Sources page biographical material

5.H.3. PATH FORMING PUZZLES
Here we have a set of pieces and one has to join them so that some path is formed. This is often due to a chain or a snake, etc. New section. Again, Haubrich's 1995-1996 surveys, op. cit. in 5.H.4, include this as one class.

Hoffmann. 1893. Chap. III, No. 18: The endless chain, pp. 99-100 & 131 = Hoffmann Hordern, pp. 91-92, with photo. 18 pieces, some with parts of a chain, to make into an 8 x 8 array with the chain going through 34 of the cells. All the pieces are rectangles of width one. Photo shows The Endless Chain, by The Reason Manufacturing Co., 1880-1895. Hordern Collection, p. 62, shows the same and La Chaine sans fin, 1880-1905.

Loyd. Cyclopedia. 1914. Sam Loyd's endless chain puzzle, pp. 280 & 377. Chain through all 64 cells of a chessboard, cut into 13 pieces. The chessboard dissection is of type: 13: 02213 131.

Hummerston. Fun, Mirth & Mystery. 1924. The dissected serpent, p. 131. Same pieces as Hoffmann, and almost the same pattern.

Collins. Book of Puzzles. 1927. The dissected snake puzzle, pp. 126-127. 17 pieces forming an 8 x 8 square. All the piece are rectangular pieces of width one except for one L hexomino -- if this were cut into straight tetromino and domino, the pieces would be identical to Hoffmann. The pattern is identical to Hummerston.

See Haubrich in 5.H.4.

5.H.4. OTHER AND GENERAL
These all have coloured edges unless specified. See S&B, p. 36, for examples.
Edwin L[ajette] Thurston. US Patent 487,797 -- Puzzle. Applied: 30 Sep 1890; patented: 13 Dec 1892. 3pp + 3pp diagrams. Reproduced in Haubrich, About ..., 1996, op. cit. below. 4 x 4 puzzles with 6-coloured corners or edges, but assuming no colour is repeated on a piece -- indeed he uses the 15 = BC(6,2) ways of choosing 4 out of 6 colours once only and then has a sixteenth with the same colours as another, but in different order. Also a star-shaped puzzle of six parallelograms.

Edwin L. Thurston. US Patent 487,798 -- Puzzle. Applied: 30 Sep 1890; patented: 13 Dec 1892. 2pp + 1p diagrams. Reproduced in Haubrich, About ..., 1996, op. cit. below. As far as I can see, this is the same as the 4 x 4 puzzle with 6 coloured edges given above, but he seems to be emphasising the 15 pieces.

Edwin L. Thurston. US Patent 490,689 -- Puzzle. Applied: 30 Sep 1890; patented: 31 Jun 1893. 2pp + 1p diagrams. Reproduced in Haubrich, About ..., 1996, op. cit. below. The patent is for 3 x 3 puzzles with 4 coloured corners or edges, but with pieces having no repeated colours and in a fixed orientation. He selects some 8 of these pieces for reasons not made clear and mentions moving them "after the manner of the old 13, 14, 15 puzzle." S&B, p. 36, describes the Calumet Puzzle, Calumet Baking Powder Co., Chicago, which is a 3 x 3 head to tail puzzle, claimed to be covered by this patent.

Le Berger Malin. France, c1900. 3 x 3 head to tail puzzle, but the edges are numbered and the matching edges must add to 10. ??NYS -- described by K. Takizawa, N. Takashima & N. Yoshigahara; Vess Puzzle and Its Family -- A Compendium of 3 by 3 Card Puzzles; published by the authors, Tokyo, 1983. Slocum has this in two different boxes and dates it to c1900 -- I had c1915 previously. Haubrich has one version, Produced by GB&O N.K. Atlas.

Angus K. Rankin. US Patent 1,006,878 -- Puzzle. Applied: 3 Feb 1911; patented: 24 Oct 1911. 2pp + 1p diagrams. Reproduced in Haubrich, About ..., 1996, op. cit. below. Described in S&B, p. 36. Grandpa's Wonder Puzzle. 3 x 3 square puzzle. Each piece has corners coloured, using four colours, and the colours meeting at a corner must differ. The patent doesn't show the advertiser's name -- Grandpa's Wonder Soap -- but is otherwise identical to S&B's photo.

Daily Mail World Record Net Sale puzzle. 1920 1921. Instructions and picture of the pieces. Letter from Whitehouse to me describing its invention. 19 6-coloured hexagons without repeated colours. Daily Mail articles as follows. There may be others that I missed and sometimes the page number is a bit unclear. Note that 5 Dec was a Sunday.

