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winning strategy, writing words on a blackboard

Source: 1st Mathematics Regional Olympiad of Mexico Northwest 2018 P2

September 6, 2022
combinatoricswinning strategy

Problem Statement

Alicia and Bob take turns writing words on a blackboard. The rules are as follows: a) Any word that has been written cannot be rewritten. b) A player can only write a permutation of the previous word, or can simply simply remove one letter (whatever you want) from the previous word. c) The first person who cannot write another word loses. If Alice starts by typing the word ''Olympics" and Bob's next turn, who, do you think, has a winning strategy and what is it?