# A permutation with a special property question!

## Main Question or Discussion Point

Hi there,
i was wondering if you had any thoughts on the following question:

Let $$(a_{1}, a_{2}, ..., a_{2n})$$ be a permutation of $${1, 2, ..., 2n}$$ so that $$|a_{i} - a_{i+1}| \neq |a_{j} - a_{j+1}|$$, whenever $$i \neq j$$.

Show that $$a_{1} = a_{2n} + n$$, if $$1 \leq a_{2i} \leq n$$ for $$i = 1,2, ..., n$$

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