Sources page biographical material

THE 15 PUZZLE
W. W. Johnson. Notes on the 15 Puzzle -- I. Amer. J. Math. 2 (1879) 397 399.

W. E. Story. Notes on the 15 Puzzle -- II. Ibid., 399 404.

J. J. Sylvester. Editorial comment. Ibid., 404.

(This issue may have been delayed to early 1880?? Johnson & Story are not terribly readable, but Sylvester is interesting, asserting that this is the first time that the parity of a permutation has become a popular concept.)

Anonymous. Untitled editorial. New York Times (23 Feb 1880) 4. "... just now the chief amusement of the New York mind, ... a mental epidemic .... In a month from now, the whole population of North America will be at it, and when the 15 puzzle crosses the seas, it is sure to become an English mania."

Anonymous. EUREKA! The Popular but Perplexing Problem Solved at Last. "THIRTEEN -- FOURTEEN -- FIFTEEN" New York Herald (28 Feb 1880) 8. ""Fifteen" is a puzzle of seeming simplicity, but is constructed with diabolical cunning. At first sight the victim feels little or no interest; but if he stops for a single moment to try it, or to look at any one else who is trying it, the mania strikes him. ... As to the last two numbers, it depends entirely upon the way in which the blocks happen to fall in the first place .... Two or three enterprising gamblers took up the puzzle and for a time made an excellent living.... The subject was brought up in the Academy of Sciences by the veteran scientist Dr. P. H. Vander Weyde", who showed it could not be solved. The Herald reporter discovered that the problem is solvable if one turns the board 90^o, i.e. runs the numbers down instead of across, and Vander Weyde was impressed. The article implies the puzzle had already been widely known for some time.

Mary T. Foote. US Patent 227,159 -- Game apparatus. Filed: 4 Mar 1880; patented: 4 May 1880. 1p + 1p diagrams. The patent is for a box with sliding numbered blocks for teaching the multiplication tables. Lines 57-63: "I am aware that it is not novel to produce a game apparatus in which blocks are to be mixed and then replaced by a series of moves; also, that it is not novel to number such blocks, as in the "game of 15," so called, where the fifteen numbers are first mixed and then moved into place."

Persifor Frazer Jr. Three methods and forty eight solutions of the Fifteen Problem. Proc. Amer. Philos. Soc. 18 (1878 1880) 505 510. Meeting of 5 Mar 1880. Rather cryptic presentation of some possible patterns. Asserts his 26 Feb article in the Bulletin (??NYS -- ??where -- Philadelphia??) was the first "solution for the 13, 15, 14 case".

J. A. Wales. 15 - 14 - 13 -- The Great Presidential Puzzle. Puck 7 (No. 158) (17 Mar 1880) back cover.

Anonymous. Editorial: "Fifteen". New York Times (22 Mar 1880) 4. "No pestilence has ever visited this or any other country which has spread with the awful celerity of what is popularly called the "Fifteen Puzzle." It is only a few months ago that it made its appearance in Boston, and it has now spread over the entire country." Asserts that an unregenerate Southern sympathiser has introduced it into the White House and thereby disrupted a meeting of President Hayes' cabinet.

Sch. [H. Schubert]. The Boss Puzzle. Hamburgischer Correspondent (= Staats- und Gelehrte Zeitung des Hamburgischen unpartheyeischen Correspondent) No. 82 (6 Apr 1880) 11, with response on 87 (11 Apr 1880) 12 (Sprechsaal). Gives a fairly careful description of odd and even permutations and shows the puzzle is solvable if and only if it is in an even permutation. The response is signed X and says that when the problem is insoluble, just turn the box by 90^o to see another side of the problem!

Gebr. Spiro, Hofliefer (Court supplier), Jungfernsteig 3(?--hard to read), Hamburg. Hamburgischer Correspondent (= Staats- und Gelehrte Zeitung des Hamburgischen unpartheyeischen Correspondent) No. 88 (13 Apr 1880) 7. Advertises Boss Puzzles: "Kaiser-Spiel 50Pf. Bismarck-Spiel 50 Pf. Spiel der 15 u. 16, 50 Pf. Spiel der 16 separat, 15 Pf. System und Lösung, 20 Pf."

