Solving my son's math homework with Recursion.

magicbox.pl

#!/usr/bin/env perl

use feature qw{ say state signatures } ;
use strict ;
use warnings ;
use utf8 ;

use Data::Dumper ;

my $numbers = [ 3 .. 11 ] ;
my $array ;

recurse_magic_box( $numbers, $array ) ;

sub recurse_magic_box ( $numbers , $array ) {

    # numbers is the list of allowable numbers
    for my $n (@$numbers) {
        push @$array, $n ;
        if ( check_magic_box($array) ) {
            recurse_magic_box( $numbers, $array ) ;
            }
        pop @$array ;
        }
    }

sub check_magic_box ( $array ) {

    for my $n (@$array) {
        my $c = scalar grep {m{$n}} @$array ;
        return 0 if $c > 1 ;
        }

    do {
        my $sum    = 21 ;
        my $checks = [
            [ 0, 1, 2 ], # first row
            [ 3, 4, 5 ], # second row
            [ 6, 7, 8 ], # third row
            [ 0, 3, 6 ], # first col
            [ 1, 4, 7 ], # second col
            [ 2, 5, 8 ], # third col
            [ 0, 4, 8 ], # diagonal from top right
            [ 6, 4, 2 ], # diagonal from bottom right
            ] ;
        for my $check (@$checks) {
            my $s = 0 ;
            for my $p (@$check) {
                $s += $array->[$p] ;
                }
            return 0 if $s != $sum ;
            }
        say join "\t", @$array[ 0 .. 2 ] ;
        say join "\t", @$array[ 3 .. 5 ] ;
        say join "\t", @$array[ 6 .. 8 ] ;
        say '' ;
        } if scalar @$array == 9 ;
    return 1 ;
    }