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Write the numbers $1,2, \ldots, 2 n$ 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...

Question

Write the numbers $1,2, \ldots, 2 n$ 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.

Write the numbers $1,2, \ldots, 2 n$ 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.



Answers

Write the numbers $1,2, \ldots, 2 n$ 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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