G. W. Warren. Letter: Clew to the Fifteen Puzzle. The Nation 30 (No. 774) (29 Apr 1880) 326.

Anon. Shavings. The London Figaro (1 May 1880) 12. "The "15 Puzzle," which has for some months past been making a sensation in New York equal to that aroused by "H. M. S. Pinafore" last year, has at length reached this country, and bids fair to become the rage here also." (Complete item!)

George Augustus Sala. Echoes of the Week. Illustrated London News 76 (No. 2138) (22 May 1880) 491.

Mary T. Foote. US Patent 227,159 -- Game Apparatus. Applied: 4 Mar 1880; patented: 4 May 1880. 1p + 1p diagrams. Described in Hordern, p. 27. 3 x 12 puzzles based on multiplication tables. Refers to the "game of 15" and Kinsey.

Arthur Black. ?? Brighton Herald (22 May 1880). ??NYS -- mentioned by Black in a letter to Knowledge 1 (2 Dec 1881) 100.

Anonymous. Our latest gift to England. From the London Figaro. New York Times (11 Jun 1880) 2(?). ??page

The Premier. First (?) double sided version, with pictures of Gladstone and Beaconsfield, apparently produced for the 1880 UK election. Described in Hordern, pp. 32 33 & plate I.

Ahrens. MUS II 227. 1918. Story of Reichstag being distracted in 1880.

P. G. Tait. Note on the Theory of the "15 Puzzle". Proc. Roy. Soc. Edin. 10 (1880) 664 665. Brief but valid analysis. Mentions Johnson & Story. First mention of the possibility of a 3D version.

T. P. Kirkman. Question 6489 and Note on the solution of the 15 puzzle in question 6489. Mathematical Questions with their Solutions from the Educational Times 34 (1880) 113 114 & 35 (1881) 29 30. The question considers the n x n problem. The note is rather cryptic. (No use??)

Messrs. Cremer (210 Regent St. and 27 New Bond St., London). Brilliant Melancholia. Albrecht Durer's Game of the Thirty Four and "Boss" Game of the Fifteen. 1880. Small booklet, 16pp + covers, apparently instructions to fit in a box with pieces numbered 1 to 16 to be used for making magic squares as well as for the 15 puzzle. Explains that only half the positions of the 15 puzzle are obtainable and describes them by examples. (Photo in The Hordern Collection of Hoffmann Puzzles, p. 74, and in Hordern, op. cit. above, plate IV.) Possibly written by "Cavendish" (Henry Jones).

H. Schubert. Theoretische Entscheidung über das Boss Puzzle Spiel. 2nd ed., Hamburg, 1880. ??NYS (MUS, II, p. 227)

Gaston Tissandier. Les carrés magiques -- à propos du "Taquin," jeu mathématique. La Nature 8 (No. 371) (10 Jul 1880) 81 82. Simple description of the puzzle called 'Taquin' which came from America and has had a very great success for several weeks. Says it had 16 squares and was usable as a sliding piece puzzle or a magic square puzzle. Cites Frénicle's 880 magic squares of order 4.

Anon. & C. Henry. Gaz. Anecdotique Littéraire, Artistique et Bibliographique. (Pub. by G. d'Heylli, Paris) Year 5, t. II, 1880, pp. 58 59 & 87 92. ??NYS

Piarron de Mondésir. Le dernier mot du taquin. La Nature 8 (No. 382) (25 Sep 1880) 284 285. Simple description of parity decision for the 15 puzzle. Says 'la Presse illustrée' offered 500 francs for achieving the standard pattern from a random pattern, but it was impossible, or rather it was possible in only half the cases.

Jasper W. Snowdon. The "Fifteen" Puzzle. Leisure Hour 29 (1880) 493 495.

