# Manipulatives

Can you sort a stack of pancakes by size, from the smallest on the top to the largest on the bottom, using only a single plate and a spatula, flipping 2 or more pancakes at the top of the stack (possibly the entire stack) with each flip? How many flips does it take?

Join the ranks of the notables who've tackled this problem, including Bill Gates and David S. Cohen (a.k.a. David X. Cohen, writer & producer of *The Simpsons* and *Futurama*).

In this game, checkers are removed from either end of a row of black and red checkers. But there's a catch: you can only remove palindromes (sequences that are the same, forward and backward).

In this classic puzzle (often used in job interviews), you are given 3 jars, the labels of none of which match their contents. How many samples must you draw from the jars, before you're able to correctly label them?

The rules for this classic game are very simple: The player who removes the last object (from two or more initial piles of objects) wins. But is a winning strategy that simple?

Cook up some polyhedrons by following simple recipes. Invent your own recipes, too!

Is it possible to fold a strip of paper into a shape that can be “flexed”, revealing faces than weren't visible at the start?

Use simple calculations and your intuition to estimate some unexpected quantities.

Use specially shaped blocks to “stomp out” dots on a grid of squares. But if you stomp on a square without a dot, a new one appears! Can you stomp out all the dots?

Imagine building a sponge by removing portions of a cube, then removing similar portions of the cubic pieces that remain, repeating this process *n* times. Can you build such a sponge out of smaller versions of the sponge, or other building blocks?