IMO Problem 6
Five identical empty buckets of -liter capacity stand at the vertices of a regular pentagon. Cinderella and her wicked Stepmother go 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. Then the next round begins. The Stepmother’s goal is to make one of these buckets overflow. Cinderella’s goal is to prevent this. Can the wicked Stepmother enforce a bucket overflow?
This problem is from the IMO.This problem is from the IMO.This problem is part of this set .
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1 solution
Suppose that the wicked grandmother eventually gets 2.5 or more litres of water into the buckets, in any arrangement. Even with the most ideal arrangement of water in the buckets, 0.5 litre for each bucket, Cinderella is able to remove at least 1 litre, which means that Cinderella can now take away as much water is replenished, or more.