http://www.ancientcityruby.com/snake_case/

snake_case.rb

#!/usr/bin/env ruby

##
# Solution for http://www.ancientcityruby.com/snake_case/
#
# How many different paths could I take from the northwest corner to the
# southeast corner of a rectangular grid, only ever moving south or east?
#
# Usage: ./snake_case.rb <size
#        ./snake_case.rb <length> <width>
#
# where <size> is the size of a square grid, e.g., for a 2x2 grid, size is 2
# (default size is 10). Use <length> and <width> for non-square grids.
#

def factorial(x)
  return (1..x).inject(:*) || 1
end

def count_paths(length, width)
  top = factorial(length + width)
  bottom = factorial(length) * factorial(width)
  return top / bottom
end

if ARGV[0]
  if ARGV[1]
    length = ARGV[0].to_i
    width = ARGV[1].to_i
  else
    length = width = ARGV[0].to_i
  end
else
  length = width = 10
end

puts count_paths(length, width)

Replaced the recursive factorial function with an iterative one as it was hitting stack limits for large values of x.