Tuesday, 10 March 2020

Magic Knight Tours 8x10 and 8x14

On my 80th Birthday, and shortly after, I was sent a series of 80-cell magic knight tours on the 8x10 rectangle by Guenter Stertenbrink and later some by Awani Kumar. 

Some of the tours in the Stertenbrink list are closed tours with a complete braid along the bottom border. This can be extended, in four different ways, to cover a further four rows forming a magic 8x14 tour. Here is one example that I sent to these correspondents on 18 February.

These tours answer the final missing cases of Magic Knight Tours on rectangular boards.

07 62 07 52 09 56 01 58
06 51 06 61 04 59 10 55
49 08 63 08 53 12 57 02
64 05 50 05 60 03 54 11
09 48 65 04 27 30 83 86
02 67 46 11 82 85 28 31
47 10 03 66 29 26 87 84
68 01 12 45 88 81 32 25
13 44 99 70 23 34 89 80
00 69 14 43 90 79 24 33
41 16 71 98 35 22 77 92
72 97 42 15 78 91 36 21
17 40 95 74 19 38 93 76
96 73 18 39 94 75 20 37

Underlined: add 100.

The formations on the fifth to eighth ranks down are familiar: a double Beverley quad, and a Snake-head formation as in the 12x12 magic tour by the Rajah of Mysore.

I am not able to do geometrical diagrams as yet on my new computer, but have made some progress with installing HTML-Kit and Cute-FTP which will enable me to update some of the pages on my website. I have already begun to update the History section, where a lot of the links no longer work, but have not yet uploaded this work to the website. .

Next Weekend 13 -15 March I am due to play in the Blackpool Chess Congress, though I've been having doubts whether to go in view of the Coronavirus outbreak.


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