Can you arrange a set of numbers in pairs, so that the sum of each pair is a perfect square? What if the sums must be primes? What if the sums must all be distinct? Discover the surprising variations in this simple challenge.

Every journey has its costs and its rewards. Can you complete this one without any debt?

A twist on the game of Dots and Boxes – but instead of capturing as many squares as possible, you and your opponent are going after gold doubloons!

In Evenland, the citizens never invented the number one; instead, they started with 2, and built up sums and products from that starting point. What can we say about prime numbers in Evenland?

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

This fleshed out activity based upon the John Conway game "Brussels Sprouts" teaches the game and then provides a teacher's guide for leading further investigations.

In how many ways can you draw a star using all the vertices of a polygon, without lifting your pencil from the paper? Are there some polygons for which it's not possible?

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?

Can you see the light? That is, can you see the patterns in light bulbs that are left on, after repeatedly following a simple rule to switch them on and off?

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?