Saturday 15 August 2015

Magic Empress Tour

A new Diagonally Magic Empress (Knight + Rook) Tour


Numbered from c8:

31 08 01 52 29 48 41 50 
02 53 30 07 42 51 28 47 
09 32 03 54 27 46 49 40 
04 55 60 43 06 21 26 45 
61 10 05 22 59 44 39 20 
56 33 62 11 38 19 16 25 
63 12 35 58 23 14 37 18 
34 57 64 13 36 17 24 15 

While going through my notes on knight's tours and checking the file on magic two-knight tours (which are really empress tours since the connecting moves are rook moves) I found this diagonally magic tour which is not among the 14 with quaternary symmetry listed in the manuscript by H. J. R. Murray, detailed on this page of my website:

http://www.mayhematics.com/t/pi.htm#(5)

It is also not in the Glasgow Weekly Herald column of 1873-4 where examples of such tours were first published, unless it is in a part that I didn't get to see when I consulted it at Colindale Newspaper Library in 1996.

I can only conclude that it must have been found when I made a check of Murray's work by searching through the list of knight circuits in quaternary symmetry that was provided to me by T. W. Marlow in 1985 when he used a computer to check the 1882 listing by Paul de Hijo (alias the Abbe Phillippe Jolivald).

I have only now realised that it must be a new discovery.

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