2012 ToT Fall Junior A p2 Chip and Dale play a game with 222 nuts
Source:
March 22, 2020
combinatoricsgame
Problem Statement
Chip and Dale play the following game. Chip starts by splitting nuts between two piles, so Dale can see it. In response, Dale chooses some number from to . Then Chip moves nuts from the piles he prepared to a new (third) pile until there will be exactly nuts in any one or two piles. When Chip accomplishes his task, Dale gets an exact amount of nuts that Chip moved. What is the maximal number of nuts that Dale can get for sure, no matter how Chip acts? (Naturally, Dale wants to get as many nuts as possible, while Chip wants to lose as little as possible).