HMMT 2024 U3

Guts
Answer

Compute the number of even positive integers $n \leq 2024$ such that $1,2, \ldots, n$ can be split into $\frac{n}{2}$ pairs, and the sum of the numbers in each pair is a multiple of 3.

Dataset text NuminaMath olympiads. Quoted with source.

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675

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