Gwen White. Antique Toys. Batsford, London, 1971; reprinted by Chancellor Press, London, nd [1982?]. On p. 118, she says: "The French game of Taquin was played in 1880, in which 15 pieces had to be moved into 16 compartments in as few moves as possible; the word 'taquin' means 'a teaser'." She gives no references.

Tissandier. Récréations Scientifiques. 1880?

2nd ed., 1881 -- unlabelled section, pp. 143-153. As: Le taquin et les carrés magiques; seen in 1883 ed., ??NX; 1888: pp. 208-215. Adapted from the 1880 La Nature articles of Tissandier and de Mondésir. 1881 says it came from America -- 'récemment une nouvelle apparition', but this is dropped in 1888 -- otherwise the two versions are the same.

Translated in Popular Scientific Recreations, nd [c1890], pp. 731 735. Text says "Mathematical games, ..., have recently obtained a new addition .... ... from America, ...." The references to contemporary reactions are deleted and the translation is confused. E.g. the newspaper is now just "a French paper" and the English says the problem is impossible in nine cases out of ten!

Lucas. Récréations scientifiques sur l'arithmétique et sur la géométrie de situation. Sixième récréation: Sur le jeu du taquin ou du casse tête américain. Revue scientifique de France et de l'étranger (3) 27 (1881) 783 788. c= Le jeu du taquin, RM1, 1882, pp. 189 211. Revue says that Sylvester told him that it was invented 18 months ago by an American deaf mute. RM1 says "vers la fin de 1878". Cf Schubert, 1895.

Cassell's. 1881. Pp. 96 97: American puzzles "15" and "34". = Manson, pp. 246-248. Says "articles ... have appeared in many periodicals, but no one has ... publish[ed] a solution." Then sketches the parity concept and its application.

Richard A. Proctor. The fifteen puzzle. Gentlemen's Magazine 250 (No. 1801) (1881) 30 45.

"Boss". Letter: The fifteen puzzle. Knowledge 1 (11 Nov 1881) 37-38, item 13. This magazine was edited by Proctor. The letter starts: "I am told that in a magazine article which appeared some time ago, you have attempted to show that there are positions in the Fifteen Puzzle from which the won position can never be obtained." I suspect the letter was produced by Proctor. The response is signed Ed. and begins: "I thought the Fifteen Puzzle was dead, and hoped I had had some share in killing the time-absorbing monster." Notes that many people get to the position starting blank, 1, 2, 3 and view this as a win. Sketches parity argument and suggests "Boss" work on the 3 x 3 or 3 x 2 or even the 2 x 2 version.

Editorial comment. The fifteen puzzle. Knowledge 1 (25 Nov 1881) 79. "I supposed every one knew the Fifteen Puzzle." Proceeds to explain, obviously in response to readers who didn't know it.

Arthur Black. Letter: The fifteen puzzle. Knowledge 1 (2 Dec 1881) 100, item 80. Sketches a proof which he says he published in the Brighton Herald of 22 May 1880.

"Yawnups". Letter: The fifteen puzzle. Knowledge 1 (30 Dec 1881) 185. Solution from the 15-14 position obtained by turning the box. Editorial comment says the solution uses 102 moves and the editor gets an easy solution in 57 moves. Adds that a 60 move solution has been received.

Arthur Black. Letter: The fifteen puzzle. Knowledge 1 (13 Jan 1882) 230. Finds a solution from the 15-14 position in 39 moves by turning the box and asserts no shorter solution is possible. Says he also gave this in the Brighton Herald in May 1880. An addition says J. Watson has provided a similar solution, which takes 38 moves??

