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a factory has a total of 600 shoes. 300 left shoes, and 300 right shoes. they come in 3 sizes. you know there are 200 of each size. prove that there are at least 100 *pairs* of shoes. if you have two shoes, they are only a pair iff they are of the opposite type (left/right) and the same size.
hint you should use the pidgeon hole principle
hint you should use the pidgeon hole principle