Sources page biographical material

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Putnam. Puzzle Fun. 1978. No. 53: Checker star, pp. 10 & 34. Use the 10 points of a pentagram, as above, and leave one of the inner points empty. Reduce to one man. [Parity shows the one man must be at an outer point and any outer point can be achieved. If one leaves an outer point empty, then the last man must be on an inner point and any of these can be achieved.]

Hummerston. Fun, Mirth & Mystery. 1924.

Perplexity, pp. 22-23. Using the octagram board shown in 5.A, place 15 markers on it, leaving cell 16 empty. It is possible to remove all but one man. [I can't see how to apply parity to this board.]

Solplex, p. 25. In playing his Perplexity, specify where you will leave the last man?

Leap frog, Puzzle no. 22, pp. 64 & 175. Take a 4 x 3 board with the long edge extended by one more cell at the upper left and lower right. Put white counters on the 4 x 3 area, put a black counter in one of the extra cells and leave the other extra cell empty. Remove all but the black man. Counting multiple jumps of the same man as a single move, he does it in eight moves, getting the black man back to its starting point.
5.R.2. FROGS AND TOADS: BBB_WWW TO WWW_BBB
In the simplest version, one has n black men at the left and n white men at the right of a strip of 2n+1 cells, e.g. BBB_WWW. One can slide a piece forward (i.e. blacks go left and whites go right) into an adjacent place or one can jump forward over one man of the other colour into an empty place. The object is to reverse the colours, i.e. to get WWW_BBB. S&B 121 & 125, shows versions.

One finds that the solution never has a man moving backward nor a man jumping another man of the same colour. Some authors have considered relaxing these restrictions, particularly if one has more blank spaces, when these unusual moves permit shorter solutions. Perhaps the most general form of the one-dimensional problem would be the following. Suppose we have m men at the left of the board, n men at the right and b blank spaces in the middle. The usual case has b = 1, but when b > 1, the kinds of move permitted do change the number of moves in a minimal solution. First, considering slides, can a piece slide backward? Can a piece slide more than one space? If so, is there a maximum distance, s, that it is allowed to slide? (The usual problem has s = 1.) Of course s  b. Second, considering jumps, can a piece jump backward? Can a piece jump over a piece (or pieces) of its own colour and/or a blank space (or spaces) and/or a mixture of these? If so, is there a maximum number of pieces, p, that it can jump over? (The usual problem has p = 1.) It is not hard to construct simple examples with s > 1 such that shorter solutions exist when unusual moves are permitted. Are there situations where one can show that backward moves are not needed?

The game is sometimes played on a 2-dimensional board, where one colour can move down or right and the other can move up or left. See: Hyde ??; Lucas (1883); Ball; Hoffmann and 5.R.3. Chinese checkers is a later variation of this same idea. On these more complex boards, one is usually allowed to make multiple jumps and the object is usually to minimize the number of moves to accomplish the interchange of pieces.

There is a trick version to convert full and empty glasses: FFFEEE to FEFEFE in one move, which is done by pouring. I've just noted this in a 1992 book and I'll look for earlier examples.

Thomas Hyde. Historia Nerdiludii, hoc est dicere, Trunculorum; .... (= Vol. 2 of De Ludis Orientalibus, see 7.B for vol. 1.) From the Sheldonian Theatre (i.e. OUP), Oxford, 1694. De Ludo dicto Ufuba wa Hulana, p. 233. This has a 5 x 5 board with each side having 12 men, but the description is extremely brief. It seems to have two players, but this may simply refer to the two types of piece. I'm not clear whether it's played like solitaire (with the jumped pieces being removed) or like frogs & toads. I would be grateful if someone could read the Latin carefully. The name of the puzzle is clearly Arabic and Hyde cites an Arabic source, Hanzoanitas (not further identified on the pages I have) -- I would be grateful to anyone who can track down and translate Arabic sources.

American Agriculturist (Jun 1867). Spanish Puzzle. ??NYR -- copy sent by Will Shortz.

