Explore the surprising variations in conceptually simple sequences of numbers, constructed by applying one of two operations to generate each successive term. Can you make the sequence return to its starting value?

What happens when generous people sit in a circle, and share candy – under some conditions – with each other?

If we give a bunch of children several pieces of candy, and force them to share with their neighbors in a particular way (with no eating or cheating!), what happens? Let’s explore this and other related sharing scenarios.

Try to find patterns that allow you to predict colors that will appear in rows of dots. Each row is produced from the one above it, following simple rules.

A simple game of strategy, where each player attempts to claim spaces to form an unbroken chain between opposite sides of the board. (See attached image for an example.)

How fast can the cookie monster eat all of the cookies, if he must follow some simple rules?

How long can you keep a simple subtraction process going, before running out of interesting differences?

List all the divisors of *N*, including 1 and *N*, and take turns crossing out a divisor (and all of its divisors that are not yet crossed out). Win by forcing your opponent to cross out the final number on the list. Can you come up with a winning strategy?

Estimathon®, Estimathon® scoring sheet and answer key.

Written and administered by Shannon Rogers

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