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Question

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Explanation / Answer

This depends on the sophistication of the proof. It would be better if you provide the level of mathematical proof for this problem.

Suppose not. That is, we suppose that if there are ten ducks paddling in four ponds, then some ponds must contain at most two paddling ducks. Consider the function

[f(x) = leftlceil dfrac{10}{x} ight ceil]

where (x) is the number of ponds and (f(x)) is the least maximum number of ducks in a pond. Let (x = 4). Then,

[f(4) = leftlceil dfrac{10}{4} ight ceil = lceil 2.5 ceil = 3]

which is impossible. Thus, there are some ponds with at least three paddling ducks.

For more references about ceiling functions, see below:

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