Anonymous. Every Little Boy's Book A Complete Cyclopædia of in and outdoor games with and without toys, domestic pets, conjuring, shows, riddles, etc. With two hundred and fifty illustrations. Routledge, London, nd. HPL gives c1850, but the material is clearly derived from Every Boy's Book, whose first edition was 1856. But the text considered here is not in the 1856 ed of Every Boy's Book (with J. G. Wood as unnamed editor), nor in the 8th ed of 1868 (published for Christmas 1867), which was the first seriously revised edition, with Edmund Routledge as editor, nor in the 13th ed. of 1878. So this material is hard to date, though in 4.A.1, I've guessed this book may be c1868.

P. 12: Frogs and toads. "A new and fascinating game of skill for two players; played on a leather board with twelve reptiles; the toads crawling, and the frogs hopping, according to certain laws laid down in the rules. The game occupies but a few minutes, but in playing it there is scarcely any limit to the skill that can be exhibited, thus forming a lasting amusement. (Published by Jaques, Hatton Garden.)" This does not sound like our puzzle, but perhaps it is related. Unfortunately Jaques' records were destroyed in WW2, so it is unlikely they can shed any light on what the game was. Does anyone know what it was?

Hanky Panky. 1872. Checker puzzle, p. 124. Three and three, with solution.

Mittenzwey. 1880. Prob. 239, pp. 44 & 94; 1895?: 267-268, pp. 48 & 96; 1917: 267-268, pp. 44 & 91 92. Problem with 3 & 3 brown and white horses in stalls. 1895? adds a version with 4 & 4.

Bazemore Bros. (Chattanooga, Tennessee). The Great "13" Puzzle! Copyright No. 1033   O   1883. Hammond & Jones Printers. Advertising puzzle consisting of two 3 and 3 versions arranged in an X pattern.

Lucas. RM2. 1883.

Pp. 141 143. Finds number of moves for n and n.

Pp. 144 145. Considers game on 5 x 5, 7 x 7, ..., boards and gives number of moves.

Edward Hordern's collection has an example called Sphinxes and Pyramids from the 1880s.

Sophus Tromholt. Streichholzspiele. (1889; 5th ed, 1892.) Revised from 14th ed. of 1909 by R. Thiele; Zentralantiquariat der DDR, Leipzig, 1986. Prob. 11, 41, 81 are the game for 4 & 4, 2 & 2, 3 & 3.

Ball. MRE, 1st ed., 1892, pp. 49 51. 3 & 3 case, citing Lucas, with generalization to n & n; 7 x 7 board, citing Lucas, with generalization to 2n+1 x 2n+1.

Berkeley & Rowland. Card Tricks and Puzzles. 1892. German counter puzzle, p. 112. 3 & 3 case.

Hoffmann. 1893. Chap. VI, pp. 269 270 & 282 284 = Hoffmann-Hordern, pp. 182-185, with photo.

No. 17: The "Right and Left" puzzle. Three and three. Photo on p. 184 shows: a cartoon from Punch (18 Dec 1880): The Irish Frog Puzzle -- with a Deal of Croaking; and an example of a handsome carved board with square pieces with black and white frogs on the tops, registered 1880. Hordern Collection, p. 77, shows the latter board and two further versions: Combat Sino-Japonais (1894 1895) and Anglais & Boers (1899-1902).

No. 18. Extends to a 7 x 5 board.

Puzzles with draughtsmen. The Boy's Own Paper 17 or 18?? (1894??) 751. 3 and 3.

Lucas. L'Arithmétique Amusante. 1895. Prob. XXXV: Le bal des crapauds et des grenouilles, pp. 117-124. Does 2 and 2, 3 and 3, 4 and 4 and the general case of n and n, showing it can be done in n(n+2) moves -- n² jumps and 2n steps. The general solution is attributed to M. Van den Berg. M. Schoute notes that each move should make as little change as possible from the previous with respect to the two aspects of changing type of piece and changing type of move.

Clark. Mental Nuts. 1904, no. 72; 1916, no. 62. A good study. 3 and 3.

