A guy reads a book. He read for 81 hours last 10 days. Prove that there has been two consecutive days when he read for at least 17 hours.
81 hours / 10 days equals 8,1 hour a day. 2 * 8,1 = 16,2. It isn't 17 hours or I'm missing something. Any suggestions please?
Suppose the hours are undivisible (like marbles)
First we divided the ten days into 5 pairs of 2 consecutive days(we call these 5 consecutive pairs: bins). since $\frac{81}{5}>16$ then by the pidgeonhole principle at least one of these 5 bins has 17 or more days.( since if all of these had 16 or less hours we would have at most 80 hours in the whole period of 10 days).