Funny, about 13 years ago, someone told me about this exact problem / solution. His professor said that it was impossible to solve the problem without recursion

Funny, about 13 years ago, someone told me about this exact problem / solution. His professor said that it was impossible to solve the problem without recursion. He solved it with the exact solution given, and basically got an A in his class for it (a bet with the professor). Oh well. moving on.