A. B. Letter: The fifteen puzzle. Knowledge 2 (20 Oct 1882) 345, item 598. Finds a box-turning solution in 39 moves.

C. J. Malmsten. Göteborg Handl 1882, p. 75. ??NYS -- cited by Ahrens in his Encyklopadie article, op. cit. in 3.B, 1904.

Anonymous. Enquire Within upon Everything. Houlston and Sons, London. This was a popular book with editions almost every year -- I don't know when the following material was added. Section 2591: Boss; or the Fifteen Puzzle, p. 363. Place the pieces 'indifferently' in the box. Half the positions are unsolvable. Cites Cavendish for the solution by turning the box 90^o but notes this only works with round pieces. Goes on to The thirty-four puzzle, citing Dürer. I found this material in the 66th ed., 862nd thousand, of 1883, but I didn't find the material in the 86th ed of 1892.

Letters received and short answers. Knowledge 4 (16 Nov 1883) 310. 'Impossible'.

P. G. Tait. Listing's Topologie. Philosophical Mag. (5) 17 (No. 103) (Jan 1884) 30 46 & plate opp. p. 80. Section 11, p. 39. Simple but cryptic solution.

Letters received and short answers. Letter from W. S. B. asks how to solve the problem when the last row has 13, 14, 15 [sic!]; Answer by Ed. points out the misprint and says the easiest solution is to remove the 15 and put it after the 14, or to invert the 6 and 9. Knowledge 6 (No. 159) (14 Nov 1884) 412 & 6 (No. 160) (21 Nov 1884) 429.

Don Lemon. Everybody's Pocket Cyclopedia .... Saxon & Co., London, (1888), revised 8th ed., 1890. P. 137: The fifteen puzzle. Brief description, with pieces placed randomly in the box -- "to get the last three into order is often a puzzle indeed".

John D. Champlin & Arthur E. Bostwick. The Young Folk's Cyclopedia of Games and Sports. 1890. ??NYS Cited in Rohrbough; Brain Resters and Testers; c1935; Fifteen Puzzle, p. 20. Describes idea of parity of number of exchanges. [Another reference provided more details of Champlin & Bostwick.]

Lemon. 1890. A trick puzzle, no. 202, pp. 31 & 105 (= Sphinx, no. 422, pp. 60 & 112). 15 puzzle with lines on the pieces to arrange as "a representation of a president with only one eye". The solution is a spelling of the word 'president'. Attributed to Golden Days -- ??. After The Premier puzzle of c1880, this is the second suggestion of using a picture and the first publication of the idea that I have seen.

G. A. Hutchison, ed. Indoor Games and Recreations. The Boy's Own Bookshelf. (1888); New ed., Religious Tract Society, London, 1891. (See M. Adams; Indoor Games for a much revised version, but which doesn't contain this material.) Chap. 19: The American Puzzles., pp. 240 241. "These puzzles, known as the 'Thirty four Game' and the 'Fifteen Game,' on their introduction amongst us some years ago ...." "The '15' puzzle would appear to have been, on its coming to England a few years ago, strictly a new introduction ...." He sketches the parity concept. [NOTE. I have seen a reference to the editor as Hutchinson, but the book definitely omits the first n.]

Daniel V. Brown. US Patent 471,941 -- Puzzle. Applied: 23 Apr 1891; patented: 29 Mar 1892, 2pp + 1p diagrams. Double-sided 16 block puzzle to spell George Washington on one side and Benjamin Harrison on the other. No sliding involved.

Berkeley & Rowland. Card Tricks and Puzzles. 1892. American fifteen puzzle, pp. 105-107. "The Fifteen Puzzle was introduced by a shrewd American some ten years ago, ...." Refers to Tait's 1880 paper. Says half the positions are impossible, but solves them by turning the box 90^o or by inverting the 6 and the 9.

