Sources page biographical material

6.F.1. OTHER CHESSBOARD DISSECTIONS
See S&B, pp. 12 14. See also 6.F.5 for dissections of uncoloured boards.
Jerry Slocum. Compendium of Checkerboard Puzzles. Published by the author, 1983. Outlines the history and shows all manufactured versions known then to him: 33 types in 61 versions. The first number in Slocum's numbers is the number of pieces.

Jerry Slocum & Jacques Haubrich. Compendium of Checkerboard Puzzles. 2nd ed., published by Slocum, 1993. 90 types in 161 versions, with a table of which pieces are in which puzzles, making it much easier to see if a given puzzle is in the list or not. This gives many more pictures of the puzzle boxes and also gives the number of solutions for each puzzle and sometimes prints all of them. The Slocum numbers are revised in the 2nd ed. and I use the 2nd ed. numbers below. (There was a 3rd ed. in 1997, with new numbering of 217 types in 376 versions. NYR. Haubrich is working on an extended version with Les Barton providing information.)

Henry Luers. US Patent 231,963 -- Game Apparatus or Sectional Checker Board. Applied: 7 Aug 1880; patented: 7 Sep 1880. 1p + 1p diagrams. 15: 01329. Slocum 15.5.1. Manufactured as: Sectional Checker Board Puzzle, by Selchow & Righter. Colour photo of the puzzle box cover is on the front cover of the 1st ed. of Slocum's booklet. B&W photo is on p. 14 of S&B.

?? UK patent application 16,810. 1892. Not granted, so never published. I have spoken to the UK Patent Office and they say the paperwork for ungranted applications is destroyed after about three to five years. (Edward Hordern's collection has an example with this number on it, by Feltham & Co. In the 2nd ed., the cover is reproduced and it looks like the number may be 16,310, but that number is for a locomotive vehicle.) 14: 00149. Slocum 14.20.1. Manufactured as: The Chequers Puzzle, by Feltham & Co.

Hoffmann. 1893. Chap. III, no. 16: The chequers puzzle, pp. 97 98 & 129 130 = Hoffmann Hordern, pp. 88-89, with photos. 14: 00149. Slocum 14.20.1. Says it is made by Messrs. Feltham, who state it has over 50 solutions. He gives two solutions. Photo on p. 89 of a example by Feltham & Co., dated 1880-1895.

At the end of the solution, he says Jacques & Son are producing a series of three "Peel" puzzles, which have coloured squares which have to be arranged so the same colour is not repeated in any row or column. Photo on p. 89 shows an example, 9: 023, with the trominoes all being L-trominoes. This makes a 5 x 5 square, but the colours have almost faded into indistinguishability.

Montgomery Ward & Co. Catalog N^o 57, Spring & Summer, 1895. Facsimile by Dover, 1969, ??NX. P. 237 describes item 25470: "The "Wonder" Puzzle. The object is to place 18 pieces of 81 squares together, so as to form a square, with the colors running alternately. It can be done in several different ways."

Dudeney. Problem 517 -- Make a chessboard. Weekly Dispatch (4 & 18 Oct 1903), both p. 10. 8: 00010 12111 001. Slocum 8.3.1.

Benson. 1904. The chequers puzzle, pp. 202 203. As in Hoffmann, with only one solution.

Dudeney. The Tribune (20 & 24 Dec 1906) both p. 1. ??NX Dissecting a chessboard. Dissect into maximum number of different pieces. Gets 18: 2,1,4,10,0, 0,0,1. Slocum 18.1, citing later(?) Loyd versions.

Loyd. Sam Loyd's Puzzle Magazine (Apr-Jul 1908) -- ??NYS, reproduced in: A. C. White; Sam Loyd and His Chess Problems; 1913, op. cit. in 1; no. 58, p. 52. = Cyclopedia, 1914, pp. 221 & 368, 250 & 373. = MPSL2, prob. 71, pp. 51 & 145. = SLAHP: Dissecting the chessboard, pp. 19 & 87. Cut into maximum number of different pieces -- as in Dudeney, 1906.

