1. May 27, 2009 #1

   Hells_Kitchen

   

   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

   Hells_Kitchen, May 27, 2009
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3. May 29, 2009 #2

   Hells_Kitchen

   

   still no ideas??

    

   Hells_Kitchen, May 29, 2009
4. May 29, 2009 #3

   olliemath

   

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

    

   Last edited: May 29, 2009

   olliemath, May 29, 2009

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