I want to add a 17th fun experiment to my project: infact there is a properties I have still not shown: the number in a specific tile is also the number of different shortest path from the top tile (no backwards move nor lateral ones).

I want to show (colorizing them) all distinct paths in sequence and to do it I need a serie of coordinates: given the following structure

               0-0
            1-0   1-1
         2-0   2-1   2-2
      3-0   3-1   3-2   3-3
   4-0   4-1   4-2   4-3   4-4
5-0   5-1   5-2   5-3   5-4   5-5
[download]

if the user click the node 3-1 i need to have back:

0-0 1-0 2-0 3-1
0-0 1-0 2-1 3-1
0-0 1-1 2-1 3-1
[download]

I have asked in the chatterbox some days ago and oiskuu, Eily and Lanx were so kind to suggest various approach, but franckly i was not able to implement a simple way: infact not all combinations are valid: 0-0 1-0 1-1 2-1 3-1 contains the illigal lateral move 1-0 1-1

Well I can produce all combinations and then throw away solutions with too much moves.. but for sure exists a simpler perlish way.

Squeezing my brain I only ended with naive method to highlight the area of such valid tiles:

sub enum_area{
    my ($x,$y) = split '-', $_[0];
    my $minus = $x - $y; 
    print "$_ " for grep {  
          my ($cx,$cy) = split '-',$_; 
          $cy > $cx  ? 0 : ( $cx-$cy < $minus + 1  ? 1 : 0)
        } 
        glob '{'.(join ',',0..$x).'}-'.
        '{'.(join ',',0..$y).'}';
    
}
[download]

thanks in advance

L*