Burren Loughlin & L. L. Flood. Bright-Wits Prince of Mogador. H. M. Caldwell Co., NY, 1909. The rug, pp. 7-13 & 65. 14: 00149. Not in Slocum.

Loyd. A battle royal. Cyclopedia, 1914, pp. 97 & 351 (= MPSL1, prob. 51, pp. 49 & 139). Same as Dudeney's prob. 517 of 1903.

Dudeney. AM. 1917. Prob. 293: The Chinese chessboard, pp. 87 & 213 214. Same as Loyd, p. 221.

Western Puzzle Works, 1926 Catalogue. No. 79: "Checker Board Puzzle, in 16 pieces", but the picture only shows 14 pieces. 14: 00149. Picture doesn't show any colours, but assuming the standard colouring of a chess board, this is the same as Slocum 14.15.

John Edward Fransen. US Patent 1,752,248 -- Educational Puzzle. Applied: 19 Apr 1929; patented: 25 Mar 1930. 1p + 1p diagrams. 'Cut thy life.' 11: 10101 43001. Slocum 11.3.1.

Emil Huber-Stockar. Patience de l'echiquier. Comptes-Rendus du Premier Congrès International de Récréation Mathématique, Bruxelles, 1935. Sphinx, Bruxelles, 1935, pp. 93-94. 15: 01329. Slocum 15.5. Says there must certainly be more than 1000 solutions.

Emil Huber-Stockar. L'echiquier du diable. Comptes-Rendus du Deuxième Congrès International de Récréation Mathématique, Paris, 1937. Librairie du "Sphinx", Bruxelles, 1937, pp. 64-68. Discusses how one solution can lead to many others by partial symmetries. Shows several solutions containing about 40 altogether. Note at end says he has now got 5275 solutions. This article is reproduced in Sphinx 8 (1938) 36-41, but without the extra pages of diagrams. At the end, a note says he has 5330 solutions. Ibid., pp. 75-76 says he has got 5362 solutions and ibid. 91-92 says he has 5365. By use of Bayes' theorem on the frequency of new solutions, he estimates c5500 solutions. Haubrich has found 6013. Huber-Stocker intended to produce a book of solutions, but he died in May 1939 [Sphinx 9 (1939) 97].

F. Hansson. Sam Loyd's 18-piece dissection -- Art. 48 & probs. 4152 4153. Fairy Chess Review 4:3 (Nov 1939) 44. Cites Loyd's Puzzles Magazine. Asserts there are many millions of solutions! He determines the number of chequered handed n-ominoes for n = 1, 2, ..., 8 is 2, 1, 4, 10, 36, 110, 392, 1371. The first 17 pieces total 56 squares. Considers 8 ways to dissect the board into 18 different pieces. Problems ask for the number of ways to choose the pieces in each of these ways and for symmetrical solutions. Solution in 4:6 (Jun 1940) 93-94 (??NX of p. 94) says there are a total of 3,309,579 ways to make the choices.

C. Dudley Langford. Note 2864: A chess board puzzle. MG 43 (No. 345) (Oct 1959) 200. 15: 01248. Not in Slocum. Two diagrams followed by the following text. "The pieces shown in the diagrams can be arranged to form a square with either side uppermost. If the squares of the underlying grid are coloured black and white alternately, with each white square on the back of a black square, then there is at least one more way of arranging them as a chess-board by turning some of the pieces over." I thought this meant that the pieces were double-sided with the underside having the colours being the reverse of the top and the two diagrams were two solutions for this set of pieces. Jacques Haubrich has noted that the text is confusing and that the second diagram is NOT using the set of double-sided pieces which are implied by the first diagram. We are not sure if the phrasing is saying there are two different sets of pieces and hence two problems or if we are misinterpreting the description of the colouring.

