When I coached a programming team, I once had them algorithmically solve this problem for a N-star flag. The constraints were to find all possible combinations

When I coached a programming team, I once had them algorithmically solve this problem for a N-star flag. The constraints were to find all possible combinations where the rows alternated in length by 1. It ended up being a great teaching experience because it was really easy for the students to visualize it and play around with the problem on the whiteboard. It's also a really easy problem to solve without code so the students can easily verify their code and gain confidence.