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MathNet 2020 — Math Olympiad Vault — Part 01 Question 15

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 01

Question 15

Juli has a deck of 54 cards and proposes the following game to Bruno. Juli puts the cards in a row, some face up and the others face down. Bruno may repeatedly choose a card and turn over that card and its two neighbors, changing face-up cards to face-down and vice versa. Bruno wins if this makes every card face up; otherwise Juli wins. Decide which player has a winning strategy and explain it.