B. D. Josephson. EDSAC to the rescue. Eureka 24 (Oct 1961) 10 12 & 32. Uses the EDSAC computer to find two solutions of a 12 piece chessboard dissection. 12: 00025 41. Slocum 12.9.

Leonard J. Gordon. Broken chessboards with unique solutions. G&PJ 10 (1989) 152 153. Shows Dudeney's problem has four solutions. Finds other colourings which give only one solution. Notes some equivalences in Slocum.

6.F.2. COVERING DELETED CHESSBOARD WITH DOMINOES
See also 6.U.2.

There is nothing on this in Murray.

Pál Révész. Op. cit. in 5.I.1. 1969. On p. 22, he says this problem comes from John [von] Neumann, but gives no details.

Max Black. Critical Thinking, op. cit. in 5.T. 1946 ed., pp. 142 & 394, ??NYS. 2nd ed., 1952, pp. 157 & 433. He simply gives it as a problem, with no indication that he invented it.

H. D. Grossman. Fun with lattice points: 14 -- A chessboard puzzle. SM 14 (1948) 160. (The problem is described with 'his clever solution' from M. Black, Critical Thinking, pp. 142 & 394.)

S. Golomb. 1954. Op. cit. in 6.F.

M. Gardner. The mutilated chessboard. SA (Feb 1957) = 1st Book, pp. 24 & 28.

Gamow & Stern. 1958. Domino game. Pp. 87 90.

Robert S. Raven, proposer; Walter P. Targoff, solver. Problem 85 -- Deleted checkerboard. In: L. A. Graham; Ingenious Mathematical Problems and Methods; Dover, 1959, pp. 52 & 227.

R. E. Gomory. (Solution for deletion of any two squares of opposite colour.) In: M. Gardner, SA (Nov 1962) = Unexpected, pp. 186 187. Solution based on a rook's tour. (I don't know if this was ever published elsewhere.)

Michael Holt. What is the New Maths? Anthony Blond, London, 1967. Pp. 68 & 97. Gives the 4 x 4 case as a problem, but doesn't mention that it works on other boards. (I include this as I haven't seen earlier examples in the educational literature.)

David Singmaster. Covering deleted chessboards with dominoes. MM 48 (1975) 59 66. Optimum extension to n dimensions. For an n-dimensional board, each dimension must be  2. If the board has an even number of cells, then one can delete any n-1 white cells and any n-1 black cells and still cover the board with dominoes (i.e. 2 x 1 x 1 x ... x 1 blocks). If the board has an odd number of cells, then let the corner cells be coloured black. One can then delete any n black cells and any n-1 white cells and still cover the board with dominoes.

I-Ping Chu & Richard Johnsonbaugh. Tiling deficient boards with trominoes. MM 59:1 (1986) 34-40. (3,n) = 1 and n  5 imply that an n x n board with one cell deleted can be covered with L trominoes. Some 5 x 5 boards with one cell deleted can be tiled, but not all can.
6.F.3. DISSECTING A CROSS INTO Zs AND Ls
The L pieces are not always drawn carefully, and in some cases the unit pieces are not all square. I have enlarged and measured those which are not clear and approximated them as n-ominoes.
Minguet. 1733. Pp. 119-121 (1755: 85-86; 1822: 138-139; 1864: 116-117). The problem has two parts. The first is a cross into 5 pieces: L-tetromino, 2 Z-pentominoes, L hexomino, Z-hexomino. The two hexominoes are like the corresponding pentominoes lengthened by one unit. Similar to Les Amusemens, but one Z is longer and one L is shorter. The diagram shows 8 L and Z shaped pieces formed from squares, but it is not clear what the second part of the problem is doing -- either a piece or a label is erroneous or missing. Says one can make different figures with the pieces.

Les Amusemens. 1749. P. xxxi. Cross into 3 Z pentominoes and 2 L pieces. Like Minguet, but the Ls are much lengthened and are approximately a L-heptomino and an L octomino.

