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# There are ten meerkats in a colony

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There are ten meerkats in a colony. Every night, three meerkats stand guard while the others sleep. During a certain period of nights, every group of three meerkats has stood guard exactly once. During that period, how many nights of sleep does each meerkat get?

Nov 3, 2020

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There are $$\binom{10}{3} = 120$$ different combinations of 3 meerkats that have to stand guard. Therefore each meerkat has to stand guard $$\frac{120}{10} = 12$$ nights. That means each meerkat gets 108 nights of sleep.

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If this answer is incorrect, or you are looking for a different answer, feel free to ask me and I can look at the question again :D

Nov 3, 2020