9 Nov 1920, p. 5. "Daily Mail" puzzle. To be issued on 7 Dec.

13 Nov 1920, p. 4. Hexagon mystery.

17 Nov 1920, p. 5. New mystery puzzle. Asserts the inventor does not know the solution -- i.e. the solution has been locked up in a safe.

20 Nov 1920, p. 4. What is it?

23 Nov 1920, p. 5. Fascinating puzzle. The most fascinating puzzle since "Pigs in Clover".

25 Nov 1920, p. 5. Can you do it?

29 Nov 1920, p. 5. £250 puzzle.

1 Dec 1920, p. 4. Mystery puzzle clues.

2 Dec 1920, p. 5. £250 puzzle race.

3 Dec 1920, p. 5. The puzzle.

4 Dec 1920, p. 4. The puzzle. Amplifies on the inventor not knowing the solution -- after the idea was approved, a new pattern was created by someone else and locked up.

6 Dec 1920, unnumbered back page. Photo with caption: £250 for solving this.

7 Dec 1920, p. 7. "Daily Mail" Puzzle. Released today. £100 for getting the locked up solution. £100 for the first alternative solution and £50 for the next alternative solution. "It is believed that more than one solution is possible."

8 Dec 1920, p. 5. "Daily Mail" puzzle.

9 Dec 1920, p. 5. Can you do it?

10 Dec 1920, p. 4. It can be done.

13 Dec 1920, p. 9. Most popular pastime. "More than 500,000 Daily Mail Puzzles have been sold."

15 Dec 1920, p. 4. Puzzle king & the 19 hexagons. Dudeney says he does not think it can be solved "except by trial."

16 Dec 1920, p. 4. Tantalising 19 hexagons.

16 Dec 1920, unnumbered back page. Banner at top has: "The Daily Mail" puzzle. Middle of page has a cartoon of sailors trying to solve it.

17 Dec 1920, p. 5? The Xmas game.

18 Dec 1920, p. 7. Puzzle Xmas 'card'.

20 Dec 1920, p. 7. Hexagon fun.

22 Dec 1920, p. 3. 3,000,000 fascinated. It is assumed that about 5 people try each example and so this indicates that nearly 600,000 have been sold.

23 Dec 1920, p. 3. Too many cooks.

23 Dec 1920, unnumbered back page. Cartoon: The hexagonal dawn!

28 Dec 1920, p. 3? Puzzled millions. "On Christmas Eve the sales exceeded 600,000 ...."

29 Dec 1920, p. 3? "I will do it."

30 Dec 1920, p. 8. Puzzle fun.

3 Jan 1921, p. 3. The Daily Mail Puzzle. C. Lewis, aged 21, a postal clerk solved it within two hours of purchase and submitted his solution on 7 Dec. Hundreds of identical solutions were submitted, but no alternative solutions have yet appeared. There are two pairs of identical pieces: 1 & 12, 4 & 10.

3 Jan 1921, p. 10 = unnumbered back page. Hexagon Puzzle Solved, with photo of C. Lewis and diagram of solution.

10 Jan 1921, p. 4. Hexagon puzzle. Since no alternative hexagonal solutions were received, the other £150 is awarded to those who submitted the most ingenious other solution -- this was judged to be a butterfly shape, submitted by 11 persons, who shared the £150.

Horace Hydes & Francis Reginald Beaman Whitehouse. UK Patent 173,588 -- Improvements in Dominoes. Applied: 29 Sep 1920; complete application: 29 Jun 1921; accepted: 29 Dec 1921. Reproduced in Haubrich, About ..., 1996, op. cit. below. 3pp + 1p diagrams. This is the patent for the above puzzle, corresponding to provisional patent 27599/20 on the package. The illustration shows a solved puzzle based on 'A stitch in time saves nine'.

George Henry Haswell. US Patent 1,558,165 -- Puzzle. Applied: 3 Jul 1924; patented: 11 Sep 1925. Reproduced in Haubrich, About ..., 1996, op. cit. below. 2pp + 1p diagrams. For edge-matching hexagons with further internal markings which have to be aligned. [E.g. one could draw a diagonal and require all diagonals to be vertical -- this greatly simplifies the puzzle!] If one numbers the vertices 1, 2, ..., 6, he gives an example formed by drawing the diagonals 13, 15, 42, 46 which produces six triangles along the edges and an internal rhombus.

