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I wrote a simple program to check the 5!3 (1,728,000) arrangements for N=5.
There were no solutions. The closest was 9 out of 10 pairs (below).
alt text http://content.screencast.com/users/Tom/folders/Jing/media/29da38ee-690b-4a91-9ed5-4e42465a5106/2010-07-25_1939.png