On Algebra and Logic

Postgame Analysis: the Towers of Hanoi

I recently gave my juniors the classic Towers of Hanoi puzzle to play with in small groups.  It went something like this:

You have three plates, and plate #1 has a stack of 5 pancakes, in order from the largest one on the bottom to the smallest on top.  The puzzle is to get the stack onto plate #2 using as few moves as possible.

Two rules: (i) you can only move the top pancake on a stack, and (ii) at no time can any larger pancake be on top of a smaller pancake.

They spent a couple minutes getting familiar with the mechanics of it, and then settled into working together, shifting pancakes and keeping a count of their moves.