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MathNet 2019-part-02 — 184 problems (EN–VI) Question 123

Math Olympiad Vault · MathNet 2019-part-02 — 184 problems (EN–VI)

Question 123

42 pebbles are placed on a table. Two players take turns making moves. When making a move, a player has to take at least one pebble, but no more than half of the remaining pebbles. The player after whose move there is exactly one pebble left on the table, wins.
Which player can win regardless of how his opponent plays?
(United Kingdom 2014)