Problem: A social worker has 77 days to make his visits. He wants to make at least one visit a day, and has 133 visits to make. Must there always be a period of consecutive days in which he makes 23 visits? Why?
Using the pigeonhole principle didn't help me conclude anything, which leads me to believe that there is not a period of consecutive days where he makes 23 visits. But how would I prove this? With a counterexample?