The Blocks Problem (from Private Universe Project in Mathematics)
From the popular Annenberg/CPB Channel workshop "Private Universe Project in Mathematics," this Shockwave simulation provides a hands-on way to introduce combinatorics through inquiry: You have two colors of cubes available with which to build towers. Your homework task is to make as many different looking towers as is possible, each exactly four cubes high. A tower always points up, with the little knob on top. Find a way to convince yourself and others that you have found all possible towers four cubes high and that you have no duplicates.