C. Dudley Langford. Note 2829: Dominoes numbered in the corners. MG 43 (No. 344) (May 1959) 120 122. Considers triangles, squares and hexagons with numbers at the corners. There are the same number of pieces as with numbers on the edges, but corner numbering gives many more kinds of edges. E.g. with four numbers, there are 24 triangles, but these have 16 edge patterns instead of 4. The editor (R. L. Goodstein) tells Langford that he has made cubical dominoes "presumably with faces numbered". Langford suggests cubes with numbers at the corners. [I find 23 cubes with two corner numbers and 333 with three corner numbers. ??check]

Piet Hein. US Patent 4,005,868 -- Puzzle. Applied: 23 Jun 1975; patented: 1 Feb 1977. Front page + 8pp diagrams + 5pp text. Basically non-matching puzzles using marks at the corners of faces of the regular polyhedra. He devises boards so the problems can be treated as planar.

Kiyoshi Takizawa; Naoaki Takashima & Nob. Yoshigahara. Vess Puzzle and Its Family -- A Compendium of 3 by 3 Card Puzzles. Published by the authors, Tokyo, Japan, 1983. Studies 32 types (in 48 versions) of 3 x 3 'head to tail' matching puzzles and 4 related types (in 4 versions). All solutions are shown and most puzzles are illustrated with colour photographs of one solution. (Haubrich counts 51 versions -- check??)

Melford D. Clark. US Patent 4,410,180 -- Puzzle. Applied: 16 Nov 1981; patented: 18 Oct 1983. Reproduced in Haubrich, About ..., 1996, op. cit. in 5.H.4. 2pp + 2pp diagrams. Corner matching squares, but with the pieces marked 1, 2, ..., so that the pieces marked 1 form a 1 x 1 square, the pieces marked 2 allow this to be extended to a 2 x 2 square, etc. There are n² - (n-1)² pieces marked n.

Jacques Haubrich. Compendium of Card Matching Puzzles. Printed by the author, Aeneaslaan 21, NL-5631 LA Eindhoven, Netherlands, 1995. 2 vol., 325pp. describing over 1050 puzzles. He classifies them by the nine most common matching rules: Heads and Tails; Edge Matching (i.e. MacMahon); Path Matching; Corner Matching; Corner Dismatching; Jig-Saw-Like; Continuous Path; Edge Dismatching; Hybrid. He does not include Jig-Saw-Like puzzles here. Using the number of cards and their shape, then the matching rules, he has 136 types. 31 different numbers of cards occur: 4, 6-16, 18-21, 23-25, 28, 30, 36, 40, 45, 48, 56, 64, 70, 80, 85, 100. There is an index of 961 puzzle names. He says Hoffmann is the earliest published example. He notes that most path puzzles have a global criterion that the result have a single circuit which slightly removes them from his matching criterion and he does not treat them as thoroughly. He has developed computer programs to solve each type of puzzle and has checked them all.

Jacques Haubrich. About, Beyond and Behind Card Matching Puzzles. [= Vol. 3 of above]. Ibid, Apr 1996, 87pp. This is a general discussion of the different kinds of puzzles, how to solve them and their history, reproducing ten patents and two obituaries.

5.I. LATIN SQUARES AND EULER SQUARES
This topic ties in with certain tournament problems but I have not covered them. See also Hoffmann and Loughlin & Flood in 5.A.2 for examples of two orthogonal 3 x 3 Latin squares. The derangement problems in 5.K.2 give Latin rectangles.
Ahrens-1 & Ahrens-2. Opp. cit. in 7.N. 1917 & 1922. Ahrens-1 discusses and cites early examples of Latin squares, going back to medieval Islam (c1200), where they were used on amulets. Ahrens-2 particularly discusses work of al Buni -- see below.

(Ahmed [the h should have an underdot] ibn ‘Alî ibn Jûsuf) el Bûni, (Abû'l ‘Abbâs, el Qoresî.) = Abu l‘Abbas al Buni. (??= Muhyi'l Dîn Abû’l-‘Abbâs al Bûnî -- can't relocate my source of this form.) Sams al ma‘ârif = Shams al ma‘ârif al kubrâ = Šams al-ma‘ārif. c1200. ??NYS. Ahrens-1 describes this briefly and incorrectly. He expands and corrects this work in Ahrens-2. See 7.N for more details. Ahrens notes that a 4 x 4 magic square can be based on the pattern of two orthogonal Latin squares of order 4, and Al-Buni's work indicates knowledge of such a pattern, exemplified by the square

8, 11, 14, 1; 13, 2, 7, 12; 3, 16, 9, 6; 10, 5, 4, 15 considered (mod 4). He also has Latin squares of order 4 using letters from a name of God. He goes on to show 7 Latin squares of order 7, using the same 7 letters each time -- though four are corrupted. (Throughout, the Latin squares also have 'Latin' diagonals, i.e. the diagonals contain all the values.) These are arranged so each has a different letter in the first place. It is conjectured that these are associated with the days of the week or the planets.

