# A permutation with a special property question!

1. May 27, 2009

### Hells_Kitchen

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 $$i = 1,2, ..., n$$

Last edited: May 27, 2009
2. May 29, 2009

### Hells_Kitchen

still no ideas??

3. May 29, 2009

### olliemath

According to my calculations (proof) it's not possible.. Try proving this..

Last edited: May 29, 2009