MathDB

Amy and Bob play a game. They alternate turns, with Amy going first. At the start of the game, there are

20

cookies on a red plate and

14

on a blue plate. A legal move consists of eating two cookies taken from one plate, or moving one cookie from the red plate to the blue plate (but never from the blue plate to the red plate). The last player to make a legal move wins; in other words, if it is your turn and you cannot make a legal move, you lose, and the other player has won. Which player can guarantee that they win no matter what strategy their opponent chooses? Prove that your answer is correct.

Problem Statement