $square (@{$possible->{$key}}) {
            print "$_ is contained within '@$square'\n";
        }
    }
    else {
        print "No solution for $_\n";
    }
}

sub powerset {
    # Choose any powerset iterator you want - ensure ascending order output
    # I used my own from  [id://394168]
    die "Implementation left as an exercise for the user";
}