Burren Loughlin & L. L. Flood. Bright-Wits Prince of Mogador. H. M. Caldwell Co., NY, 1909. Doola's Game, pp. 42-43 & 61-62. 3 and 3.

Anon. Prob. 47: The monkey's dilemma. Hobbies 30 (No. 762) (21 May 1910) 168 & 182 & (No. 765) (11 Jun 1910) 228. Basically 3 & 3, but there are eight posts for crossing a river, with the monkeys on 1,2,3 and 6,7,8. The monkeys can jump onto the bank and we want the monkeys to all get to the bank they are headed for, so this is not the same as BBB..WWW to WWW..BBB. The solution doesn't spell out all the steps, so it's not clear what the minimum number of moves is -- could we have a monkey jumping another of the same colour?

Ahrens. MUS I. 1910. Pp. 17-19. Basically repeats some of Lucas's work from 1883 & 1895.

Williams. Home Entertainments. 1914. The cross-over puzzle, pp. 119-120. 3 and 3 with red and white counters. Doesn't say how many moves are required.

Dudeney. AM. 1917. Prob. 216: The educated frogs, pp. 59-60 & 194. _WWWBBB to BBBWWW_ with frogs able to jump either way over one or two men of either colour. Solution in 10 jumps.

Ball. MRE, 9th ed., 1920, pp. 77-79, considers the m & n case, giving the number of steps in the solution.

Blyth. Match-Stick Magic. 1921. Matchstick circle transfer, pp. 81 82. 3 and 3 in 15 moves.

Hummerston. Fun, Mirth & Mystery. 1924. The frolicsome frogs, Puzzle no. 2, pp. 17 & 172. Two 3 & 3 problems with the boards crossing at the centre cell. He notes that the easiest solution is to solve the boards one at a a time. He says: "It is not good play to jump a counter over another of the same colour."

Lynn Rohrbough, ed. Socializers. Handy Series, Kit G, Cooperative Recreation Service, Delaware, Ohio, 1925. Six Frogs, p. 5. Dudeney's 1917 problem done in 11 moves.

Botermans et al. The World of Games. Op. cit. in 4.B.5. 1989. P. 235 describes this as The Sphinx Puzzle, "very popular around the turn of the century, particularly in the United States and France" and they show an example of the period labelled The Sphinx and Pyramid Puzzle -- An Egyptian Novelty.

Haldeman-Julius. 1937. No. 162: Checker problem, pp. 18 & 29. 3 & 3.

See Harbin in 5.R.4 for a 1963 example.

Doubleday - 1. 1969.

Prob. 77: Square dance, pp. 93 & 171. = Doubleday - 5, pp. 103-104. Start with _WWWBBB. He says they must change places, with a piece able to move into the vacant space by sliding (either way) or by jumping one or two pieces of any colour. Asks for a solution in 10 moves. His solution gets to BBBWWW_, which does not seem to be 'changing places' to me.

Prob. 79: All change, pp. 95 & 171. = Doubleday - 5, pp. 105-106. BB_WW

Start with the pattern at the right and change the whites and BB_WW

blacks in 10 moves, where a piece can slide one place into an

adjacent vacant square or jump one or two pieces into a vacant square. However, the solution simply does each row separately.

Katharina Zechlin. (Dekorative Spiele zum Selbermachen; Verlag Frech, WWWWW

Stuttgart-Botnang, 1973.) Translated as: Making Games in Wood Games BWWWW

you can build yourself. Sterling, 1975, pp. 24-27: The chess knight game. BBOWW

5 x 5 board with 12 knights of each of two colours, arranged as at the right. BBBBW

The object is to reverse them by knight's moves. Says it can be done within BBBBB

50 moves and 'is almost impossible to do it in less than 45'.

Wickelgren. How to Solve Problems. Op. cit. in 5.O. 1974. Discrimination reversal problem, pp. 78 81. _WWWBBB to BBBWWW with the extra place not specified in the goal, with pieces allowed to move into the vacant space by sliding or by hopping over one or two pieces. Gets to BBBWW_W in 9 moves. [I find it takes 10 moves to get to BBBWWW_ .]

