Hells_Kitchen
- 61
- 0
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]
Last edited: