2 players game of Greed, moving stones between piles, winning strategy
Source: Irmo 2018 p2 q10
September 16, 2018
game strategycombinatorics
Problem Statement
The game of Greed starts with an initial configuration of one or more piles of stones.
Player and Player take turns to remove stones, beginning with Player . At each turn, a player has two choices:
• take one stone from any one of the piles (a simple move);
• take one stone from each of the remaining piles (a greedy move).
The player who takes the last stone wins.
Consider the following two initial configurations:
(a) There are piles, with either or stones in each pile.
(b) There are four piles, with , and stones, respectively.
In each case, find an appropriate strategy that guarantees victory to one of the players.