Joe Celko. Jumping frogs and the Dutch national flag. Abacus 4:1 (Fall 1986) 71-73. Same as Wickelgren. Celko attributes this to Dudeney. Gives a solution to BBBWWW_ in 10 moves and asks for results for higher numbers.

Johnston Anderson. Seeing induction at work. MG 75 (No. 474) (Dec 1991) 406-414. Example 2: Frogs, pp. 408-411. Careful proof that BB...BB_WW...WW to WW...WW_BB...BB, with n counters of each colour, requires n² + 2n moves.
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.
5.R.4. REVERSING FROGS AND TOADS: _12...n TO _n...21 , ETC.
A piece can slide into the empty cell or jump another piece into the empty cell.
Dudeney. AM. 1917.

Prob. 214: The six frogs, pp. 59 & 193. Case of n = 6, solved in 21 moves, which he says is minimal. In general, the minimal solution takes n(n+1)/2 moves, including n steps, when n is even and (n²+3n-8)/2 moves, including 2n-4 steps, when n is odd. "This complete general solution is published here for the first time."

Prob. 215: The grasshopper puzzle, pp. 59 & 193-194. Problem for a circular arrangement. Example has n = 12. Says he invented it in 1900. Solvable in 44 moves. General solution is complex -- he says that for n > 4, it can be done in (n²+4n-16)/4 moves when n is even and in (n²+6n-31)/4 moves when n is odd.

Rohrbough. Puzzle Craft. 1932. The Reversible Frogs, p. 22 (= The Jumping Frogs, pp. 20 21 of 1940s?). n = 8, citing Dudeney, AM.

Robert Harbin. Party Lines. Op. cit. in 5.B.1. 1963. Hopover, p. 89. First gives 3 and 3 Frogs and Toads, then asks for complete reversal from 123_456 to 654_321.

[Henry] Joseph and Lenore Scott. Master Mind Pencil Puzzles. Tempo Books (Grosset & Dunlap), NY, 1973 (& 1978?? -- both dates are given -- I'm presuming the 1978 is a 2nd ptg or a reissue under a different imprint??). Reverse the numbers, pp. 117 118. Give the problem for n = 6 and a solution in 21 moves. For n even, the method gives a solution in n(n+1)/2, it is not shown that this is optimal, nor is a general method given for odd n.

[Henry] Joseph & Lenore Scott. Master Mind Brain Teasers. 1973. Op. cit. in 5.E. 13-hour clock, pp. 43-44. Case n = 12 considered in a circle can be done in 44 moves.

Joe Celko. Jumping frogs and the Dutch national flag. Abacus 4:1 (Fall 1986) 71-73. Cites Dudeney and gives the results.

Jim Howson. The Computer Weekly Book of Puzzlers. Computer Weekly Publications, Sutton, Surrey, 1988, unpaginated. [The material comes from his column which started in 1966, so an item may go back to then.] Prob. 54 -- same as the Scotts in Master Mind Pencil Puzzles.
5.R.5. FOX AND GEESE, ETC.
There are a number of similar games on different boards -- too many to describe completely here, so I will generally just cite extensive descriptions. See any of the main books on games mentioned at the beginning of 4.B, such as Bell or Falkener. The key feature is that one side has more, but weaker, pieces. These are sometimes called hunt games. The standard Fox and Geese is played on a 33 hole Solitaire board, with diagonal moves allowed. I have recently acquired but not yet read Murray's History of Board Games other than Chess which should have lots of material.
Gretti's Saga, late 12C. Mention of Fox and Geese. Also in Edward IV's accounts. ??NYS -- cited by Botermans et al, below.

Shackerley (or Schackerley or Shakerley) Marmion. A Fine Companion (a play). 1633. IN: The Dramatic Works of Shackerley Marmion; William Paterson, Edinburgh & H. Sotheran & Co., London, 1875. II, v, pp. 140-141. "..., let him sit in the shop ..., and play at fox and geese with the foreman, ....." Earliest English occurrence of fox-and-geese. Quoted by OED and cited by Fiske, below.