Catel. Kunst-Cabinet. 1790. Das mathematische Kreuz, p. 10 & fig. 27 on plate I. As in Les Amusemens, but the Ls are approximately a 9-omino and a 10-omino.

Bestelmeier. 1801. Item 274 -- Das mathematische Kreuz. Cross into 6 pieces, but the picture has an erroneous extra line. It should be the reversal of the picture in Catel.

Charles Babbage. The Philosophy of Analysis -- unpublished collection of MSS in the BM as Add. MS 37202, c1820. ??NX. See 4.B.1 for more details. F. 4r is "Analysis of the Essay of Games". F. 4v has the dissection of the cross into 3 Z pentominoes and two L pieces. I don't have a copy of this, but my sketch looks like the Ls are a tetromino and a pentomino, or possibly a pentomino and a hexomino.

Manuel des Sorciers. 1825. Pp. 204-205, art. 21. ??NX. Dissect a cross into three Zs and two Ls. My notes don't indicate the size of the Ls.

Boy's Own Book. 1843 (Paris): 435 & 440, no. 3. As in Les Amusemens, but with the Ls apparently intended to be a pentomino and a hexomino. = Boy's Treasury, 1844, pp. 424-425 & 428. = de Savigny, 1846, pp. 353 & 357, no. 2, except the solution has been redrawn with some slight changes and so the proportions are less clear.

Family Friend 3 (1850) 330 & 351. Practical puzzle, No. XXI. As in Les Amusemens.

Magician's Own Book. 1857. Prob. 31: Another cross puzzle, pp. 276 & 299. As in Les Amusemens.

Landells. Boy's Own Toy-Maker. 1858. P. 152. As in Les Amusemens.

Book of 500 Puzzles. 1859. Prob. 31: Another cross puzzle, pp. 90 & 113. As in Les Amusemens. = Magician's Own Book.

Indoor & Outdoor. c1859. Part II, p. 127, prob. 5: The puzzle of the cross. As in Les Amusemens.

Illustrated Boy's Own Treasury. 1860. Practical Puzzles, No. 24, pp. 399 & 439. Identical to Magician's Own Book.

Boy's Own Conjuring book. 1860. Prob. 30: Another cross puzzle, pp. 239 & 263. = Magician's Own Book, 1857.

Leske. Illustriertes Spielbuch für Mädchen. 1864?

Prob. 584-2, pp. 286 & 404. 4  Z pentominoes to make a (Greek) cross. (Also entered in 6.F.5.)

Prob. 584-8, pp. 287 & 405. 3 Z pentominoes, L tetromino and L pentomino to make a Greek cross. Despite specifically asking for a Greek cross, the answer is a standard Latin cross with height : width = 4 : 3.

Mittenzwey. 1880. Prob. 173-174, pp. 33 & 85; 1895?: 198-199, pp. 38 & 87; 1917: 198 199, pp. 35 & 84. The first is 3 Z pentominoes, L tetromino and L pentomino to make a cross. The second is 4  Z pentominoes to make a (Greek) cross. (Also entered in 6.F.5.)

Cassell's. 1881. P. 93: The magic cross. = Manson, 1911, p. 139. Same pattern as Les Amusemens, but one end of the Zs is decidedly longer than the other and the middle 'square' of the Zs is decidedly not square. The Ls are approximately a pentomino and a heptomino, But the middle 'square' of the Zs is almost a domino and that makes the Zs into heptominoes, with the Ls being a hexomino and a nonomino.

S&B, p. 20, shows a 7 piece cross dissection, Jeu de La Croix, into 3 Zs, 2 Ls and 2 straights, from c1890. The Zs are pentominoes, with the centre 'square' lengthened a bit. The Ls appear to be a heptomino and an octomino and the straights appear to be a hexomino and a tetromino. Cf Hoffmann-Hordern for a version without the straight pieces.

