winning strategy on a game in m x n array , winning condition |x|\ge N
Source: Canada Repêchage 2019/5 CMOQR
March 1, 2020
gamegame strategywinning strategycombinatorics
Problem Statement
Let be a triple of positive integers. Bruce and Duncan play a game on an m\times n array, where the entries are all initially zeroes. The game has the following rules.
The players alternate turns, with Bruce going first.
On Bruce's turn, he picks a row and either adds to all of the entries in the row or subtracts from all the entries in the row.
On Duncan's turn, he picks a column and either adds to all of the entries in the column or subtracts from all of the entries in the column.
Bruce wins if at some point there is an entry with .
Find all triples such that no matter how Duncan plays, Bruce has a winning strategy.