N-Queens Problem and Feynman

Some time back, I received a group mail from the only mailing list that I subscribe to outside of my institute. The sender conjectures from empirical evidence that if the solutions of the N-Queen problem are seen as elements of S(N), then the group generated by them inside S(N) (let’s call it Q(N)) seems to be isomorphic to S(N) for N>=7. She has already verified it for N=7, 8, 9 and 10 computationally.

[He also has checked that Q(4) = Z_4, Q(5) is a semidirect product of Z_5 and Z_4, Q(6) = Z_6. ]

Old habits die hard. The first thing I did was to look up wikipedia on N-Queen problem. Right there towards the end, in the Related Problems section, it says that In 1992, Demirörs, Rafraf, and Tanik published a method for converting some magic squares into n queens solutions, and vice versa.

It was a surprise to learn about my pet little idea from wikipedia. I had even published an article on a closely related idea in an obscure bilingual magazine called Leelavati’s Page, at the end of which I had declared that the ideas discussed led to certain interesting algorithms to find solutions to the N-Queen problem. However, when I went with my article next month, I learned that the magazine had to be closed down. Mathematics wasn’t exactly the hottest thing from the place I hail.

But I must confess that I only had a nice dependable and working algorithm (checked with a computer). I had no idea why it worked.

Since then I had been sitting on the idea, waiting for some leisure when I could attack the problem with all my concentration. I guess now I’ll read their paper instead.

The only silver lining here is a comment made by Feynman, pointed out by A (the one I wrote the screenplay with). He said that one starts by rediscovering ideas from the ancient times, and goes on discovering more and more recent ideas. Eventually, one catches up with his own time, and thenceforth he can call his ideas his own. So I am in 1992 right now. I have two more decades (roughly) to catch up with.

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Incorrigible Introvert

I wouldn't pretend I have a worthy tale to tell, I have only the ramifications of a twisted mind to sell.
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One Response to N-Queens Problem and Feynman

  1. murat tanik says:

    I just noticed your note….I am one of the authors. The others were my students.
    we have much more on that. I teach at university level.

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