gistfile1.txt

my $pairs = 5;
my $size = $pairs + 1;

my @x;
@x[0] = 1 xx $size;

for 1 ..^ $size -> $row {
    for reverse 0 .. ($size - $row - 1) -> $col {
	@x[$row][$col] = (@x[$row][$col+1]//0) + @x[$row-1][$col];
    }
}

.say for @x;

my %hash;

for ^1000 {
    my $r = $size-1;
    my $c = 0;

    my $string = '';

    loop {
	if not defined @x[$r][$c+1] {
	    if $r == 0 {
		last;
	    }
	    else {
		$r -= 1;
		$string ~= '[';
	    }
	}
	elsif $r == 0 {
	    $c += 1;
	    $string ~= ']';
	}
	elsif (@x[$r-1][$c] + @x[$r][$c+1]) * rand < @x[$r-1][$c] {
	    $r -= 1;
	    $string ~= '[';
	}
	else {
	    $c += 1;
	    $string ~= ']';
	}
    }

    %hash{$string}++;
}

for %hash.pairs.sort(*.key) {
    say .key, '  ', .value;
}