Hanoi
move the tower. big never sits on small.
tower of hanoi, 4 disks — chase the minimum 15
Four disks move to another peg in a minimum of fifteen moves, and each extra disk doesn't add a few moves, it doubles the total: the signature of a problem where one small piece doubles the whole task.
Concepts: recursion, puzzles.
An interactive you play with one thumb, on Wundr.