At some arm wrestling championship, the champion had to face at least one opponent per hour, but had no more than 125 meetings over a period of 75 hours. (Here one hours means a period starting at an exact time and going to the next hour.) Knowing this, show that there is a period of consecutive hours during which the champion had exactly 24 matches.
At some pigeon holing championship, the champion had to place at least one pigeon per hole, but had no more than 125 pigeons in 75 holes. Knowing this, show that there are a number of consecutive holes in which the champion had placed exactly 24 pigeons.