sub wgc {
    return if $seen{"@_"}++;
    my%x=@_;
    if ($x{b} && $x{c} && $x{g} && $x{w}) {
        print+(sort keys%$_),"\n" for @h;
        exit;
    } elsif ((!$x{b} && ($x{c} && $x{g} || $x{g} && $x{w})) || 
                 ($x{b} && (!$x{c} && !$x{g} || !$x{g} && !$x{w}))) {
        return;
    } else {
        if ($x{b}) {
            delete $x{b};
            for ('xx', keys %x) {
                my %y=%x;
                delete $y{$_};
                local @h=(@h, \%y);
                wgc(%y);
            }
        } else {
            $x{b}=1; {
                local (@h) = (@h, \%x);
                wgc(%x);
            }
            for my $k (qw(c g w)) {
                if (!$x{$k}) {
                    my %y=(%x,$k,1);
                    local (@h) = (@h, \%y);
                    wgc(%y);
                };
            }
        }
    }
}

wgc

##</code><code>##

bg
g
bcg
c
bcw
cw
bcgw

##</code><code>##

sub w{return if$s{"@_"}++;my%x=@_;if($x{b}&$x{c}&$x{g}&$x{w}){print+(sort keys%$_),"\n"for@h;exit;}elsif(($x{b}||!($x{c}&&$x{g}||$x{g}&&$x{w}))&&(!$x{b}||!(!$x{c}&&!$x{g}||!$x{g}&&!$x{w}))){if($x{b}){delete$x{b};for(A,keys%x){my%y=%x;delete$y{$_};local@h=(@h,\%y);w(%y)}}else{$x{b}=1;{local@h=(@h,\%x);w(%x);}for(qw(c g w)){if(!$x{$_}){my%y=(%x,$_,1);local@h=(@h,\%y);w(%y)}}}}}w