Tagliente. Libro de Abaco. (1515). 1541. F. 18v. 7 x 7 Latin square with entries 1, 13, 2, 14, 3, 10, 4 cyclically shifted forward -- i.e. the second row starts 13, 2, .... This is an elaborate plate which notes that the sum of each file is 47 and has a motto: Sola Virtu la Fama Volla, but I could find no text or other reason for its appearance!

Inscription on memorial to Hannibal Bassett, d. 1708, in Meneage parish church, St. Mawgan, Cornwall. I first heard of this from Chris Abbess, who reported it in some newsletter in c1993. However, [Peter Haining; The Graveyard Wit; Frank Graham, Newcastle, 1973, p. 133] cites this as being at Cunwallow, near Helstone, Cornwall. [W. H. Howe; Everybody's Book of Epitaphs Being for the Most Part What the Living Think of the Dead; Saxon & Co., London, nd [c1895] (facsimile by Pryor Publications, Whitstable, 1995); p. 173] says it is in Gunwallow Churchyard. Spelling and punctuation vary a bit. The following gives a detailed account.

Alfred Hayman Cummings. The Churches and Antiquities of Cury & Gunwalloe, in the Lizard District, including Local Traditions. E. Marlborough & Co., London & Truro, 1875, pp. 130-131. ??NX. "It has been said that there once existed ... the curious epitaph --" and gives a considerable rearrangement of the inscription below. He continues "But this is in all probability a mistake, as repeated search has been made for it, not only by the writer, but by a former Vicar of Gunwalloe, and it could nowhere be found, while there is a plate with an inscription in the church at Mawgan, the next parish, which might be very easily the one referred to." He gives the following inscription, saying it is to Hannibal Basset, d. 1708-9. Chris Weeks was kind enough to actually go to the church of St. Winwaloe, Gunwalloe, where he found nothing, and to St. Mawgan in Meneage, a few miles away. Chris Weeks sent pictures of Gunwallowe -- the church is close to the cliff edge and it looks like there could once have been more churchyard on the other side of the church where the cliff has fallen away. In the church at St. Mawgan is the brass plate with 'the Acrostic Brass Inscription', but it is not clearly associated with a grave and I wonder if it may have been moved from Gunwallowe when a grave was eroded by the sea. It is on the left of the arch by the pulpit. I reproduce Chris Weeks' copy of the text. He has sent a photograph, but it was dark and the photo is not very clear, but one can make out the Latin square part.

Hanniball Baet here Inter'd doth lye

Who dying lives to all Eternitye

hee departed this life the 17^th of Ian

1709/8 in the 22^th year of his age ~

A lover of learning
Shall wee all dye

Wee shall dye all

all dye shall wee

dye all wee shall

The  are old style long esses. The superscript th is actually over the numeral. The 9 is over the 8 in the year and there is no stroke. This is because it was before England adopted the Gregorian calendar and so the year began on 25 Mar and was a year behind the continent between 1 Jan and 25 Mar. Correspondence of the time commonly would show 1708/9 at this time, and I have used this form for typographic convenience, but with the 9 over the 8 as on the tomb.

A word game book points out that this inscription is also palindromic!!

Richard Breen. Funny Endings. Penny Publishing, UK, 1999, p. 35. Gives the following form: Shall we all die? / We shall die all. / All die shall we? / Die all we shall and notes that it is a word palindrome and says it comes from Gunwallam [sic], near Helstone.
Joseph Sauveur. Construction générale des quarrés magiques. Mémoires de l'Académie Royale des Sciences 1710(1711) 92 138. ??NYS -- described in Cammann 4, p. 297, (see 7.N for details of Cammann) which says Sauveur invented Latin squares and describes some of his work.

