One of my math professors came up with a variation on Nim (Nim - Wikipedia, the free encyclopedia) that our math club has been puzzling over for a while. Any ideas?
Take some number of coins, and arrange them on a table in piles. Two players, taking turns. A turn consists of removing some number of coins from any pile or piles, with one restriction: you must remove the same number of coins from each pile you take any from. The goal is to remove the final coin or coins.