Exercise 11.3.1: Applying the pigeonhole principle - heights and times. About Apply the pigeonhole principle to answer the following questions. If the pigeonhole principle can not be applied, give a specific counterexample. (a) A team of three high jumpers all have a personal record that is at least 6 feet and less than 7 feet. Is it necessarily true that two of the team members must have personal records that are within four inches of each other