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Omni-MATH / Allen and Yang want to share the numbers 1,2,3,4,5,6,7,8,9,10. How many ways are there to split all ten numbers among Allen and Yang so that each person gets at least one number, a…

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problem

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?
Plain-text mathematical notation (without MathML)
Allen and Yang want to share the numbers 1,2,3,4,5,6,7,8,9,10. 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?
Original LaTeX notation
Allen and Yang want to share the numbers \(1,2,3,4,5,6,7,8,9,10\). 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?

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