I wrote a simple [program][1] to check the 5!<sup>3</sup> (1,728,000) arrangements for N=5.

There were no solutions.  The closest was 9 out of 10 pairs (below).

![alt text][2]


  [1]: http://pastebin.com/n1AK9qGE
  [2]: https://content.screencast.com/users/Tom/folders/Jing/media/29da38ee-690b-4a91-9ed5-4e42465a5106/2010-07-25_1939.png