HMMT November 2024 H7
- Theme
- Answer
Jasper and Rose are playing a game. Twenty-six 32 -ounce jugs are in a line, labeled Quart A through Quart Z from left to right. All twenty-six jugs are initially full. Jasper and Rose take turns making one of the following two moves:
- Remove a positive integer number of ounces from the leftmost nonempty jug, possibly emptying it
- Remove an equal positive integer number of ounces from the two leftmost nonempty jugs, possibly emptying one or both of them. (Attempting to remove more ounces from a jug than it currently contains is not allowed.)
Jasper plays first. A player's score is the number of ounces they take from Quart Z. If both players play to maximize their score, compute the maximum score that Jasper can guarantee.
Dataset text NuminaMath olympiads. Quoted with source.
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