Handy Book for Boys and Girls. Showing How to Build and Construct All Kinds of Useful Things of Life. Worthington, NY, 1892. Pp. 320-321: The cross puzzle. As in Cassell's.

Hoffmann. 1893. Chap. III, no. 29: Another cross puzzle, pp. 103 & 136 = Hoffmann Hordern, pp. 100-101, with photo. States that the two Ls are the same shape, but the solution is as in Les Amusemens, with the Ls approximately a hexomino and a heptomino. Hordern has corrected the problem statement. Photo on p. 100 shows an ivory version, dated 1850-1900, of the same proportions. Hordern Collection, p. 65, shows two wood versions, La Croix Brisée and Jeu de la Croix, dated 1880-1905, both with Ls being approximately a heptomino and an octomino.

Benson. 1904. The Latin cross puzzle, p. 200. As in Hoffmann, but the solution is longer, as in Les Amusemens.

Wehman. New Book of 200 Puzzles. 1908. Another cross puzzle, p. 32. As in Les Amusemens, with the Ls being a pentomino and a hexomino.

S. Szabo. US Patent 1,263,960 -- Puzzle. Filed: 20 Oct 1917; patented: 23 Apr 1918. 1p + 1p diagrams. As in Les Amusemens, with even longer Ls, approximately a 10-omino and an 11-omino.
6.F.4. QUADRISECT AN L TROMINO, ETC.
See also 6.AW.1 & 4.

Mittenzwey and Collins quadrisect a hollow square obtained by removing a 2 x 2 from the centre of a 4 x 4.

Bile Beans quadrisects a 5 x 5 after deleting corners and centre.
Minguet. 1733. Pp. 114-115 (1755: 80; 1822: 133-134; 1864: 111-112). Quadrisect L tromino.

Alberti. 1747. Art. 30: Modo di dividere uno squadro di carta e di legno in quattro squadri equali, p. ?? (131) & fig. 56, plate XVI, opp. p. 130.

Les Amusemens. 1749. P. xxx. L-tromino ("gnomon") into 4 congruent pieces.

Vyse. Tutor's Guide. 1771? Prob. 9, 1793: p. 305, 1799: p. 317 & Key p. 358. Refers to the land as a parallelogram though it is drawn rectangular.

Charles Babbage. The Philosophy of Analysis -- unpublished collection of MSS in the BM as Add. MS 37202, c1820. ??NX. See 4.B.1 for more details. F. 4r is "Analysis of the Essay of Games". F. 4v has an entry "8½ a Prob of figure" followed by the L tromino. 8½ b is the same with a mitre and there are other dissection problems adjacent -- see 6.F.3, 6.AQ, 6.AW.1, 6.AY, so it seems clear that he knew this problem.

Jackson. Rational Amusement. 1821. Geometrical Puzzles, no. 3, pp. 23 & 83 & plate I, fig. 2.

Manuel des Sorciers. 1825. Pp. 203-204, art. 20. ??NX. Quadrisect L-tromino.

Family Friend 2 (1850) 118 & 149. Practical Puzzle -- No. IV. Quadrisect L-tromino of land with four trees.

Family Friend 3 (1850) 150 & 181. Practical puzzle, No. XV. 15/16 of a square with 10 trees to be divided equally. One tree is placed very close to another, cf Magician's Own Book and Hoffmann, below.

Parlour Pastime, 1857. = Indoor & Outdoor, c1859, Part 1. = Parlour Pastimes, 1868. Mechanical puzzles, no. 8, p. 179 (1868: 190). Land in the shape of an L-tromino to be cut into four congruent parts, each with a cherry tree.

Magician's Own Book. 1857.

Prob. 3: The divided garden, pp. 267 & 292. 15/16 of a square to be divided into five (congruent) parts, each with two trees. The missing 1/16 is in the middle. One tree is placed very close to another, cf Family Friend 3, above, and Hoffmann below.

