a grim knight [cont’d]

October 19, 2016
By

(This article was first published on R – Xi'an's Og, and kindly contributed to R-bloggers)

As discussed in the previous entry, there are two interpretations to this question from The Riddler:

“…how long is the longest path a knight can travel on a standard 8-by-8 board without letting the path intersect itself?”

riddlerechckas to what constitutes a path. As a (terrible) chess player, I would opt for the version on the previous post, the knight moving two steps in one direction and one in the other (or vice-versa). But one can consider instead the graph of the moves of that knight, as in the above picture. And since I could not let the problem go I also wrote an R code (as clumsy as the previous one!) to explore at random (with some minimal degree of annealing) the maximum length of a self-avoiding knight canter. riddlerechkThe maximal length I found this way is 32 (I first erased the resulting path by mistake but then recovered it by re-running the code a few times), although I also came by hand to a spiralling solution with a length of 33.

riddlerechckRunning the R code longer however led to a path of length 34, while the exact solution to the riddle is 35, as provided by the Riddler (and earlier in many forms, including Martin Gardner’s and Donald Knuth’s).

[An unexpected side-effect of this riddle was ending up watching half of Bergman’s Seventh Seal in Swedish…]

Filed under: Books, Kids, pictures, R, Statistics Tagged: chess, Donald Knuth, Ingmar Bergman, knight, Martin Gardner, self-avoiding random walk, The Riddler, The Seventh Seal

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