MathDB
2 piles with 2000 and 2017 coins winning strategy

Source: JBMO Shortlist 2017 C3

July 25, 2018
combinatoricsgame strategycoins

Problem Statement

We have two piles with 20002000 and 20172017 coins respectively. Ann and Bob take alternate turns making the following moves: The player whose turn is to move picks a pile with at least two coins, removes from that pile tt coins for some 2t42\le t \le 4, and adds to the other pile 11 coin. The players can choose a different tt at each turn, and the player who cannot make a move loses. If Ann plays first determine which player has a winning strategy.