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Use the pigeonhole principle to solve: In an anonymous survey of a group of 20 men and 20 women, the men reported a total of

Use the pigeonhole principle to solve:

In an anonymous survey of a group of 20 men and 20 women, the men reported a total of 81 sexual encounters with women in the group, and all women reported having at most 4 sexual encounters with men in the group. Is everyone telling the truth?

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