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3

Part of 2015 Federal Competition For Advanced Students

Problems(1)

Problem 3 — Cut the (Pearl) Rope

Source: 46th Austrian Mathematical Olympiad National Competition Part 1 Problem 3

7/14/2018
Alice and Bob play a game with a string of 20152015 pearls.
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?
(Theresia Eisenkölbl)
Austriagame strategy