gistfile1.txt

== Attempt 1

sub all-possible-orderings(@a, @prefix=[]) {
    return [@prefix] unless @a.elems;
    return gather for @a.kv -> $k, $v {
        my @others = @a[0..^$k, $k^..^*];
        take all-possible-orderings(@others, [@prefix.values, $v])
    }
}

sub langford(@a) {
    for 1..(@a/2) -> $n {
        for @a.kv -> $k1, $v1 {
            if $v1 == $n {
                for @a[$k1^..^*].kv -> $k2, $v2 {
                    if $v2 == $n {
                        return False if $k2 != $n
                    }
                }
            }
        }
    }
    return True
};

say $_.join() for all-possible-orderings([1,1,2,2,3,3]).grep({ langford($_) }).uniq

== Attempt 2

sub langford(@candidates, @slots = [0 xx 2*@candidates]) {

    return [@slots] unless @slots.grep: { !$_ };

    my @found;

    for @candidates -> $c {
        for @slots[0..@slots-$c-2].kv -> $k, $v {
            if !$v && !@slots[$k+$c+1] {
                my @new-slots = @slots; @new-slots[$k, $k+$c+1] = $c, $c;
                push @found,
                     langford((grep { $_ != $c }, @candidates),
                              @new-slots);
                last;
            }
        }
    }

    return @found;
}

.join.say for langford(1..4)