sflitman,
Ok, I have one final contribution. This solution is still roughly O(N) where N is the number of names to check but it turns looking through the 206 unique squares into a hash lookup. It also has a couple of advantages over my previous solution. It only precalculates all solutions once and subsequently loads them from disk. Additionally, it displays all matching solutions, not just the first one found. 
#!/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 o
+utput
    # I used my own from  [id://394168]
    die "Implementation left as an exercise for the user";
}

[download]

Cheers - L~R

In reply to Re: magic squares by Limbic~Region
in thread magic squares by sflitman

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