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MathNet 2015-part-01 — 191 problems (EN–VI) Question 29

Math Olympiad Vault · MathNet 2015-part-01 — 191 problems (EN–VI)

Question 29

In each move, one player cuts the string between two pearls and the other player chooses one of the resulting parts of the string while the other part is discarded.
In the first move, Alice cuts the string, thereafter, the players take turns.
A player loses if he or she obtains a string with a single pearl such that no more cut is possible.
Who of the two players does have a winning strategy?