Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, March 27, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Vincent Kusters

Cinderella and the Wicked Stepmother

"Five empty buckets of capacity b stand in the corners of a regular pentagon. Cinderella and her wicked stepmother play a game that goes through a sequence of rounds: at the beginning of every round, the stepmother takes one liter of water from the nearby river, and distributes it arbitrarily over the five buckets. Then Cinderella chooses a pair of neighboring buckets, empties them into the river, and puts them back into the pentagon. Then the next round begins. The stepmother's goal is to make one of these buckets overflow. Cinderella's goal is to prevent this. For which bucket sizes b can the Stepmother eventually enforce a bucket overflow? And for which bucket sizes can Cinderella keep the game running forever?"

This puzzle was proposed (but not selected) for the 50th International Mathematical Olympiad for high-school students that took place in Germany in summer 2009. We consider optimal strategies and characterize optimal bucket sizes for many cases of this game.

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