If anyone would like more samples to try their code with, I found the following on the web: * http://www.gtoal.com/wordgames/alphametic/testscript * http://www.gtoal.com/wordgames/alphametic/testscript.out The first is a script which poses the problems to their own solving- program. The second shows the solutions that their program produces. Some of the sample equations have multiple solutions, such as 'eins +eins=zwei'. 'united+states=america' has no solutions. And of the few that I've tested with my own solution, 'saturn+pluto+uranus +neptune=planets' takes the longest to solve. Eric ---- Interested in hands-on, on-site Ruby training? See http://LearnRuby.com for information about a well-reviewed class.