Sources page biographical material

Tit tat toe [Gomme II 296 298]. This is a game using a slate marked with a circle and numbered sectors. The player closes his eyes and taps three times with a pencil and tries to land on a good sector. Gomme gives the verse:

Tit, tat, toe, my first go,

Three jolly butcher boys all in a row

Stick one up, stick one down,

Stick one in the old man's ground.

But cf Games and Sports for Young Boys, 1859, below.

The OED entries under Tick tack, Tip tap and Tit give a number of variant spellings and several quotations, which are often clearly to this game, but are sometimes unclear. Also some forms seem to refer to backgammon.

In her 'Memoir on the study of children's games' [Gomme II 472 473], Gomme gives a somewhat Victorian explanation of the origin of Old Nick as the winner of a tie game as stemming from "the primitive custom of assigning a certain proportion of the crops or pieces of land to the devil, or other earth spirit."

Franco Agostini & Nicola Alberto De Carlo. Intelligence Games. (As: Giochi della Intelligenza; Mondadori, Milan, 1985.) Simon & Schuster, NY, 1987. P. 81 says examples of boards were discovered in the lowest level of Troy and in the Bronze Age tombs in Co. Wicklow, Ireland. Their description is a bit vague but indicates that the Italian version of Tic-tac-toe is actually Three Men's Morris.

Anonymous. Play the game. Guardian Education section (21 Sep 1993) 18-19. Shows a stone board with the # incised on it 'from Bet Shamesh, Israel, 2000 BC'. This might be the same as the first board below??

A small exhibition of board games organized by Irving Finkel at the British Museum, 1991, displayed the following.

Stone slab with the usual # Tick-Tac-Toe board incised on it, but really a 4 x 3 board. With nine stone men. From Giza, >-850. BM items EA 14315 & 14309, donated by W. M. Flinders Petrie. Now on display in Room 63, Case C.

Stone Nine Holes board from the Temple of Artemis, Ephesus, 2C-4C. Item BM GR 1873.5.5.150. This is a 3 x 3 array of depressions. Now on display in Room 69, Case 9.

Robbie Bell & Michael Cornelius. Board Games Round the World. CUP, 1988. P. 6 states that the crossed square board has been found at Kurna (c-1400) and at the Ptolemaic temple at Komombo (c-300). They state that Three Men's Morris is the game mentioned by Ovid in Ars Amatoria. They say that it was known to the Chinese at the time of Confucius (c-500) under the name of Yih, but is now known as Luk tsut k'i. They also say the game is also known as Nine Holes -- which seems wrong to me.

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. (There was also an edition by Arnald Steiger, Geneva, 1941.) See 4.B.5 for more details of this work. Vol. 2, f. 93v, p. CLXXXVI, shows a doubly crossed square board. ??NX -- need to study text.

Pieter Bruegel (the Elder). Children's Games. Painting dated 1560 at the Kunsthistorisches Museum, Vienna. In the right background, children are playing a game involving throwing balls into holes in the ground, but the holes appear to be in a straight line.

Anonymous. Games of the 16th Century. 1950. Op. cit. in 4.A.3. P. 134 describes nine-holes, quoting an unknown poet of 1611: "To play at loggats, Nine-holes, or Ten-pinnes". The author doesn't specify what positions the balls are to be rolled into. P. 152 describes Troll-my-dames or Troule-in-madame: "they may have in the end of a bench eleven holes made, into which to troll pummets, or bowls of lead, ...."

William Wordsworth. The Prelude, Book 1. Completed 1805, published 1850. Lines 509 513.

At evening, when with pencil, and smooth slate

In square divisions parcelled out and all

With crosses and with cyphers scribbled o'er,

We schemed and puzzled, head opposed to head

In strife too humble to be named in verse.

It is not clear if this is referring to Noughts and Crosses.

