Question 11
The game of *Greed* starts with an initial configuration of one or more piles of stones. Player 1 and Player 2 take turns to remove stones, beginning with Player 1. 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 2018 piles, with either 20 or 18 stones in each pile.
(b) There are four piles, with 17, 18, 19, and 20 stones, respectively.
In each case, find an appropriate strategy that guarantees victory to one of the players.
* 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 2018 piles, with either 20 or 18 stones in each pile.
(b) There are four piles, with 17, 18, 19, and 20 stones, respectively.
In each case, find an appropriate strategy that guarantees victory to one of the players.