Prob. 22: Puzzle of the four tenants, pp. 273 & 296. Same as Parlour Pastime, but with apple trees. (= Illustrated Boy's Own Treasury, 1860, No. 10, pp. 397 & 437.)

Prob. 28: Puzzle of the two fathers, pp. 275-276 & 298. Each father wants to divide 3/4 of a square. One has L tromino, other has the mitre shape. See 6.AW.1.

Landells. Boy's Own Toy-Maker. 1858.

P. 144. = Magician's Own Book, prob. 3.

Pp. 148-149. = Magician's Own Book, prob. 27.

Book of 500 Puzzles. 1859.

Prob. 3: The divided garden, pp. 81 & 106. Identical to Magician's Own Book.

Prob. 22: Puzzle of the four tenants, pp. 87 & 110. Identical to Magician's Own Book.

Prob. 28: Puzzle of the two fathers, pp. 89-90 & 112. Identical to Magician's Own Book. See also 6.AW.1.

Charades, Enigmas, and Riddles. 1860: prob. 28, pp. 59 & 63; 1862: prob. 29, pp. 135 & 141; 1865: prob. 573, pp. 107 & 154. Quadrisect L-tromino, attributed to Sir F. Thesiger.

Boy's Own Conjuring book. 1860.

Prob. 3: The divided garden, pp. 229 & 255. Identical to Magician's Own Book.

Prob. 21: Puzzle of the four tenants, pp. 235 & 260. Identical to Magician's Own Book.

Prob. 27: Puzzle of the two fathers, pp. 237 238 & 262. Identical to Magician's Own Book.

Illustrated Boy's Own Treasury. 1860. Prob. 21, pp. 399 & 439. 15/16 of a square to be divided into five (congruent) parts, each with two trees. c= Magician's Own Book, prob. 3.

Leske. Illustriertes Spielbuch für Mädchen. 1864? Prob. 175, p. 88. L-tromino into four congruent pieces, each with two trees. The problem is given in terms of the original square to be divided into five parts, where the father gets a quarter of the whole in the form of a square and the four sons get congruent pieces.

Hanky Panky. 1872. The divided orchards, p. 130. L tromino into 4 congruent pieces, each with two trees.

Boy's Own Book. The divided garden. 1868: 675. = Magician's Own Book, prob. 3.

Mittenzwey. 1880.

Prob. 192, pp. 36 & 89; 1895?: 217, pp. 40 & 91; 1917: 217, pp. 37 & 87. Cut 1 x 1 out of the centre of a 4 x 4. Divide the rest into five parts of equal area with four being congruent. He cuts a 2 x 2 out of the centre, which has a 1 x 1 hole in it, then divides the rest into four L-trominoes.

Prob. 213, pp. 38 & 90; 1895?: 238, pp. 42 & 92; 1917: 238, pp. 39 & 88. Usual quadrisection of an L-tromino.

Prob. 214, pp. 38 & 90; 1895?: 239, pp. 42 & 92; 1917: 239, pp. 39 & 88. Square garden with mother receiving 1/4 and the rest being divided into four congruent parts.

Cassell's. 1881. P. 90: The divided farm. = Manson, 1911, pp. 136-137. = Magician's Own Book, prob. 3.

Lemon. 1890.

The divided garden, no. 259, pp. 38 & 107. = Magician's Own Book, prob. 3.

Geometrical puzzle, no. 413, pp. 55 & 113 (= Sphinx, no. 556, pp. 76 & 116). Quadrisect L-tromino.

Hoffmann. 1893. Chap. X, no. 41: The divided farm, pp. 352 353 & 391 = Hoffmann Hordern, p. 250. = Magician's Own Book, prob. 3. [One of the trees is invisible in the original problem, but Hoffmann-Hordern has added it, in a more symmetric pattern than in Magician's Own Book.]

Loyd. Origin of a famous puzzle -- No. 18: An ancient puzzle. Tit Bits 31 (13 Feb & 6 Mar 1897) 363 & 419. Nearly 50 years ago he was told of the quadrisection of 3/4 of a square, but drew the mitre shape instead of the L tromino. See 6.AW.1.