Charles Babbage. The Philosophy of Analysis -- unpublished collection of MSS in the BM as Add. MS 37202, c1820. ??NX. F. 4r is part of the Table of Contents. It shows Noughts and Crosses games played on the # board and on a 4 x 4 board adjacent to entry 4: The Mill. Ff. 124-146 are: Essay 10 -- Of questions requiring the invention of new modes of analysis. On f. 128.r, he refers to a game in which "the relative positions of three of the marks is the object of inquiry." Though the reference is incomplete, a Noughts and Crosses game is drawn on the facing page, f. 127.v. Ff. 134-144 are: Essay 10 Part 5. At the top of f. 134.r, he has added a note: "This is probably my earliest Note on Games of Skill. I do not recollect the date. 3 March 1865". The Essay begins: "Amongst the simplest of those games requiring any degree of skill which amuse our early years is one which is played at in the following manner." He then describes the game in detail and makes some simple analysis, but he never uses a name for it.

Charles Babbage. Notebooks -- unpublished collection of MSS in the BM as Add. MS 37205. ??NX. On f. 304, he starts on analysis of games. Ff. 310-383 are almost entirely devoted to Tit-Tat-To, with some general discussions. Most of this material comprises a few sheets of working, carefully dated, sometimes amended and with the date of the amendment. A number of sheets describe parts of the automaton that he was planning to build which would play the game, but no such machine was built until 1949. The sheets are not always in strict chronological order.

F. 310.r is the first discussion of the game, called Tit Tat To, dated 17 Sep 1842. On F. 312.r, 20 Sep 1843, he says he has "Reduced the 3024 cases D to 199 which include many Duplicates by Symmetry." F. 321.r, 10 Sep 1860, is the beginning of a summary of his work on games of skill in general. He refers to Tit-tat-too. F. 322.r continues and he says: "I have found no game of skill more simple that that which children often play and which they call Tit tat-to." F. 324-333, Oct 1844, studies "General laws for all games of Skill between two players" and draws flow charts showing the basic recursive analysis of a game tree (ff. 325.v & 325.r). On f. 332, he counts the number of positions as 9! + 8! + ... + 1!  = 409,113. F. 333 has an idea of the tree structure of a game. On ff. 337-338, 8 Sep 1848, he has Tit-tat too. On ff. 347.r-347.v, he suggests Nine Men's Morris boards in triangular and pentagonal shapes and does various counting on the different shapes. On ff. 348-349, 26 Oct 1859, he uses Tit-Tat-To.

John M. Dubbey. The Mathematical Work of Charles Babbage. CUP, 1978, pp. 96 97 & 125 130. He discusses the above Babbage material. On p. 127, Dubbey has: "After a surprisingly lengthy explanation of the rules, he attempts a mathematical formulation. The basic problem is one that appears not to have been previously considered in the history of mathematics." Babbage represents the game using roots of unity. Dubbey, on p. 129, says: "This analysis ... must count as the first recorded stochastic process in the history of mathematics." However, it is really a deterministic two-person game.

Games and Sports for Young Boys. Routledge, nd [1859 - BLC]. P. 70, under Rhymes and Calls: "In the game of Tit-tat-toe, which is played by very young boys with slate and pencil, this jingle is used:--

Tit, tat, toe, my first go:

Three jolly butcher boys all in a row;

Stick one up, stick one down.

Stick one on the old man's crown."

Baron Tassilo von Heydebrand und von der Lasa. Ueber die griechischen und römischen Spiele, welche einige ähnlichkeit mit dem Schach hatten. Deutsche Schachzeitung (1863) 162-172, 198-199, 225-234, 257-264. ??NYS -- described on Fiske 121-122 & 137, who says van der Linde I 40-47 copies much of it. Von der Lasa asserts that the Parva Tabella of Ovid is Kleine Mühle (Three Men's Morris). He says the game is called Tripp, Trapp, Trull in the Swedish book Hand-Bibliothek för Sällkapsnöjen, of 1839, vol. II, p. 65 (or 57) -- ??NYS. Van der Linde says that the Dutch name is Tik, Tak, Tol. Fiske notes that both of these refer to Noughts and Crosses, but it is unclear if von der Lasa or van der Linde recognised the difference between Three Men's Morris and Noughts and Crosses.

C. Babbage. Passages from the Life of a Philosopher. 1864. Chapter XXXIV -- section on Games of Skill, pp. 465 471. (= pp. 152 156 in: Charles Babbage and His Calculating Engines, Dover, 1961.) Partial analysis. He calls it tit tat to.

