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MathNet 2010 — Part 01 Question 135

Math Olympiad Vault · MathNet 2010 — Part 01

Question 135

Two cats, Bill and Tom, play the following game. They, in turn (Bill starts), eat fishes from the heap of 50 fishes. Per move it is allowed to eat exactly 1, or exactly 4, or exactly 7 fishes. The player wins if he eats the last fish of the heap.
Who of the cats wins if both of them play to win?