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Jack, Charlie, and Andrew went on an egg hunt today, each of them carrying one basket. 300 eggs were hidden at the beginning of the day. At the end of the day, the numbers of eggs in each of the boys' baskets are three consecutive integers.
In how many ways could this happen?
Clarification: Order doesn't matter. For example, in the order of Charlie, Andrew, and Jack, \((3,2,1)\) and \((2,3,1) \) both count as one way.