The Play Room: or, In-door Games for Boys and Girls. Dick & Fitzgerald(?), 1866. [Reprinted as: How to Amuse an Evening Party. Dick & Fitzgerald, NY, 1869.] ??NX -- the 1869 was seen at Shortz's. P. 22: Tit-tat-to. Uses O and +. "This is a game that small boys enjoy, and some big ones who won't own it."

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 text is clearly derived from Every Boy's Book, whose first edition was 1856. But the main part of the text considered here is not in the 1856 ed of Every Boy's Book (with J. G. Wood as unnamed editor), but is in the 8th ed of 1868 (published for Christmas 1867), which was the first seriously revised edition, with Edmund Routledge as editor. So this may be c1868. This is the first published use of the term Noughts and Crosses found so far -- the OED's 1861 quote is to Oughts and Crosses..

Pp. 46-47: Slate games: Noughts and crosses. "This is a capital game, and one which every school-boy truly enjoys." Though the example shown is a draw, there is no mention of the fact that the game should always be a tie.

Pp. 85-86: Nine-holes. This has nine holes in a row and each player has a hole. The ball is rolled to them and the person in whose hole it lands must run and pick up the ball and try to hit one of the others who are running away. So this has nothing to do with our games or other forms of Nine Holes.

P. 106: Nine-holes or Bridge-board. This has nine holes in an upright board and the object is get one's marbles through the holes. (This material is in the 1856 ed. of Every Boy's Book.)

Correspondent to Notes and Queries (1875) ??NYS -- quoted by Strutt-Cox 257. Describes a game called Three Mans' Marriage [sic] in Derbyshire which seems to be Noughts and Crosses played on a crossed square board. Pieces are not described as moving, but in the next description of a Nine Men's Morris, they are specifically described as moving. However, the use of a crossed square board may indicate that diagonals were not considered.

Cassell's. 1881. Slate Games: Noughts and Crosses, or Tit Tat To, p. 84, with cross reference under Tit-Tat-To, p. 87. = Manson, 1911, pp. 202-203 & 208.

Albert Norman. Ungdomens Bok [Book for Youth] (in Swedish). 2nd ed., Stockholm, 1883. Vol. I, p. 162++. ??NYS -- quoted and described in Fiske 134-136. Description of Tripp, Trapp, Trull, with winning cry: "Tripp, trapp, trull, min qvarn är full." (Qvarn = mill.)

Lucas. RM2, 1883. Pp. 73-99. Analysis of Three Men's Morris, on a board with the main diagonals drawn, with moves of only one square along a winning line. He shows this is a first person game. If the first player is not permitted to play in the centre, then it is a tie game. No mention of Tic-Tac-Toe.

Albert Ellery Berg, ed. The Universal Self Instructor. Thomas Kelly, NY, 1883. Tit tat to, p. 379. Brief description.

Mark Twain. The Adventures of Huckleberry Finn. 1884. Chap. XXXIV, about half-way through. "It's as simple as tit-tat-toe, three-in-a-row, ..., Huck Finn."

"A wrangler and late master at Harrow school." The science of naughts and crosses. Boy's Own Paper 10: (No. 498) (28 Jul 1888) 702 703; (No. 499) (4 Aug 1888) 717; (No. 500) (11 Aug 1888) 735; (No. 501) (18 Aug 1888) 743. Exhaustive analysis, including odds of second player making a correct response to each opening. For first move in: middle, side, corner, the odds of a correct response are: 1/2, 1/2, 1/8. He implies that the analysis is not widely known.

"Tom Wilson". Illustred Spelbok (in Swedish). Nd [late 1880s??]. ??NYS -- described by Fiske 136-137. This gives Tripp, Trapp, Trull as a Three Men's Morris game on the crossed square, with moves "according to one way of playing, to whatever points they please, but according to another, only to the nearest point along the lines on which the pieces stand. This last method is always employed when the board has, in addition to the right lines, or lines joining the middles of the exterior lines, also diagonals connecting the angles". He then describes a drawn version using the # board and 0 and + (or 1 and 2 in the North) which seems to be genuinely Noughts and Crosses. Fiske says the book seems to be based on an early edition of the Encyclopédie des Jeux or a similar book, so it is uncertain how much the above represents the current Swedish game. Fiske was unable to determine the author's real name, though he was still living in Stockholm at the time.

