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?

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?

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

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*).

Fold a long strip of paper in half several times. Can you see a pattern in the creases formed along the length of the paper? What sorts of route do we trace if we use the creases to direct our turns along a path?