# Lattice paths

*Author: Felix Herrmann*

https://projecteuler.net/problem=15

Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

How many such routes are there through a 20×20 grid?

Source code: prob015-felher.pl

use v6; # This program doesn't really simulate anything and is only here for the # sake of completeness. But to show something cool about perl6 let's at # least introduce the factorial as the ! postfix operator my Int sub postfix:<!>(Int $n) { [*] 1 .. $n } # The strategy for this Problem is quite straight-forward: To move from the # upper left to the lower right corner of an NxN grid without ever going in # the wrong direction one has to go down N times and one has to go right N # times. The problem is therefore equivalent to "How many distinguishable # ways exist to order N white and N black balls?" and the answer to that # problem is: my \N = 20; say (2 * N)!/(N! * N!);