There are ten meerkats in a colony. Every night, two meerkats stand guard while the others sleep. During a certain period of nights, every meerkat stands guard with every other meerkat exactly once. During that period, how many nights of sleep does each meerkat get?
I can use the combination formula to find the number of ways to choose two meerkats out of ten: C(10,2) = 10! / (2! * 8!) = 45. So there are 45 possible pairs of meerkats, and each pair stands guard once. That means the period of nights is 45 nights long. During that time, each meerkat stands guard nine times, since there are nine other meerkats to pair with. Therefore, each meerkat sleeps 45 - 9 = 36 nights. 