Question: Write the numbers 1, 2, . . . , 2n on a blackboard, where n is an odd integer. Pick any two of the numbers,

Write the numbers 1, 2, . . . , 2n on a blackboard, where n is an odd integer. Pick any two of the numbers, j and k, write |j − k| on the board and erase j and k. Continue this process until only one integer is written on the board. Prove that this integer must be odd.

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