Ozanam. 1725. 1725: vol. IV, prob. 29, p. 434 & fig. 35, plate 10 (12). Two 4 x 4 orthogonal squares, using A, K, Q, J of the 4 suits, but it looks like:

J, A, K, Q; Q, K, A, J; A, J, Q, K; K, Q, J, A; but the  and  look very similar. From later versions of the same diagram, it is clear that the first row should have its  and  reversed. Note the diagonals also contain all four ranks and suits. (I have a reference for this to the 1723 edition.)

Minguet. 1733. Pp. 146-148 (1864: 142-143; not noticed in other editions). Two 4 x 4 orthogonal squares, using A, K, Q, J (= As, Rey, Caballo (knight), Sota (knave)) of the 4 suits, but the Spanish suits, in descending order, are: Espadas, Bastos, Oros, Copas. The result is described but not drawn, as:

RO, AE, CC, SB; SC, CB, AO, RE; AB, RC, SE, CO; CE, SO, RB, AC;

which would translate into the more usual cards as:

K, A, Q, J; J, Q, A, K; A, K, J, Q; Q, J, K, A.

However, I'm not sure of the order of the Caballo and Sota; if they were reversed, which would interchange Q and J in the latter pattern, then both Ozanam and Minguet would have the property that each row is a cyclic shift or reversal of A, K, Q, J.

Alberti. 1747. Art. 29, p. 203 (108) & fig. 36, plate IX, opp. p. 204 (108). Two 4 x 4 orthogonal squares, figure simplified from the correct form of Ozanam, 1725.

L. Euler. Recherches sur une nouvelle espèce de Quarrés Magiques. (Verhandelingen uitgegeven door het zeeuwsch Genootschap der Wetenschappen te Vlissingen (= Flessingue) 9 (1782) 85 239.) = Opera Omnia (1) 7 (1923) 291 392. (= Comm. Arithm. 2 (1849) 302 361.)

Manuel des Sorciers. 1825. Pp. 78-79, art. 39. ??NX Correct form of Ozanam.

The Secret Out. 1859. How to Arrange the Twelve Picture Cards and the four Aces of a Pack in four Rows, so that there will be in Neither Row two Cards of the same Value nor two of the same Suit, whether counted Horizontally or Perpendicularly, pp. 90-92. Two 4 x 4 orthogonal Latin squares, not the same as in Ozanam.

Bachet-Labosne. Problemes. 3rd ed., 1874. Supp. prob. XI, 1884: 200 202. Two 4 x 4 orthogonal squares.

Berkeley & Rowland. Card Tricks and Puzzles. 1892. Card Puzzles, No. XVI, pp. 17-18. Similar to Ozanam.

Hoffmann. 1893. Chap. X, no. 14: Another card puzzle, pp. 342 & 378-379 = Hoffmann Hordern, pp. 234 & 236. Two orthogonal Latin squares, but the diagonals do not contain all the suits and ranks.

A, J, Q, K; J, A, K, Q; Q, K, A, J; K, Q, J, A.

G. Tarry. Le probleme de 36 officiers. Comptes Rendus de l'Association Française pour l'Avancement de Science Naturel 1 (1900) 122 123 & 2 (1901) 170 203. ??NYS

Dudeney. Problem 521. Weekly Dispatch (1 Nov, 15 Nov, 1903) both p. 10.

H. A. Thurston. Latin squares. Eureka 9 (Apr 1947) 19-21. Survey of current knowledge.

T. G. Room. Note 2569: A new type of magic square. MG 39 (No. 330) (Dec 1955) 307. Introduces 'Room Squares'. Take the 2n(2n 1)/2 combinations from 2n symbols and insert them in a 2n 1 x 2n 1 grid so that each row and column contains all 2n symbols. There are n entries and n 1 blanks in each row and column. There is an easy solution for n = 1. n = 2 and n = 3 are impossible. Gives a solution for n = 4. This is a design for a round robin tournament with the additional constraint of 2n 1 sites such that each player plays once at each site.

Parker shows there are two orthogonal Latin squares of order 10 in 1959.

R. C. Bose & S. S. Shrikande. On the falsity of Euler's conjecture about the nonexistence of two orthogonal Latin squares of order 4t+2. Proc. Nat. Acad. Sci. (USA) 45: 5 (1959) 734 737.

Gardner. SA (Nov 1959) c= New MD, chap. 14. Describes Bose & Shrikande's work. SA cover shows a 10 x 10 counterexample in colour. Kara Lynn and David Klarner actually made a quilt of this, thereby producing a counterpane counterexample! They told me that the hardest part of the task was finding ten sufficiently contrasting colours of material.

