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Author: bighairymike Big gold star, 5000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 5865  
Subject: Re: Jealous Neighbors Date: 8/14/2014 5:48 PM
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Now swap spots between center and one of its neighbors top/bottom etc. that produces 26 moves. One neighbor moves twice, but all others once. - Foolman

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I used a different move pattern to arrive at the same answer of 26 moves. I was in the process of posting a solution when I realized that when that last guy moves, either he or whoever he swaps with ends up in a spot that was not one of his adjacent neighbors before anybody moved. One of them ends up in a diagonal spot from his original position. So with that, I came to the conclusion the problem as stated has no solution.

Your rotating rings approach was very creative but I think it leads to this same problem. You have the center guy, swap up or down, so after the move the intial center guy is OK. But the guy he swapped with used to be diagonal from that center before the inner ring rotated so although he moved twice, he remains jealous.

I am anxious to hear the published answer. Good puzzle. Thanks for posting.
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