Sources page biographical material

6.F.1. OTHER CHESSBOARD DISSECTIONS
See S&B, pp. 12 14. See also 6.F.5 for dissections of uncoloured boards.
Jerry Slocum. Compendium of Checkerboard Puzzles. Published by the author, 1983. Outlines the history and shows all manufactured versions known then to him: 33 types in 61 versions. The first number in Slocum's numbers is the number of pieces.

Jerry Slocum & Jacques Haubrich. Compendium of Checkerboard Puzzles. 2nd ed., published by Slocum, 1993. 90 types in 161 versions, with a table of which pieces are in which puzzles, making it much easier to see if a given puzzle is in the list or not. This gives many more pictures of the puzzle boxes and also gives the number of solutions for each puzzle and sometimes prints all of them. The Slocum numbers are revised in the 2nd ed. and I use the 2nd ed. numbers below. (There was a 3rd ed. in 1997, with new numbering of 217 types in 376 versions. NYR. Haubrich is working on an extended version with Les Barton providing information.)

Henry Luers. US Patent 231,963 -- Game Apparatus or Sectional Checker Board. Applied: 7 Aug 1880; patented: 7 Sep 1880. 1p + 1p diagrams. 15: 01329. Slocum 15.5.1. Manufactured as: Sectional Checker Board Puzzle, by Selchow & Righter. Colour photo of the puzzle box cover is on the front cover of the 1st ed. of Slocum's booklet. B&W photo is on p. 14 of S&B.

?? UK patent application 16,810. 1892. Not granted, so never published. I have spoken to the UK Patent Office and they say the paperwork for ungranted applications is destroyed after about three to five years. (Edward Hordern's collection has an example with this number on it, by Feltham & Co. In the 2nd ed., the cover is reproduced and it looks like the number may be 16,310, but that number is for a locomotive vehicle.) 14: 00149. Slocum 14.20.1. Manufactured as: The Chequers Puzzle, by Feltham & Co.

Hoffmann. 1893. Chap. III, no. 16: The chequers puzzle, pp. 97 98 & 129 130 = Hoffmann Hordern, pp. 88-89, with photos. 14: 00149. Slocum 14.20.1. Says it is made by Messrs. Feltham, who state it has over 50 solutions. He gives two solutions. Photo on p. 89 of a example by Feltham & Co., dated 1880-1895.

At the end of the solution, he says Jacques & Son are producing a series of three "Peel" puzzles, which have coloured squares which have to be arranged so the same colour is not repeated in any row or column. Photo on p. 89 shows an example, 9: 023, with the trominoes all being L-trominoes. This makes a 5 x 5 square, but the colours have almost faded into indistinguishability.

Montgomery Ward & Co. Catalog N^o 57, Spring & Summer, 1895. Facsimile by Dover, 1969, ??NX. P. 237 describes item 25470: "The "Wonder" Puzzle. The object is to place 18 pieces of 81 squares together, so as to form a square, with the colors running alternately. It can be done in several different ways."

Dudeney. Problem 517 -- Make a chessboard. Weekly Dispatch (4 & 18 Oct 1903), both p. 10. 8: 00010 12111 001. Slocum 8.3.1.

Benson. 1904. The chequers puzzle, pp. 202 203. As in Hoffmann, with only one solution.

Dudeney. The Tribune (20 & 24 Dec 1906) both p. 1. ??NX Dissecting a chessboard. Dissect into maximum number of different pieces. Gets 18: 2,1,4,10,0, 0,0,1. Slocum 18.1, citing later(?) Loyd versions.

Loyd. Sam Loyd's Puzzle Magazine (Apr-Jul 1908) -- ??NYS, reproduced in: A. C. White; Sam Loyd and His Chess Problems; 1913, op. cit. in 1; no. 58, p. 52. = Cyclopedia, 1914, pp. 221 & 368, 250 & 373. = MPSL2, prob. 71, pp. 51 & 145. = SLAHP: Dissecting the chessboard, pp. 19 & 87. Cut into maximum number of different pieces -- as in Dudeney, 1906.