H. Howard Frisinger. Note: The solution of a famous two-centuries-old problem: the Leonhard Euler-Latin square conjecture. HM 8 (1981) 56-60. Good survey of the history.

Jacques Bouteloup. Carrés Magiques, Carrés Latins et Eulériens. Éditions du Choix, Bréançon, 1991. Nice systematic survey of this field, analysing many classic methods. An Eulerian square is essentially two orthogonal Latin squares.
5.I.1. EIGHT QUEENS PROBLEM
See MUS I 210-284. S&B 37 shows examples. See also 5.Z. See also 6.T for examples where no three are in a row.
Ahrens. Mathematische Spiele. Encyklopadie article, op. cit. in 3.B. 1904. Pp. 1082 1084 discusses history and results for the n queens problem, with many references.

Paul J. Campbell. Gauss and the eight queens problem. HM 4:4 (Nov 1977) 397 404. Detailed history. Demonstrates that Gauss did not obtain a complete solution and traces how this misconception originated and spread.

"Schachfreund" (Max Bezzel). Berliner Schachzeitung 3 (Sep 1848) 363. ??NYS

Solutions. Ibid. 4 (Jan 1849) 40. ??NYS (Ahrens says this only gives two solutions. A. C. White says two or three. Jaenisch says a total of 5 solutions were published here and in 1854.)

Franz Nauck. Eine in das Gebiet der Mathematik fallende Aufgabe von Herrn Dr. Nauck in Schleusingen. Illustrirte Zeitung (Leipzig) 14 (No. 361) (1 Jun 1850) 352. Reposes problem. [The papers do not give a first name or initial. The only Nauck in the first six volumes of Poggendorff is Ernst Friedrich (1819-1875), a geologist. Ahrens gives no initial. Campbell gives Franz.]

Franz Nauck. Briefwechseln mit Allen für Alle. Illustrirte Zeitung (Leipzig) 15 (No. 377) (21 Sep 1850) 182. Complete solution.

Editorial comments: Briefwechsel. Illustrirte Zeitung (Leipzig) 15 (No. 378) (28 Sep 1850) 207. Thanks 6 correspondents for the complete solution and says Nauck reports that a blind person has also found all 92 solutions.

Gauss read the Illustrirte Zeitung and worked on the problem, corresponding with his friend Schumacher starting on 1 Sep 1850. Campbell discusses the content of the letters, which were published in: C. A. F. Peters, ed; Briefwechsel zwischen C. F. Gauss und H. C. Schumacher; vol. 6, Altona, 1865, ??NYS. John Brillhart writes that there is some material in Gauss' Werke, vol. XII: Varia kleine Notizen verschiednen Inhalts ... 5, pp. 19-28, ??NYS -- not cited by Campbell.

F. J. E. Lionnet. Question 251. Nouvelles Annales de Mathématiques 11 (1852) 114 115. Reposes problem and gives an abstract version.

Giusto Bellavitis. Terza rivista di alcuni articoli dei Comptes Rendus dell'Accademia delle Scienze di Francia e di alcuni questioni des Nouvelles Annales des mathématiques. Atti dell'I. R. Istituto Veneto di Scienze, Lettere ed Arti (3) 6 [= vol. 19] (1860/61) 376-392 & 411 436 (as part of Adunanza del Giorno 17 Marzo 1861 on pp. 347 436). The material of interest is: Q. 251. Disposizione sullo scacchiere di otto regine, on pp. 434 435. Gives the 12 essentially different solutions. Lucas (1895) says Bellavitis was the first to find all solutions, but see above. However this may be the first appearance of the 12 essentially different solutions.

C. F. de Jaenisch. Op. cit. in 5.F.1. 1862. Vol. 1, pp. 122-135. Gives the 12 basic solutions and shows they produce 92. Notes that in every solution, 4 queens are on white squares and 4 are on black.

A. C. Cretaine. Études sur le Problème de la Marche du Cavalier au Jeu des Échecs et Solution du Problème des Huit Dames. A. Cretaine, Paris, 1865. ??NYS -- cited by Lucas (1895). Shows it is possible to solve the eight queens problem after placing one queen arbitrarily.

G. Bellavitis. Algebra N. 72 Lionnet. Atti dell'Istituto Veneto (3) 15 (1869/70) 844 845.

Siegmund Günther. Zur mathematische Theorie des Schachbretts. Grunert's Archiv der Mathematik und Physik 56 (1874) 281-292. ??NYS. Sketches history of the problem -- see Campbell. He gives a theoretical, but not very practical, approach via determinants which he carries out for 4 x 4 and 5 x 5.

