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ข้อความเดิมเขียนโดยคุณ Anonymous314

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Let $N$ be postive integer. Some integers are written in a blackboard. Suppose that :

1. The written number is all belong to $1,\ 2,\ \cdots N.$

2. Each of integer of $1,\ 2,\ \cdots N$ is written at least one.

3. The sum of numbers written in the black board is even.

If we mark $X$ to some numbers written and mark $Y$ to all remaining numbers, then prove that we can set the sum of numbers marked $X$ are equal to that of numbers marked $Y$.

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