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MathNet 2023-part-01 — 191 problems (EN–VI) Question 25

Math Olympiad Vault · MathNet 2023-part-01 — 191 problems (EN–VI)

Question 25

We have 10 bottles, each with 1-liter capacity. Initially, 9 of them are empty and the other is completely filled with orange juice. A move consists of picking a non-empty bottle, dividing its content into 3 equal parts, and placing these 3 parts in any 3 bottles. Is it possible, after a sequence of moves, that all 10 bottles contain the same amount of orange juice?