Hanoi
move the tower. big never sits on small.
tower of hanoi, 4 disks — chase the minimum 15
Four disks can be rebuilt on another peg in a true minimum of fifteen moves, and each additional disk doesn’t add a few more moves — it doubles the total. That doubling, 2^n − 1, is the signature of a certain kind of hard problem, where adding one small piece can make the whole task twice as long.
Concepts: recursion, puzzles.
An interactive you play with one thumb, on Wundr.