J. W. L. Glaisher. On the problem of the eight queens. Philosophical Magazine (4) 48 (1874) 457-467. Gives a sketch of Günther's history which creates several errors, in particular attributing the solution to Gauss -- see Campbell, who suggests Glaisher could not read German well. (However, in 1921 & 1923, Glaisher published two long articles involving the history of 15-16C German mathematics, showing great familiarity with the language.) Simplifies and extends Günther's approach and does 6 x 6, 7 x 7, 8 x 8 boards.

Lucas. RM2, 1883. Note V: Additions du Tome premier. Pp. 238-240. Gives the solutions on the 9 x 9 board, due to P. H. Schoute, in a series of articles titled Wiskundige Verpoozingen in Eigen Haard. Gives the solutions on the 10 x 10 board, found by M. Delannoy.

S&B, p. 37, show an 1886 puzzle version of the six queens problem.

A. Pein. Aufstellung von n Königinnen auf einem Schachbrett von n² Feldern. Leipzig. ??NYS -- cited by Ball, MRE, 4th ed., 1905 as giving the 92 inequivalent solutions on the 10 x 10.

Ball. MRE, 1st ed., 1892. The eight queens problem, pp. 85-88. Cites Günther and Glaisher and repeats the historical errors. Sketches Günther's approach, but only cites Glaisher's extension of it. He gives the numbers of solutions and of inequivalent solutions up through 10 x 10 -- see Dudeney below for these numbers, but the two values in ( ) are not given by Dudeney. He states results for the 9 x 9 and 10 x 10, citing Lucas. Says that a 6 x 6 version "is sold in the streets of London for a penny".

Hoffmann. 1893.

Chap. VI, pp. 272 273 & 286 = Hoffmann-Hordern, pp. 187-189, with photo.

No. 24: No two in a row. Eight queens. Photo on p. 188 shows Jeu des Sentinelles, by Watilliaux, dated 1874-1895.

No. 25: The "Simple" Puzzle. Nine queens. Says a version was sold by Messrs. Feltham, with a notched board but the pieces were allowed to move over the gaps, so it was really a 9 x 9 board.

Chap. X, No. 18: The Treasure at Medinet, pp. 343 344 & 381 = Hoffmann-Hordern, pp. 237-239. This is a solution of the eight queens problem, cut into four quadrants and jumbled. The goal is to reconstruct the solution. Photo on p. 239 shows Jeu des Manifestants, with box.

Hordern Collection, p. 94, and S&B, p. 37, show a version of this with same box, but which divides the board into eight 2 x 4 rectangles.

Brandreth Puzzle Book. Brandreth's Pills (The Porous Plaster Co., NY), nd [1895]. P. 1: The famous Italian pin puzzle. 6 queens puzzle. No solution.

Lucas. L'Arithmétique Amusante. 1895. Note IV: Section I: Les huit dames, pp. 210-220. Asserts Bellavitis was the first to find all solutions. Discusses symmetries and shows the 12 basic solutions. Correctly describes Jaenisch as obscure. Gives an easy solution of Cretaine's problem which can be remembered as a trick. Shows there are six solutions which can be superimposed with no overlap, i.e. six solutions using disjoint sets of cells.

C. D. Locock, conductor. Chess Column. Knowledge 19 (Jan 1896) 23-24; (Feb 1896) 47 48; (May 1896) 119; (Jul 1896) 167-168. This series begins by saying most players know there is a solution, "but, possibly, some may be surprised to learn that there are ninety-two ways of performing the feat, ...." He then enumerates them. Second article studies various properties of the solutions, particularly looking for examples where one solution shifts to produce another one. Third article notes some readers' comments. Fourth article is a long communication from W. J. Ashdown about the number of distinct solutions, which he gets as 24 rather than the usual 12.

T. B. Sprague. Proc. Edinburgh Math. Soc. 17 (1898-9) 43-68. ??NYS -- cited by Ball, MRE, 4th ed., 1905, as giving the 341 inequivalent solutions on the 11 x 11.

Benson. 1904. Pins and dots puzzle, p. 253. 6 queens problem, one solution.

