Sources page biographical material

4.A.4. NIM
Nim is the game with a number of piles and a player can take any number from one of the piles. Normally the last one to play wins.
David Parlett. (Originally: The Oxford Guide to Card Games; OUP, 1990); reissued as: A History of Card Games. Penguin, 1991. Pp. 174-175. "Early references to 'les luettes', said to have been played by Anne de Bretagne and Archduke Philip the Fair in 1503, and by Gargantua in 1534, seem to suggest a game of the Nim family (removing numbers of objects from rows and columns)."

Charles L. Bouton. Nim: a game with a complete mathematical theory. Annals of Math. (2) 3 (1901/02) 35 39. He says Nim is played at American colleges and "has been called Fan Tan, but as it is not the Chinese game of that name, the name in the title is proposed for it." He says Paul E. More showed him the misère (= last player loses) version in 1899, so it seems that Bouton did not actually invent the game himself.

Ahrens. "Nim", ein amerikanisches Spiel mit mathematischer Theorie. Naturwissenschaftliche Wochenschrift 17:22 (2 Mar 1902) 258 260. He says that Bouton has admitted that he had confused Nim and Fan Tan. Fan Tan is a Chinese game where you bet on the number of counters (mod 4) in someone's hand. Parker, Ancient Ceylon, op. cit. in 4.B.1, pp. 570-571, describes a similar game, based on odd and even, as popular in Ceylon and "certainly one of the earliest of all games".

For more about Fan-Tan, see the following.

Stewart Culin. Chess and playing cards. Catalogue of games and implements for divination exhibited by the United States National Museum in connection with the Department of Archæology and Paleontology of the University of Pennsylvania at the Cotton States and International Exposition, Atlanta, Georgia, 1895. IN: Report of the U. S. National Museum, year ending June 30, 1896. Government Printing Office, Washington, 1898, HB, pp. 665-942. [There is a reprint by Ayer Co., Salem, Mass., c1990.] Fan-Tan (= Fán t‘án = repeatedly spreading out) is described on pp. 891 & 896, with discussion of related games on pp. 889-902.

Alan S. C. Ross. Note 2334: The name of the game of Nim. MG 37 (No. 320) (May 1953) 119 120. Conjectures Bouton formed the word 'nim' from the German 'nimm'. Gives some discussion of Fan Tan and quotes MUS I 72.

J. L. Walsh. Letter: The name of the game of Nim. MG 37 (No. 322) (Dec 1953) 290. Relates that Bouton said that he had chosen the word from the German 'nimm' and dropped one 'm'.

W. A. Wythoff. A modification of the game of Nim. Nieuw Archief voor Wiskunde (Groningen) (2) 7 (1907) 199 202. He considers a Nim game with two piles allows the extra move of taking the same amount from both piles. [Is there a version with more piles where one can take any number from one pile or equal amounts from two piles?? See Barnard, below for a three pile version.]

Ahrens. MUS I. 1910. III.3.VII: Nim, pp. 72 88. Notes that Nim is not the same as Fan Tan, has been known in Germany for decades and is played in China. Gives a thorough discussion of the theory of Nim and of an equivalent game and of Wythoff's game.

E. H. Moore. A generalization of the game called Nim. Annals of Math. (2) 11 (1910) 93 94. He considers a Nim game with n piles and one is allowed to take any number from at most k piles.

Ball. MRE, 5th ed., 1911, p. 21. Sketches the game of Nim and its theory.

A. B. Nordmann. One Hundred More Parlour Tricks and Problems. Wells, Gardner, Darton & Co., London, nd [1927 -- BMC]. No. 13: The last match, pp. 10-11. Thirty matches divided at random into three heaps. Last player loses. Explanation of how to win is rather cryptic: "you must try and take away ... sufficient ... to leave the matches in the two or three heaps remaining, paired in ones, twos, fours, etc., in respect of each other."

Loyd Jr. SLAHP. 1928. A tricky game, pp. 47 & 102. Nim (3, 4, 8).

Emanuel Lasker. Brettspiele der Völker. 1931. See comments in 4.A.5. Jörg Bewersdorff [email of 6 Jun 1999] says that Lasker considered a three person Nim and found an equilibrium for it -- see: Jörg Bewersdorff; Glück, Logik und Bluff Mathematik im Spiel -- Methoden, Ergebnisse und Grenzen; Vieweg, 1998, Section 2.3 Ein Spiel zu dritt, pp. 110-115.