Richard Lovelace. To His Honoured Friend On His Game of Chesse-Play or To Dr. F. B. on his Book of Chesse. 1656?, published in his Posthume Poems, 1659. Lines 1-4. My edition of Lovelace notes that F. B. was Francis Beale, author of 'Royall Game of Chesse Play,' 1656. Lovelace died in 1658.

Sir, now unravell'd is the Golden Fleece,

Men that could onely fool at Fox and Geese,

Are new-made Polititians by the Book,

And can both judge and conquer with a look.

Henry Brooke. Fool of Quality. [A novel.] 1766-1768. Vol. I, p. 367. ??NYS -- quoted by Fiske, below. "Can you play at no kind of game, Master Harry?" "A little at fox and geese, madam."

Catel. Kunst-Cabinet. 1790.

Das Fuchs- und Hühnerspiel, pp. 51-52 & fig. 168 on plate VI. 11 chickens against one fox on a 4 x 4 board with all diagonals drawn, giving 16 + 9 playing points.

Das Schaaf- und Wolfspiel, p. 52 & fig. 169 on plate VI, is the same game on the 33-hole solitaire board with 11 sheep and one wolf, no diagonals

Bestelmeier. 1801.

Item 83: Das Schaaf- und Wolfspiel. Same diagram and game as Catel, p. 52.

Item 833: Ein Belagerungspiel. 33 hole board with a fortress on one arm, with diagonals drawn.

Strutt. Op. cit. in 4.B.1. Fox and Geese. 1833: Book IV, chap. II, art. XIV, pp. 318 319. = Strutt-Cox, p. 258 & plate opp. p. 246. Fig. 107 (= plate opp. p. 246) shows the 33 hole board with its diagonals drawn.

Gomme. Op. cit. in 4.B.1. I 141 142 refers to Strutt and Micklethwaite.

Illustrated Boy's Own Treasury. 1860. Fox and Geese, pp. 406 407. 33 hole Solitaire board with diagonals drawn.

Leske. Illustriertes Spielbuch für Mädchen. 1864? Prob. 320, p. 152: Fuchs und Gänse. Shows 33 hole solitaire board with diagonals drawn.

Stewart Culin. Chinese Games with Dice and Dominoes. From the Report of the U. S. National Museum for 1893, pp. 489 537. Pp. 874-877 describes: the Japanese game of Juroku Musashi (Sixteen Soldiers) with 16 men versus a general; the Chinese game of Shap luk kon tséung kwan (The sixteen pursue the commander); another Chinese game of Yeung luk sz' kon tséung kwan with 27 men against a commander (described by Hyde -- ?? I didn't see this); the Malayan game of Dam Hariman (Tiger Game), identical to the Hindu game of Mogol Putt'han (= Mogul Pathan (Mogul against Pathan)), similar to a Peruvian game of Solitario and the Mexican game of Coyote; the Siamese game of Sua ghin gnua (Tiger and Oxen) and the similar Burmese game of Lay gwet kyah, with three big tigers versus 11 or 12 little tigers; the Samoan game of Moo; the Hawaiian game of Konane; a similar Madagascarian game; the Hindu game of Pulijudam (Tiger Game) with three tigers versus 15 lambs.

