# Unkown Blogger Pursues a Deranged Quest for Normalcy

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## Salesman on a Circle

Posted by ubpdqn on June 20, 2013

I explore a puzzle about arranging a set of integers (1,2,3,…14) in a circle such that the any pair of numbers next to each have the property that their sum is prime and the absolute difference is prime. I came across this from a tweet by Professor Strogatz (the link is here).

This is the “Travelling Salesman” problem in disguise.  The mindless brute force approaches of  testing permutations (all the pairs) and finding gives an insight into the scalability issue of this problem. The issue of whether a solution exists for the small scale was resolved by finding it! Whether it s unique is a harder but fortunately the enormity of comparisons can be whittled down.

After a little thought, the property defines the way in which the integers are linked. It is a bipartite graph as the odd numbers must link to even numbers. This can be seen…

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