Ball. MRE, 4th ed., 1905. The eight queens problem, pp. 114-120. Corrects some history by citing MUS, 1st ed., 1901. Gives one instance of Glaisher's method -- going from 4 x 4 to 5 x 5 and its results going up to 8 x 8. Says the 92 inequivalent solutions on the 10 x 10 were given by Pein and the 341 inequivalent solutions on the 11 x 11 were given by Sprague. The 5th ed., pp. 113-119 calls it "One of the classical problems connected with a chess-board" and adds examples of solutions up to 21 x 21 due to Mr. Derington.

Pearson. 1907. Part III, no. 59: Stray dots, pp. 59 & 130. Same as Hoffmann's Treasure at Medinet.

Burren Loughlin & L. L. Flood. Bright-Wits Prince of Mogador. H. M. Caldwell Co., NY, 1909. The eight provinces, pp. 14-15 & 65. Same as Hoffmann's Treasure at Medinet.

A. C. White. Sam Loyd and His Chess Problems. 1913. Op. cit. in 1. P. 101 says Loyd discovered that all solutions have a piece at d1 or equivalent.

Williams. Home Entertainments. 1914. A draughtboard puzzle, p. 115. "Arrange eight men on a draughtboard in such a way that no two are upon the same line in any direction." This is not well stated!! Gives one solution: 52468317 and says "Work out other solutions for yourself."

Dudeney. AM. 1917. The guarded chessboard, pp. 95 96. Gives the number of ways of placing n queens and the number of inequivalent ways. The values in ( ) are given by Ball, but not by Dudeney.

n 4 5 6 7 8 9 10 11 12 13

ways 2 10 4 40 92 (352) (724)   - -

inequivalent ways 1 2 1 6 12 46 92 341 (1766) (1346)
Ball. MRE, 9th ed., 1920. The eight queens problem, pp. 113-119. Omits references to Pein and Sprague and adds the number of inequivalent solutions for the 12 x 12 and 13 x 13.

Blyth. Match-Stick Magic. 1921. No pairs allowed, p. 74. 6 queens problem.

Hummerston. Fun, Mirth & Mystery. 1924. No two in a line, p. 48. Chessboard. Place 'so that no two are upon the same line in any direction along straight or diagonal lines?' Gives one solution: 47531682, 'but there are hundreds of other ways'. You can let someone place the first piece.

Rohrbough. Puzzle Craft. 1932. Houdini Puzzle, p. 17. 6 x 6 case.

Rohrbough. Brain Resters and Testers. c1935. Houdini Puzzle, p. 25. 6 x 6 problem. "-- From New York World some years ago, credited to Harry Houdini." I have never seen this attribution elsewhere.

Pál Révész. Mathematik auf dem Schachbrett. In: Endre Hódi, ed. Mathematisches Mosaik. (As: Matematikai Érdekességek; Gondolat, Budapest, 1969.) Translated by Günther Eisenreich. Urania Verlag, Leipzig, 1977. Pp. 20 27. On p. 24, he says that all solutions have 4 queens on white and 4 on black. He says that one can place at most 5 non attacking queens on one colour.

Doubleday - 2. 1971. Too easy?, pp. 97-98. The two solutions on the 4 x 4 board are disjoint.

Dean S. Clark & Oved Shisha. Proof without words: Inductive construction of an infinite chessboard with maximal placement of nonattacking queens. MM 61:2 (1988) 98. Consider a 5 x 5 board with queens in cells (1,1), (2,4), (3,2), (4,5), (5,3). 5 such boards can be similarly placed within a 25 x 25 board viewed as a 5 x 5 array of 5 x 5 boards and this has no queens attacking. Repeating the inflationary process gives a solution on the board of edge 5³, then the board of edge 5⁴, .... They cite their paper: Invulnerable queens on an infinite chessboard; Annals of the NY Acad. of Sci.: Third Intern. Conf. on Comb. Math.; to appear. ??NYS.

Liz Allen. Brain Sharpeners. Op. cit. in 5.B. 1991. Squares before your eyes, pp. 21 & 106. Asks for solutions of the eight queens problem with no piece on either main diagonal. Two of the 12 basic solutions have this, but one of these is the symmetric case, so there are 12 solutions of this problem.

Donald E. Knuth. Dancing links. 25pp preprint of a talk given at Oxford in Sep 1999, sent by the author. See the discussion in 6.F. He finds the following numbers of solutions for placing n queens, n = 1, 2, ..., 18.

1, 0, 0, 2, 10, 4, 40, 92, 352, 724, 2680, 14200, 73712, 3 65596, 22 79184, 147 72512, 958 15104, 6660 90624.