Burren Loughlin & L. L. Flood. Bright-Wits Prince of Mogador. H. M. Caldwell Co., NY, 1909. The rug, pp. 7-13 & 65. 14: 00149. Not in Slocum.

Loyd. A battle royal. Cyclopedia, 1914, pp. 97 & 351 (= MPSL1, prob. 51, pp. 49 & 139). Same as Dudeney's prob. 517 of 1903.

Dudeney. AM. 1917. Prob. 293: The Chinese chessboard, pp. 87 & 213 214. Same as Loyd, p. 221.

Western Puzzle Works, 1926 Catalogue. No. 79: "Checker Board Puzzle, in 16 pieces", but the picture only shows 14 pieces. 14: 00149. Picture doesn't show any colours, but assuming the standard colouring of a chess board, this is the same as Slocum 14.15.

John Edward Fransen. US Patent 1,752,248 -- Educational Puzzle. Applied: 19 Apr 1929; patented: 25 Mar 1930. 1p + 1p diagrams. 'Cut thy life.' 11: 10101 43001. Slocum 11.3.1.

Emil Huber-Stockar. Patience de l'echiquier. Comptes-Rendus du Premier Congrès International de Récréation Mathématique, Bruxelles, 1935. Sphinx, Bruxelles, 1935, pp. 93-94. 15: 01329. Slocum 15.5. Says there must certainly be more than 1000 solutions.

Emil Huber-Stockar. L'echiquier du diable. Comptes-Rendus du Deuxième Congrès International de Récréation Mathématique, Paris, 1937. Librairie du "Sphinx", Bruxelles, 1937, pp. 64-68. Discusses how one solution can lead to many others by partial symmetries. Shows several solutions containing about 40 altogether. Note at end says he has now got 5275 solutions. This article is reproduced in Sphinx 8 (1938) 36-41, but without the extra pages of diagrams. At the end, a note says he has 5330 solutions. Ibid., pp. 75-76 says he has got 5362 solutions and ibid. 91-92 says he has 5365. By use of Bayes' theorem on the frequency of new solutions, he estimates c5500 solutions. Haubrich has found 6013. Huber-Stocker intended to produce a book of solutions, but he died in May 1939 [Sphinx 9 (1939) 97].

F. Hansson. Sam Loyd's 18-piece dissection -- Art. 48 & probs. 4152 4153. Fairy Chess Review 4:3 (Nov 1939) 44. Cites Loyd's Puzzles Magazine. Asserts there are many millions of solutions! He determines the number of chequered handed n-ominoes for n = 1, 2, ..., 8 is 2, 1, 4, 10, 36, 110, 392, 1371. The first 17 pieces total 56 squares. Considers 8 ways to dissect the board into 18 different pieces. Problems ask for the number of ways to choose the pieces in each of these ways and for symmetrical solutions. Solution in 4:6 (Jun 1940) 93-94 (??NX of p. 94) says there are a total of 3,309,579 ways to make the choices.

C. Dudley Langford. Note 2864: A chess board puzzle. MG 43 (No. 345) (Oct 1959) 200. 15: 01248. Not in Slocum. Two diagrams followed by the following text. "The pieces shown in the diagrams can be arranged to form a square with either side uppermost. If the squares of the underlying grid are coloured black and white alternately, with each white square on the back of a black square, then there is at least one more way of arranging them as a chess-board by turning some of the pieces over." I thought this meant that the pieces were double-sided with the underside having the colours being the reverse of the top and the two diagrams were two solutions for this set of pieces. Jacques Haubrich has noted that the text is confusing and that the second diagram is NOT using the set of double-sided pieces which are implied by the first diagram. We are not sure if the phrasing is saying there are two different sets of pieces and hence two problems or if we are misinterpreting the description of the colouring.

B. D. Josephson. EDSAC to the rescue. Eureka 24 (Oct 1961) 10 12 & 32. Uses the EDSAC computer to find two solutions of a 12 piece chessboard dissection. 12: 00025 41. Slocum 12.9.

Leonard J. Gordon. Broken chessboards with unique solutions. G&PJ 10 (1989) 152 153. Shows Dudeney's problem has four solutions. Finds other colourings which give only one solution. Notes some equivalences in Slocum.