Fiske. Op. cit. in 4.B.1. 1905. Fox-and-Geese, pp. 146-156 & 359, discusses the history of the game, especially as to whether it is identical to the old Norse game of Hnefatafl. On p. 359, he says that John of Salisbury (c1150) used 'vulpes' as the name of a game, but there is no indication of what it was. He says "the fox-and-geese board, in comparatively modern times, has begun to be used for games more or less different in their nature, especially for one called in England solitaire and in France "English solitaire", and for another, known in Spain and Italy as asalto (assalto), in French as assaut, in Danish as belejringsspel." He then surveys the various sources that he treated under Mérelles -- see 4.B.1 and 4.B.5 for details. He is not sure that Brunet is really describing the game in the Alfonso MS (op. cit. in 4.B.5 and below). He cites an 1855 Italian usage as Jeu de Renard or Giuoco della Volpe. In Come Posso Divertirmi? (Milan, 1901, pp. 231-233), it is said that the game is usually played with 17 geese rather than 13 -- Fiske notes that this assertion is of "some historical value, if it be true." Moulidars calls it Marelle Quintuple, quotes Maison des Jeux Académiques (Paris, 1668) for a story that it was invented by the Lydians and gives the game with 13 or 17 geese. Asalto has 2 men against 24. Fiske quotes Shackley Marmion, above, for the oldest English occurrence of fox-and-geese and then Henry Brooke, above. Fiske follows with German, Swedish and Icelandic (with 13 geese) references.

H. Parker. Ancient Ceylon. Op. cit. in 4.B.1, 1909. Pp. 580-583 & 585 describe four forms of The Leopards Game, with one tiger against seven leopards, three leopards against 15 dogs, two leopards against 24 cattle and one leopard against six cattle on a 12 x 12 board. The first two are played on a triangular board.

Robert Kanigel. The Man Who Knew Infinity. A Life of the Genius Ramanujan. (Scribner's, NY, 1991); Abacus (Little, Brown & Co. (UK)), London, 1992. Pp. 18 & 377: Ramanujan and his mother used to play the game with three tigers and fifteen goats on a kind of triangular board.

The Spanish Treatise on Chess-Play written by order of King Alfonso the Sage in the year 1283. [= Libro de Acedrex, Dados e Tablas of Alfonso El Sabio, generally known as the Alfonso MS.] MS in Royal Library of the Escorial (j.T.6. fol). Complete reproduction in 194 Phototypic Plates. 2 vols., Karl W. Hirsemann, Leipzig, 1913. See 4.B.5 for more details of this work. See below.

Botermans et al. The World of Games. Op. cit. in 4.B.5. 1989. P. 147 says De Cercar La Liebre (Catch the Hare) occurs in the Alfonso MS and is the earliest example of a hunt game in European literature, but undoubtedly derived from an Arabic game of the Alquerque type -- I didn't see this when I briefly looked at the facsimile -- ??NYS. They say Murray has noted that hunt games are popular in Asia, but not in Africa, leading to the conjecture that they originated in Asia. They describe it on a 5 x 5 array of points with verticals and horizontals and some diagonals drawn, with one hare against 12 hunters.

Botermans et al. continue on pp. 148-155 to describe the following.

Shap Luk Kon Tseung Kwan (Sixteen Pursue the General) played on a 5 x 5 board like Catch the Hare with an extra triangle on one side and capturing by interception.

Yeung Luk Sz'Kon Tseung Kwan, seen in Nanking by Hyde and described by him in 1694, somewhat similar to the above, but with 26 rebels against a general. (??NYS)

Fox and Geese, mentioned in Gretti's Saga of late 12C and in Edward IV's accounts. They give a version called Lupo e Pecore from a 16C Venetian book, using a Solitaire board extended by three points on each arm, giving 45 points. They give a 1664 engraving showing Le Jeu du Roi which they say is a rather complex form of fox and geese, but looks like a four-handed game on a cross-shaped board with 7 x 5 arms on a 7 x 7 central square and 4 groups of 7 x 4 men.

Leopard games, from Southeast Asia, with a kind of triangular board. Len Choa, from Thailand, has a tiger against six leopards. Hat Diviyan Keliya, from Sri Lanka, has a tiger against seven leopards.

Tiger games, also from Southeast Asia, are similar to leopard games, but use an extended Alquerque board (as in Catch the Hare). Rimau (Tiger), from Malaysia, has 24 men versus a tiger and Rimau-Rimau (Tigers) is a version with two tigers versus 22 men.

Murray. 1913.

P. 347 cites a 1901 Indian book for 2 lions against 32 goats on a chessboard.

P. 371 cites a Soyat (North Asia) example (19C?) of Bouge Shodra (Boar's Chess) with 2 boars against 24 calves on a chessboard.

