Its very nicely coded and credit to the author, but I think people might infer from your description something more than its actually doing, which is basically

Its very nicely coded and credit to the author, but I think people might infer from your description something more than its actually doing, which is basically 'brute force' - trying every combination and crossing them off when they fail (hence your quoted code above). The alternative approach would be to work like humans do, looking for the next 'right' square (rather than this, which looks for the next 'wrong' combination). This would be much more difficult but would solve the hard problems much faster and computationally elegantly (though its only a matter of seconds anyway!). [EDIT] I created an derivative version in ruby for anyone who is interested (42 lines of code - probably could be shorter) - http://pastebin.com/ecjQzzU6 http://pastebin.com/ecjQzzU6