61 hours of sleep over 10 nights, and the pigeonhole principle > A student in MATH 2P71 class slept for 61 hours over 10 nights. Show that on some pair of consecutive nights, he slept at least 13 hours. Assume that the student only sleeps an integer number of hours. Could someone take me step by step on how I would apply the pigeon principle to this question and achieve the right answer? I am very lost… I understand the principle itself, I just have trouble applying it to the question.

Divide the ten nights as follows:


1 2 | 3 4 | 5 6 | 7 8 | 9 0


Since we have five pairs of nights but 61 hours of sleep, by the pigeonhole principle there must be at least one pair of nights with $\left\lceil\frac{61}5\right\rceil=13$ or more hours of sleep. This proves the statement.