Problem: A supermarket has crates of apples. Each crate contains at least apples and at most apples. What is the largest integer such that there must be at least crates containing the same number of apples?
Answer Choices:
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Solution:
There are 25 different possibilities for the number of apples a crate can contain. If there were no more than five crates containing any given number of apples, there could be at most crates. Since there are 128 crates, . But also, , since it is possible that there are six crates containing apples for and five crates containing apples for .