Potato Farm
Four algorithms (for kids I use the words "recipes") are applied repeatedly to split up farmland. You must figure out how they work before I explain them.
Inductive problem-solving is undervalued and underrepresented in our curriculum. It's the type of problem-solving that has you struggling to find a pattern. You know "2, 4, 6, 8 what comes next?" Well that's just the start. We should be teaching inductive problem-solving throughout K-12.
I call these mini-mathematical-universes. It is on puzzles like this that students first learn the scientific method. It is so much better to learn it here than trying to grapple with the real universe. These universes were created to reveal their secrets. The real world is non-compliant in this respect! ;-)