Hoffmann. 1893. Chap IV, no. 69: The "Fifteen" or "Boss" puzzles, pp. 161 162 & 217 218 = Hoffmann-Hordern, pp. 142-144, with photo of five early examples, two or three of which also are thirty-four puzzles. (Hordern Collection, p. 74, has a photo of a version by Cremer, cf above.) "This, like a good many of the best puzzles, hails from America, where, some years ago, it had an extraordinary vogue, which a little later spread to this country, the British public growing nearly as excited over the mystic "Fifteen" as they did at a later date over the less innocent "Missing Word" competitions." He distinguishes between the ordinary Fifteen where one puts the pieces in at random, and the Boss or Master puzzle which has the 14 and 15 reversed. "Notwithstanding the enormous amount of energy that has been expended over the "Fifteen" Puzzle, no absolute rule for its solution has yet been discovered and it appears to be now generally agreed by mathematicians that out of the vast number of haphazard positions ... about half admit [of solution]. To test whether ... the following rule has been suggested." He then says to count the parity of the number of transpositions.

Hoffmann. 1893. Chap. IV, no. 70: The peg away puzzle, pp. 163 & 218 = Hoffmann Hordern, p. 145. This is a 3 x 3 version of the Fifteen puzzle, made by Perry & Co. Start with a random pattern and get to standard form. "The possibility of success in solving this puzzle appears to be governed by precisely the same rule as the "Fifteen" Puzzle." Hoffmann-Hordern has no photo of this -- do any examples exist??

H. Schubert. Zwölf Geduldspiele. Dümmler, Berlin, 1895. [Taken from his columns in Naturwissenschaftlichen Wochenschrift, 1891-1894.] Chap. VII: Boss-Puzzle oder Fünfzehner-Spiel, pp. 75-94?? Pp. 75-77 sketches the history, saying it was called "Jeu du Taquin" (Neck-Spiel) in France and was popular in 1879-1880 in Germany. Cites Johnson & Story and his own 1880 booklet. Gives the story of a deaf and dumb American inventing it in Dec 1878, saying "Sylvester communicated this at the annual meeting of the Association Française pour l'Avancement des Sciences at Reims". Cf Lucas, 1881. [There is a second edition, Teubner??, Leipzig, 1899, ??NYS. However this material is almost identical to the beginning of Chap. 15 in Schubert's Mathematische Mussestunden, 3rd ed., Göschen, Leipzig, 1909, vol. 2. The later version omits only some of the Hamburg details of 1879-1880. Hence the 2nd ed. of Zwölf Geduldspiele is probably very close to these versions.]

Dudeney. Problem 49: The Victoria Cross puzzle. Tit Bits 32 (4 & 25 Sep 1897) 421 & 475. = AM, 1917, prob. 218, pp. 60 & 194. B7. 3 x 3 board with letters Victoria going clockwise around the edges, leaving the middle empty, and starting with V in a corner. Slide to get Victoria starting at an edge cell, in the fewest moves. Does it in 18 moves, by interchanging the i's and says there are 6 such solutions.

Dudeney. Problem 65: The Spanish dungeon. Tit Bits 33 (1 Jan & 5 Feb 1898) 257 & 355. = AM, 1917, prob. 403, pp. 122-123 & 244. B14. Convert 15 Puzzle, with pieces in correct order, into a magic square. Does it in 37 moves.

Conrad F. Stein. US Design 29,649 -- Design for a Game-Board. Applied: 29 Sep 1898; patented: 8 Nov 1898 as No. 692,242. 1p + 1p diagrams. This appears to be a 3 x 4 puzzle with a picture of a city with a Spanish flag on a tower. Apparently the object is to move an American flag to the tower.

Anon. & Dudeney. A chat with the Puzzle King. The Captain 2 (Dec? 1899) 314-320; 2:6 (Mar 1900) 598-599 & 3:1 (Apr 1900) 89. The eight fat boys. 3 x 3 square with pieces: 1 2 3; 4 X 5; 6 7 8 to be shifted into a magic square. Two solutions in 19 moves. Cf Dudeney, 1917.

Addison Coe. US Patent 785,665 -- Puzzle or Game Apparatus. Applied: 17 Nov 1904; patented: 1 Mar 1905. 4pp + 3pp diagrams. Gives a 3 x 5 flat version and a 3 dimensional version -- cf 5.A.2.

Dudeney. AM. 1917.

