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HMMT 2018 U3

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Allen and Yang want to share the numbers 1,2,3,4,5,6,7,8,9,101,2,3,4,5,6,7,8,9,10. How many ways are there to split all ten numbers among Allen and Yang so that each person gets at least one number, and either Allen's numbers or Yang's numbers sum to an even number?

Dataset text NuminaMath olympiads. Quoted with source.

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1022

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