Pp. 569 & 616 617 cite the Alfonso MS of 1283 for 'De cercar la liebre', played on a 5 x 5 board with 10, 11 or 12 men against a hare.

P. 585 shows Cott. 6 (c1275) of 8 pawns against a king on a chessboard.

Pp. 587 & 590 give Cott. 11 = K6: Le Guy de Alfins with king and 4 bishops against a king on a chessboard.

Pp. 589-590 shows K4 = CB249: Le Guy de Dames and No. 5 = K5: Le Guy de Damoyselles, which have 16 pawns against a king on a chessboard.

P. 617 discusses Fox and Geese, with 13, 15 or 17 geese against a fox on the solitaire board. Edward IV, c1470, bought "two foxis and 46 hounds". Murray says more elaborate forms exist and refers to Hyde and Fiske (see 4.B.1 and 5.F.1 for more on these), ??NYS.

Pp. 675 & 692 show CB258: Partitum regis Francorum with king and four pawns against king on the chessboard. It says the first side wins.

P. 758 describes a 16C Venetian board (then) at South Kensington (V&A??) with the Solitaire board for Fox and Geese and an enlarged board for Fox and Geese.

P. 857 mentions Fox and Geese in Iceland.

Family Friend 2 (1850) 59. Fox and geese. 4 geese against 1 fox on a chess board.

The Sociable. 1858. Fox and geese, p. 281. 17 geese against a fox on the solitaire board. Four men versus a king on the draughts board, saying the first side wins even allowing the king to be placed anywhere against the men who start on one side.

Stewart Culin. Korean Games, op. cit. in 4.B.5, 1895. Pp. 76-77 describes some games of this type, in particular a Japanese game called Yasasukari Musashi with 16 soldiers versus a general on a 5 x 5 board, taken from a 1714 (or 1712) Japanese book: Wa Kan san sai dzu e "Japanese, Chinese, Three Powers picture collection", published in Osaka.

Anonymous. Enquire Within upon Everything. 66th ed., 862nd thousand, Houlston and Sons, London, 1883, HB. Section 2593: Fox and Geese, p. 364. 33 hole Solitaire board with 17 geese against a fox. 4 geese against a fox on the chessboard. Says the geese should win in both cases.

Slocum. Compendium. Shows Solitaire and Solitaire & Tactic Board from Gamage's 1913 catalogue. Like Bestelmeier's 833, but without diagonals.

Bell & Cornelius. Board Games Round the World. Op. cit. in 4.B.1. 1988. Games involving unequal forces, pp. 43-52. Discusses the following.

The Maharajah and the Sepoys. 1 against 16 on a chessboard.

Fox and Geese. Cites an Icelandic work of c1300 (probably Gretti's Saga?). 1 against 13 or 17 on a Solitaire board.

Lambs and Tigers, from India. 3 against 15.

Cows and Leopards, from SE Asia. 2 against 24.

Vultures and Crows, also called Kaooa, from India. 1 against 7 on a pentagram board.

The New Military Game of German Tactics, c1870. 2 against 24 on a Solitaire Board with a fortress, as in Bestelmeier.

Yuri I. Averbakh. Board games and real events. IN: Alexander J. de Voogt, ed.; New Approaches to Board Games Research: Asian Origins and Future Perspectives; International Institute for Asian Studies, Leiden, 1995; pp. 17-23. Notes that Murray believes hunt games evolved from war games, but he feels the opposite is true. He describes a Nepalese game of Baghachal with four tigers versus 20 goats -- this is Murray's 5.6.22. He corrects some of Murray's assertions about Boar Chess and describes other Tuvinian hunt games: Bull's Chess and Calves' Chess, probably borrowed from the Mongols. The latter has a three-in-a-row pattern and he wonders if there is some connection with morris or noughts and crosses (which he says is "played everywhere"). He mentions Cercar la Liebre from the Alfonso MS. Fox and Geese type games are mentioned in the Icelandic sagas as 'the fox game'. He describes several forms.