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## Main Question or Discussion Point

Hi there,

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

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

Show that [tex]a_{1} = a_{2n} + n[/tex], if [tex] 1 \leq a_{2i} \leq n [/tex] for [tex]i = 1,2, ..., n[/tex]

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

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

Show that [tex]a_{1} = a_{2n} + n[/tex], if [tex] 1 \leq a_{2i} \leq n [/tex] for [tex]i = 1,2, ..., n[/tex]

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