Prob. 401: Eight jolly gaol birds, pp. 122 & 243. E23. Same as 'The eight fat boys' (see Anon. & Dudeney, 1899) with the additional condition that one person refuses to move, which occurs in one of the two previous solutions.

Prob. 403: The Spanish dungeon, pp. 122-123 & 244. = Tit-Bits prob. 65 (1898). B14.

Prob. 404: The Siberian dungeons, pp. 123 & 244. B16. 2 x 8 array with prisoners 1, 2, ..., 8 in top row and 9, 10, ..., 16 in bottom row. Two extra rows of 4 above the right hand end (i.e. above 5, 6, 7, 8) are empty. Slide the prisoners into a magic square. Gives a solution in 14 moves, due to G. Wotherspoon, which they feel is minimal. This allows long moves -- e.g. the first move moves 8 up two and left 3.

"H. E. Licks" [pseud. of Mansfield Merriman]. Recreations in Mathematics. Van Nostrand, NY, 1917. Art. 28, pp. 20 21. 'About the year 1880 ... invented in 1878 by a deaf and dumb man....'

[From sometime in the 1980s, I suspected the author's name was a pseudonym. On pp. 132-138, he discusses the Diaphote Hoax, from a Pennsylvania daily newspaper of 10 Feb 1880, which features the following people: H. E. Licks, M. E. Kannick, A. D. A. Biatic, L. M. Niscate. The diaphote was essentially a television. He says this report was picked up by the New York Times and the New York World. An email from Col. George L. Sicherman on 5 Jun 2000 agrees that the name is false and suggested that the author was "the eminent statistician Mansfield Merriman" who wrote the article on The Cattle Problem of Archimedes in Popular Science Monthly (Nov 1905), which is abridged on pp. 33-39 of the book, but omitting the author's name. Sichermann added that Merriman was one of the authors of Pillsbury's List. William Hartston says this was an extraordinary list of some 30 words which Pillsbury, who did memory feats, was able to commit to memory quite rapidly. Sicherman continued to investigate Merriman and got Prof. Andri Lange interested and Lange corresponded with a James A. McLennan, author of a history of the physics department at Lehigh University where Merriman had been. McLennan found Merriman's obituary from the American Society of Civil Engineers which states that Merriman used H. E. Licks as a pseudonym. [Email from Sicherman on 25 Feb 2002.]]

Stephen Leacock. Model Memoirs and Other Sketches from Simple to Serious. John Lane, The Bodley Head, 1939, p. 300. "But this puzzle stuff, as I say, is as old as human thought. As soon as mankind began to have brains they must have loved to exercise them for exercise' sake. The 'jig-saw' puzzles come from China where they had them four thousand years ago. So did the famous 'sixteen puzzle' (fifteen movable squares and one empty space) over which we racked our brains in the middle eighties."

G. Kowalewski. Boss Puzzle und verwandte Spiele. K. F. Kohler Verlag, Leipzig, 1921 (reprinted 1939). Gives solution of general polygonal versions, i.e. on a graph with a Hamilton circuit and one or more diagonals.

Hummerston. Fun, Mirth & Mystery. 1924.
1 2

9 Push, pp. 22 & 25. This is played on the board

3 10 11 4 shown at the left with its orthogonal lines, like

12 13 3, 10, 11, 4, and its diagonal lines, like

5 14 15 6 1, 9, 11, 13, 6. 10, 15 and 11, 14 are not

16 connected, so this is an octagram. Take 16

7 8 numbered counters and place them at random on

the board and remove counter 16. Move the pieces

to their correct locations. He asserts that 'unlike the original ["Sixteen" Puzzle],

no position can be set up in "Push" that cannot be solved'.

The six bulls puzzle, Puzzle no. 34, pp. 90 & 177. This uses the 2 x 3 + 1 0    

board shown at the right, where the 0 is the blank space. Exchange 1 2 3

3 and 6 and 4 and 5. He does it in 20 moves. [This is Hordern's 4 5 6

B3, first known from 1977 under the name Bull Pen, but is a variant of