Peg Solitaire : Material in Les Tablettes du Chercheur, 1891-1896 (John, June 2013)
In addition to the material in Mercure Galant referred to elsewhere on this site, Dic Sonneveld has drawn my attention to some important material by Paul Redon and others in Les Tablettes du Chercheur (a twice-monthly journal which appeared on the 1st and 15th of the month) which I would certainly have noted in The Ins and Outs had I been aware of it.
For links to the relevant pages, click here. A summary follows.
1892, January 15 - May 15: Redon's analyses of single-vacancy single-survivor problems on the 39-hole and 41-hole boards, with proofs of the unsolvability of the three cases noted on pages 197-198 of The Ins and Outs. These proofs are in the following issues: March 15, 39-hole board, vacate d1, finish at d7 (in the notation of The Ins and Outs); April 1, 39-hole board, vacate and finish at a4; May 1, 41-hole board, vacate c1, finish at e7. They are further discussed below.
1892, June 1 - December 15: articles on the 37-hole board which subsequently formed pages 1-114 of Redon's 1893 book, the agreement being so close that I imagine the book was produced by leaving the type standing. These articles comprise the whole of the book apart from a couple of valedictory paragraphs on page 115 and a table of contents on pages 116-120.
1893, January 1 - March 15: articles by Redon on a 35-hole board obtained by removing b6 and f2 from the standard 37-hole board.
1893, June 1 - 1894, December 1: further articles by Redon.
1895, July 1: a very appreciative obituary of Redon. Apparently he died at the age of 32, having been suffering from tuberculosis since the age of 18, and his mother had introduced him to peg solitaire as a comforter while he was confined to bed.
1891, November 15 - 1896, June 1: problems on various boards by A. Huber, E. de Furundarena, and others. All these appear merely to demand play from a given starting position to a given target position, no use being made of marked men and no attempt being made to minimize moves, but some are quite difficult. Among the boards used is a new 37-hole board, obtained by omitting the middle square of each edge of a 41-hole diamond board.
Redon's method of proof of unsolvability of "vacate d1, play to finish at d7" on the 39-hole board was as follows.
(a) Consider the moves needed to clear the edge squares d0, c1, b2, and so on.
(b) Now consider the moves needed to clear the resulting surpluses at d2, c3, b4, and so on.
(c) Observe that the clearances of d2, c3, etc must be jumps over the men to be cleared, they cannot be moves by them.
(d) Classify the jumps over d2 by direction, horizontal or vertical (there being a surplus of three men to be cleared after the opening move d3-d1, we can in principle hope to clear them by three horizontal jumps, or by two horizontal jumps and one vertical, or by one horizontal jump and two vertical, or by three vertical jumps).
(e) Observe that if these jumps over d2 are all vertical, or if two are horizontal and one is vertical, there will be an odd man left at d1, so no sequence of play containing such jumps can lead to a solution.
(f) If, conversely, the jumps over d2 are all horizontal, or if two are vertical and one is horizontal, classify the jumps over c3 or e3 similarly, and show that in every case there will be an odd man left somewhere, so again no sequence of play containing such jumps can lead to a solution.
His proofs in respect of the other problems (vacate and finish at a4 on the 39-hole board, vacate c1 and finish at e7 on the 41-hole board) were similar.
In essence, this amounted to a case-by-case development of techniques that were stated in a more general form by J. H. Conway and R. L. Hutchings in their resolution of difficult problems on the 33-hole board, and subsequently crystallized by Conway in his balance sheets. Did Redon therefore work out this more general theory himself, nearly seventy years before? I have to say that there is no evidence he did more than resolve these three particular problems, but it was still a fine piece of work.
Les Tablettes du Chercheur appear to be neither in the British Library nor in any other major British academic library. Once again, thank you, Dic, for bringing important material to my attention.