Il Libro del Giuochi. Florence, 1894. ??NYS -- described in Fiske, pp. 109-110. Gives doubly crossed square board and mentions a Three Men's Morris game.

T. de Moulidars. Grande Encyclopédie des Jeux. Montgredien or Librairie Illustree, Paris, nd. ??NYS -- Fiske 115 (in 1905) says it appeared 'not very long ago' and that Gelli seems to be based on it. Fiske quotes the clear description of Three Men's Morris as Marelle Simple, using a doubly crossed square, saying that pieces move to adjoining cells, following a line, and that the first player should win if he plays in the centre. Fiske notes that Noughts and Crosses is not mentioned.

J. Gelli. Come Posso Divertirmi? Milan, 1900. ??NYS -- described in Fiske 107. Fiske quotes the description of Three Men's Morris as Mulinello Semplice, essentially a translation from Moulidars.

Dudeney. CP. 1907. Prob. 109: Noughts and crosses, pp. 156 & 248. (c= MP, prob. 202: Noughts and crosses, pp. 89 & 175 176. = 536, prob. 471: Tic tac toe, pp. 185 & 390 392. Asserts the game is a tie, but gives only a sketchy analysis. MP gives a reasonably exhaustive analysis. Looks at Ovid's game.

A. C. White. Tit tat toe. British Chess Magazine (Jul 1919) 217 220. Attempt at a complete analysis, but has a mistake. See Gardner, SA (Mar 1957) = 1st Book, chap. 4.

D'Arcy Wentworth Thompson. Science and the Classics. OUP, 1940. Section V Games and Playthings, pp. 148-165. On p. 160, he quotes Ovid and says it is Noughts and Crosses, or in Ireland, Tip-top-castle.

The Home Book of Quizzes, Games and Jokes. Blue Ribbon Books, NY, 1941. This is excerpted from several books -- this material is most likely taken from: Clement Wood & Gloria Goddard; Complete Book of Games; same publisher, nd [late 1930s]. P. 150: Tit-tat-toe, noughts and crosses. Brief description of the game on the # board. "To win requires great ingenuity."

G. E. Felton & R. H. Macmillan. Noughts and Crosses. Eureka 11 (Jan 1949) 5-9. Mentions Dudeney's work on the 3 x 3 board and asks for generalizations. Mentions pegotty = go-bang. Then studies the 4 x 4 x 4 game -- see 4.B.1.a. Adds some remarks on pegotty, citing Falkener, Lucas and Tarry.

Stanley Byard. Robots which play games. Penguin Science News 16 (Jun 1950) 65-77. On p. 73, he says D. W. Davies, of the National Physical Laboratory, has built, and exhibited to the Royal Society in May 1949, an electro-mechanical noughts and crosses machine. A photo of the machine is plate 16. He also mentions Babbage's interest in such a machine and an 1874 paper to the US National Academy by a Dr. Rogers -- ??NYS.

P. C. Parks. Building a noughts and crosses machine. Eureka 14 (Oct 1951) 15-17. Cites Babbage, Rogers, Davies, Byard. Parks built a simple machine with wire and tin cans in 1950 at a cost of about £6. Says G. Eastell of Thetford, Norfolk, built a machine using sixty valves for the Festival of Britain.

Gardner. Ticktacktoe. SA (Mar 1957) c= 1st Book, chap. 4. Quotes Wordsworth, discusses Three Men's Morris (citing Ovid) and its variants (including versions on 4 x 4 and 5 x 5 boards), the misère version (the person who makes three in a row loses), three and n dimensional forms (giving L. Moser's result on the number of winning lines on a kⁿ board), go-moku, Babbage's proposed machine, A. C. White's article. Addendum mentions the Opies' assertion that the name comes from the rhyme starting "Tit, tat, toe, My first go,".

C. L. Stong. The Amateur Scientist. Ill. by Roger Hayward. S&S, 1960. A ticktacktoe machine, pp. 384-385. Noel Elliott gives a brief description of a relay logic machine to play the game.

