Дубанов И.С.

In five pots standing in a row, Rabbit poured three kilograms of honey (not necessarily into each and not necessarily equally). Winnie-the-Pooh can take any two adjacent pots. What is the maximum amount of honey that Winnie-the-Pooh can guarantee to eat?

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Evaluation. Let's assume Winnie-the-Pooh cannot take at least a kilogram of honey. This means that in any pair of adjacent pots, there is less than a kilogram of honey. This is true for both the two rightmost pots and the two leftmost pots. However, then in the middle pot, there must be more than a kilogram of honey (otherwise, the total amount of honey would be less than 3 kg). This is a contradiction. Therefore, Winnie-the-Pooh will always be able to take at least a kilogram of honey. Example. If the first, third, and fifth pots each contain 1 kg of honey, and the second and fourth pots are empty, then Winnie-the-Pooh will not be able to eat more than a kilogram of honey.

## Answer

1 kg.