Together we will work through countless problems and see how the pigeonhole principle is such a simple but powerful tool in our study of combinatorics.
Since 7 > 3 2, at least one pigeonhole contains 2. The following arrow diagram illustrates the case with seven pigeons and three pigeonholes. Consequently, using the extended pigeonhole principle, the minimum number of students in the class so that at least six students receive the same letter grade is 26. The pigeonhole principle can be used to show a surprising number of results must be true because they are too big to fail. A generalization of the pigeonhole principle states that if pigeonholes, and for some positive integer, then at least one pigeonhole contains + 1 or more pigeons.
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