Wednesday, 9 May 2018

Magic Four-Camel Tour of 1887

Following on from the four Giraffe tour reported previously I have now come across this four Camel tour in my researches in the column "Un Probleme Par Jour" conducted by A. Feisthamel in the French newspaper "Le Siecle". This tour is by "Adsum a Saint-P" (According to H.J.R. Murray this was a pen name of Charles Bouvier). It is mentioned on 13 May 1887 then presented as a problem for solution on 14 May, with the solution appearing on 21 May 1887. The diagonal sums are complementary (i.e. adding to 520). Each rank consists of pairs of complements (adding to 65). 

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

This is the earliest mention of a tour by a {1,3} mover that I am aware of. It seems surprising that later French writers on Mathematical Recreations, such as Lucas and Kraitchik, don't seem to have been aware of these results. Feisthamel indicates that they are only single examples from much more extensive work. Was the work of these composers all lost after their deaths, or is it still hidden away in some obscure French archives?

Sunday, 6 May 2018

Sources of Magic Knight Tours, Further Update

I have located another of the tours with missing sources:
(23b) Ligondes (Palamede) Le Si├Ęcle ¶2836 4/11 December 1885.
Murray gives the date as 1884, so it may also be in an earlier source,
such as Count Ligondes' own private publication which I have not seen.

This seems to be the last one-chain magic tour published in Le Si├Ęcle. 
Two and four-chain solutions continue to appear up to 30 April 1894,
which is the last date it is signed by A. Feisthamel. From 1 May 1894
the column "Un Probleme Par Jour" has a new editor, Emile Franck.