Donald Michie. Trial and error. Penguin Science Survey 2 (1961) 129-145. ??NYS. Describes his matchbox and bead learning machine, MENACE (Matchbox educable noughts and crosses engine), for the game.

Gardner. A matchbox game-learning machine. SA (Mar 1962) c= Unexpected, chap. 8. Describes Michie's MENACE. Says it used 300 matchboxes. Gardner adapts it to Hexapawn, which is much simpler, requiring only 24 matchboxes. Discusses other games playable by 'computers'. Addendum discusses results sent in by readers including other games.

Barnard. 50 Observer Brain-Twisters. 1962. Prob. 34: Noughts and crosses, pp. 39 40, 64 & 93 94. Asserts there are 1884 final winning positions. He doesn't consider equivalence by symmetry and he allows either player to start.

Donald Michie & R. A. Chambers. Boxes: an experiment in adaptive control. Machine Intelligence 2 (1968) 136-152. Discusses MENACE, with photo of the pile of boxes. Says there are 288 boxes, but doesn't explain exactly how he found them. Chambers has implemented MENACE as a general game-learning computer program using adaptive control techniques designed by Michie. Results for various games are given.

S. Sivasankaranarayana Pillai. A pastime common among South Indian school children. In: P. K. Srinivasan, ed.; Ramanujan Memorial Volumes: 1: Ramanujan -- Letters and Reminiscences; 2: Ramanujan -- An Inspiration; Muthialpet High School, Number Friends Society, Old Boys' Committee, Madras, 1968. Vol. 2, pp. 81-85. [Taken from Mathematics Student, but no date or details given -- ??] Shows ordinary tic-tac-toe is a draw and considers trying to get t in a row on an n x n board. Shows that n = t  3 is a draw and that if t  n + 1 - (n/6), then the game is a draw.

L. A. Graham. The Surprise Attack in Mathematical Problems. Dover, 1968. Tic-tac-toe for gamblers, prob. 8, pp. 19-22. Proposed by F. E. Clark, solutions by Robert A. Harrington & Robert E. Corby. Find the probability of the first player winning if the game is played at random. Two detailed analyses shows that the probabilities for first player, second player, tie are (737, 363, 160)/1260.

[Henry] Joseph & Lenore Scott. Quiz Bizz. Puzzles for Everyone -- Vol. 6. Ace Books (Charter Communications), NY, 1975. P. 143: Ha-ho-ha. Misère version of noughts and crosses proposed. No discussion.

Gyles Brandreth. Pencil and Paper Games and Puzzles. Carousel, 1976. Noughts and Crosses, pp. 11-12. Asserts "It's been played all around the world for hundreds, if not thousands, of years ...." I've included it as a typical example of popular belief about the game. = Pencil & Paper Puzzle Games; Watermill Press, Mahwah, New Jersey, 1989, Tic-Tac-Toe, pp. 11 12.

Winning Ways. 1982. Pp. 667-680. Complete and careful analysis, including various uncommon traps. Several equivalent games. Discusses extensions of board size and dimension.

Sheila Anne Barry. The World's Best Travel Games. Sterling, NY, 1987. Tic-tac-toe squared, pp. 88-89. Get 3 in a row on the 4 x 4 board. Also considers Tic-tac-toe-toe -- get 4 in a row on 5 x 5 board.

George Markovsky. Numerical tic-tac-toe -- I. JRM 22:2 (1990) 114-123. Describes and studies two versions where the moves are numbered 1, 2, .... One is due to Ron Graham, the other to P. H. Nygaard and Markowsky sketches the histories.

Ira Rosenholtz. Solving some variations on a variant of tic-tac-toe using invariant subsets. JRM 25:2 (1993) 128-135. The basic variant is to avoid making three in a row on a 4 x 4 board. By playing symmetrically, the second player avoids losing and 252 of the 256 centrally symmetric positions give a win for the second player. Extends analysis to 2n x 2n, 5 x 5, 4 x 4 x 4, etc.

Bernhard Wiezorke. Sliding caution. CFF 32 (Aug 1993) 24-25 & 33 (Feb 1994) 32. This describes a sliding piece puzzle on the doubly crossed square board -- see under 5.A.

See: Yuri I. Averbakh; Board games and real events; 1995; in 5.R.5, for a possible connection.