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MathNet 2018-part-05 — 181 problems (EN–VI) Question 133

Math Olympiad Vault · MathNet 2018-part-05 — 181 problems (EN–VI)

Question 133

Jure and Miha play a game with two containers of balls, making moves alternately. At the start of the game there are $m$ balls in the white container and $n$ balls in the black container. In each move a player either removes one ball from one of the containers or moves one ball from the white container to the black container. The player who removes the last ball from the containers wins. Depending on $m$ and $n$, determine who has a winning strategy if Jure moves first.