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

my @cube = (
    [[qw/p g p y/], [qw/g g y r/], [qw/g g r p/]],
    rotations('rprrgy'),
    rotations('ppryyg'),
);
my %cube4 = map {("@$_" => 1)} @{rotations('rrygpy')};

for my $c1 (@{$cube[0]}) {
    for my $c2 (@{$cube[1]}) {
        for my $c3 (@{$cube[2]}) {
            my $sol = find_sol($c1, $c2, $c3);
            print "@$c1\n@$c2\n@$c3\n$sol\n\n" if $cube4{$sol};
        }
    }
}

sub find_sol {
    my ($c1, $c2, $c3) = @_;
    my @sol;
    for my $i (0 .. 3) {
        my %free = map {$_ => undef} qw/r g y p/;
        delete @free{ map $_->[$i], $c1, $c2, $c3 };
        push @sol, keys %free;
    }
    return "@sol";
}

sub rotations {
    my (%seen, @rot);
    my @cube = split //, shift @_;
    for ([0 .. 3], [1, 4, 3, 5], [4, 0, 5, 2]) {
        my @col = @cube[@$_];
        push @rot, map {push @col, shift @col; $seen{"@col"}++ ? () : [@col]} 1..4;
        @col = reverse @{$rot[-1]};
        push @rot, map {push @col, shift @col; $seen{"@col"}++ ? () : [@col]} 1..4;
    }
    return \@rot;
}

##</code><code>##

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

my @cube = (
    [[qw/p g p y/], [qw/g g y r/], [qw/g g r p/]],
    rotations('rprrgy'),
    rotations('ppryyg'),
);
my %cube4 = map {("@$_" => 1)} @{rotations('rrygpy')};

my @used;
for my $c1 (@{$cube[0]}) {
    @used = map {{$_ => 1}} @$c1;
    CUBE2:
    for my $c2 (@{$cube[1]}) {
        $used[$_]{$c2->[$_]} && next CUBE2 for 0 .. 3;
        $used[$_]{$c2->[$_]} = 1 for 0 .. 3;
        CUBE3:
        for my $c3 (@{$cube[2]}) {
            $used[$_]{$c3->[$_]} && next CUBE3 for 0 .. 3;
            my $sol = find_sol($c1, $c2, $c3);
            print "@$c1\n@$c2\n@$c3\n$sol\n\n" if $cube4{$sol};
        }
        $used[$_]{$c2->[$_]} = 0 for 0 .. 3;
    }
}

sub find_sol {
    my ($c1, $c2, $c3) = @_;
    my @sol;
    for my $i (0 .. 3) {
        my %free = map {$_ => undef} qw/r g y p/;
        delete @free{ map $_->[$i], $c1, $c2, $c3 };
        push @sol, keys %free;
    }
    return "@sol";
}

sub rotations {
    my (%seen, @rot);
    my @cube = split //, shift @_;
    for ([0 .. 3], [1, 4, 3, 5], [4, 0, 5, 2]) {
        my @col = @cube[@$_];
        push @rot, map {push @col, shift @col; $seen{"@col"}++ ? () : [@col]} 1..4;
        @col = reverse @{$rot[-1]};
        push @rot, map {push @col, shift @col; $seen{"@col"}++ ? () : [@col]} 1..4;
    }
    return \@rot;
}