Lynn Rohrbough, ed. Fun in Small Spaces. Handy Series, Kit Q, Cooperative Recreation Service, Delaware, Ohio, nd [c1935]. Take Last, p. 10. Last player loses Nim (3, 5, 7).

Rohrbough. Puzzle Craft. 1932.

Japanese Corn Game, p. 6 (= p. 6 of 1940s?). Last player loses Nim (1, 2, 3, 4, 5).

Japanese Corn Game, p. 23. Last player loses Nim (3, 5, 7).

René de Possel. Sur la Théorie Mathématique des Jeux de Hasard et de Réflexion. Actualités Scientifiques et Industrielles 436. Hermann, Paris, 1936. Gives the theory of Nim and also the misère version.

Depew. Cokesbury Game Book. 1939. Make him take it, pp. 187-188. Nim (3, 4, 5), last player loses.

Edward U. Condon, Gereld L. Tawney & Willard A. Derr. US Patent 2,215,544 -- Machine to Play Game of Nim. Filed: 26 Apr 1940; patented: 24 Sep 1940. 10pp + 11pp diagrams.

E. U. Condon. The Nimatron. AMM 49 (1942) 330 332. Has photo of the machine.

Benedict Nixon & Len Johnson. Letters to the Notes & Queries Column. The Guardian (4 Dec 1989) 27. Reprinted in: Notes & Queries, Vol. 1; Fourth Estate, London, 1990, pp. 14-15. These describe the Ferranti Nimrod machine for playing Nim at the Festival of Britain, 1951. Johnson says it played Nim (3, 5, 6) with a maximum move of 3. The Catalogue of the Exhibition of Science shows this as taking place in the Science Museum.

H. S. M. Coxeter. The golden section, phyllotaxis, and Wythoff's game. SM 19 (1953) 135 143. Sketches history and interconnections.

H. S. M. Coxeter. Introduction to Geometry. Wiley, 1961. Chap. 11: The golden section and phyllotaxis, pp. 160-172. Extends his 1953 material.

A. P. Domoryad. Mathematical Games and Pastimes. (Moscow, 1961). Translated by Halina Moss. Pergamon, Oxford, 1963. Chap. 10: Games with piles of objects, pp. 61 70. On p. 62, he asserts that Wythoff's game is 'the Chinese national game tsyanshidzi ("picking stones")'. However M. K. Siu cannot recognise such a Chinese game, unless it refers to a form of jacks, which has no obvious connection with Wythoff's game or other Nim games. He says there is a Chinese character, 'nian', which is pronounced 'nim' in Cantonese and means to pick up or take things.

N. L. Haddock. Note 2973: A note on the game of Nim. MG 45 (No. 353) (Oct 1961) 245 246. Wonders if the game of Nim is related to Mancala games.

T. H. O'Beirne. Puzzles and Paradoxes. OUP, 1965. Section on misère version of Wythoff's game, p. 133. Richard Guy (letter of 27 Feb 1985) says this is one of O'Beirne's few mistakes -- cf next entry.

Winning Ways. 1982. P. 407 says Wythoff's game is also called Chinese Nim or Tsyan shizi. No reference given. See comment under Domoryad above. This says many authors have done this incorrectly.

D. St. P. Barnard. 50 Daily Telegraph Brain Twisters. Javelin Books, Poole, Dorset, 1985. Prob. 30: All buttoned up, pp. 49 50, 91 & 115. He suggests three pile game where one can take any number from one pile or an equal number from any two or all three piles. [See my note to Wythoff, above.]

Matthias Mala. Schnelle Spiele. Hugendubel, Munich, 1988. San Shan, p. 66. This describes a nim-like game named San Shan and says it was played in ancient China.

Jagannath V. Badami. Musings on Arithmetical Numbers Plus Delightful Magic Squares. Published by the author, Bangalore, India, nd [Preface dated 9 Sep 1999]. Section 4.16: The game of Nim, pp. 124-125. This is a rather confused description of one pile games (21, 5) and (41, 5), but he refers to solving them by (mentally) dividing the pile into piles. This makes me think of combining the two games, i.e. playing Nim with several piles but with a limit on the number one can take in a move.