Sources page biographical material

5.R.3. FORE AND AFT -- 3 BY 3 SQUARES MEETING AT A CORNER
This is Frogs and Toads on part of the 5 x 5 board consisting of two 3 x 3 subarrays at diagonally opposite corners. They overlap in the central square. One square has 8 black men and the other has 8 white men, with the centre left vacant.
Ball. MRE, 1st ed., 1892, pp. 51 52. 51 move solution. In the third ed., 1896, pp. 69 70, he says he believes he was the first to publish the puzzle but "that it has been since widely distributed in connexion with an advertisement and probably now is well known". He gives a 48 move solution.

Hoffmann. 1893. Chap. VI, no. 26: The "English Sixteen" puzzle, pp. 273 274 & 287 = Hoffmann-Hordern, pp. 188-189, with photo. Mentions that it is produced by Messrs Heywood, as below. Solution in 52 moves, which he believes is minimal. Hordern notes that the minimum is 46. Photo on p. 188 of the Heywood version, see next entry.

John Heywood, Manchester, produced a version called 'The English Sixteen Puzzle', undated, but by 1893 as Hoffmann cites it. Photo in Hoffmann-Hordern, p. 188, dated 1880 1895.

Charles A. Emerson. US Patent 522,250 -- Puzzle. Applied: 3 Nov 1893; patented: 3 July 1894. 2pp + 1p diagrams. The Fore and Aft Puzzle. Says it can be done in 48, 49, 50, 51 or 52 moves.

Dudeney. Problem 66: The sixteen puzzle. Tit Bits 33 (1 Jan & 5 Feb 1898) 257 & 355. "It was produced, I believe, in America, many years ago, and has since been issued over here in the form of an advertisement by a prominent commercial house." Solution in 46 moves. He says published solutions assert the minimum number of moves is 53, 52 or 50. The 46 move solution is given in Ball, MRE, 5th ed., 1911, 79 80.

Ball. MRE, 5th ed., 1911, pp. 79-80. Drops his historical claims and includes a 46 move solution due to Dudeney.

Loyd. Fore and aft puzzle. Cyclopedia, 1914, pp. 108 & 353 (solution misprinted, but claimed to be 47 moves in contrast to 52 move solutions 'in the puzzle books'.) (c= MPSL1, prob. 4, pp. 3 4 & 121 (only referring to Dudeney's 46 move solution)).

Loyd Jr. SLAHP. 1928. A joke on granddad, pp. 29 & 93. Says 'our granddaddies, who used to play this puzzle game 75 years ago, when it was universally popular. The old time books explain how the solution is accomplished in 52 moves, "the shortest possible method."' He then asks for and gives a 46 move solution.

M. Adams. Puzzles That Everyone Can Do. 1931. Prob. 24, pp. 17 & 132: "General post". Gives a solution which takes 46 moves, but gives no discussion of it.

Rohrbough. Puzzle Craft. 1932. Migration (or Fore and Aft), p. 12 (= p. 15 of 1940s?). Says it was popular 75 years ago and it has recently been shown that it can be done in 46 moves, then gives a solution which stops at 42 moves!

M. Gardner. SA (Sep 1959) = 2nd Book, pp. 210 219. Discusses the puzzle. On pp. 218 219, he gives Dudeney's 46 move solution and says 48 different solutions and several proofs that 46 is minimal were sent to him.

Uwe Schult. Das Seemanns Spiel: Mathematisch erledigt. Reported in Das Mathematische Kabinett column, Bild der Wissenschaft 19:11 (Nov 1982) 181-184. (A version is given in Neues aus dem Mathematischen Kabinett, ed. by Thiagar Devendran, Hugendubel, Munich, 1985, pp. 102 103.) There are 218,790 possible patterns of the pieces. Reversing black and white takes 46 moves and there are 1026 different halfway positions that can occur in a 46 move solution. There are two patterns which require 47 moves, namely, after reversing black and white, put one of the far corner pieces in the centre.

Nob Yoshigahara, postcard to me on 18 Aug 1994, announces he has found the worst solution -- in 58 moves.