1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A permutation with a special property question!

  1. May 27, 2009 #1
    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]
     
    Last edited: May 27, 2009
  2. jcsd
  3. May 29, 2009 #2
    still no ideas??
     
  4. May 29, 2009 #3
    According to my calculations (proof) it's not possible.. Try proving this..
     
    Last edited: May 29, 2009
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A permutation with a special property question!
Loading...