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?
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?
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?