Saturday, 13 March 2010

Chess and Mathematics

Last Monday I took part in a chess match, playing on behalf of the Hastings club against a team of four from Kent. I was on the third board. The time allowance was quite generous, which suits my slow play, and I managed a draw. Most of the time I was a knight down, but with the advantage of a passed pawn, so it was a matter of trying to get the pawn promoted. There were a lot of interesting tactical situations that arose the game. The opposing team won overall by 2.5 to 1.5.

On Wednesday I received a letter from Professor Donald E. Knuth of Stanford University. We have previously corresponded on knight's tours, but I hadn't had a letter from him for several years. He is putting together a book of his Selected Papers on Fun and Games which will include several chapters on tours, among much else. I had to look up what "potrzebie" was all about. It seems it's a Polish word adopted by MAD Magazine as a running joke back in the 1960s.

The topic Prof Knuth was asking about concerned the results obtained by Robin H. Merson on non-intersecting knight's paths. As a result I have now placed PDF versions of Robin Merson's two main letters to me, dealing with open and closed paths, on the knight's tours page of my mayhematics website. They haven't scanned very clearly; for instance the background graph lines have not come out, but that's the best I can do at present.

Prof Knuth also likes to collect the middle names of everyone whose work he cites, but I was unable to locate what Robin Merson's "H" stood for. He worked for the Royal Aircraft Establishment at Farnborough on the use of satellites for mapping the Earth, among other activities.


  1. Hi George,

    Nice to see your write-up on Chess and Mathematics. Traditionally, non-intersecting Knight's path have been confined to 2-dimensions but recently, it has been extended into 3-dimensional space as reported in (0803.4259). Please bring it to the kind notice of Prof Knuth (since his e-mail address is not available at his site).

    Robin Merson work is wonderful. He summarises (or conjectures) that maximum length of the tour decreases for n>31. This is very interesting and deserves a deeper study. Does it hold true in 3 (or higher) dimensions too? I request professional mathematicians to look into it.

    With regards,
    Awani Kumar

  2. Prof Knuth is famously not an email user. This is a deliberate policy, probably to preserve his sanity, since I imagine he would be overwhelmed with endless mathematical problems, and he still has Volume 4 of The Art of Computer Programming to finish!

  3. Robert (Robin) Henry Merson
    (courtesy of Tony Merson)
    I have forwarded to Prof. Knuth