Clark. Mental Nuts. 1897, no. 73; 1904, no. 31. Dividing the land. Quadrisect an L tromino. 1904 also has the mitre -- see 6.AW.1.

Benson. 1904. The farmer's puzzle, p. 196. Quadrisect an L tromino.

Wehman. New Book of 200 Puzzles. 1908.

The divided garden, p. 17. = Magician's Own Book, prob. 3

Puzzle of the two fathers, p. 43. = Magician's Own Book, prob. 28.

Puzzle of the four tenants, p. 46. = Magician's Own Book, prob. 22.

Dudeney. Some much discussed puzzles. Op. cit. in 2. 1908. Land in shape of an L tromino to be quadrisected. He says this is supposed to have been invented by Lord Chelmsford (Sir F. Thesiger), who died in 1878 -- see Charades, Enigmas, and Riddles (1860). But cf Les Amusemens.

M. Adams. Indoor Games. 1912. The clever farmer, pp. 23 25. Dissect L tromino into four congruent pieces.

Blyth. Match-Stick Magic. 1921. Dividing the inheritance, pp. 20-21. Usual quadrisection of L-tromino set out with matchsticks.

Collins. Book of Puzzles. 1927. The surveyor's puzzle, pp. 2-3. Quadrisect 3/4 of a square, except the deleted 1/4 is in the centre, so we are quadrisecting a hollow square -- cf Mittenzwey,

The Bile Beans Puzzle Book. 1933.

No. 22: Paper squares. Quadrisect a P-pentomino into P-pentominoes. One solution given, I find another. Are there more? How about quadrisecting into congruent pentominoes? Which pentominoes can be quadrisected into four copies of themself?

No. 41: Five lines. Consider a 5 x 5 square and delete the corners and centre. Quadrisect into congruent pentominoes. One solution given. I find three more. Are there more? One can extend this to consider quadrisecting the 5 x 5 with just the centre removed into congruent hexominoes. I find seven ways.

Depew. Cokesbury Game Book. 1939. A plot of ground, p. 227. 3/4 of XX     

a square to be quadrisected, but the shape is as shown at the right. XXX  

X XX

XXXX

Ripley's Puzzles and Games. 1966. Pp. 18 & 19, item 8. Divide an L-tromino into eight congruent pieces.

F. Göbel. Problem 1771: The L shape dissection problem. JRM 22:1 (1990) 64 65. The L tromino can be dissected into 2, 3, or 4 congruent parts. Can it be divided into 5 congruent parts?

Rowan Barnes-Murphy. Monstrous Mysteries. Piccolo, 1982. Apple-eating monsters, pp. 40 & 63. Trisect into equal parts, the shape consisting of a 2 x 4 rectangle with a 1 x 1 square attached to one of the central squares of the long side. [Actually, this can be done with the square attached to any of the squares, though if it is attached to the end of the long side, the resulting pieces are straight trominoes.]

6.F.5. OTHER DISSECTIONS INTO POLYOMINOES
Catel. Kunst-Cabinet. 1790.

Das Zakk- und Hakenspiel, p. 10 & fig. 11 on plate 1. 4 Z pentominoes and 4  L tetrominoes make a 6 x 6 square.

Die zwolf Winkelhaken, p. 11 & fig. 26 on plate 1. 8 L pentominoes and 4  L hexominoes make a 8 x 8 square.

Bestelmeier. 1801. Item 61 -- Das Zakken und Hakkenspiel. As in Catel, p. 10, but not as regularly drawn. Text copies some of Catel.

Manuel des Sorciers. 1825. Pp. 203-204, art. 20. ??NX Use four L-trominoes to make a 3 x 4 rectangle or a 4 x 4 square with four corners deleted.

Family Friend 3 (1850) 90 & 121. Practical puzzle -- No. XIII. 4 x 4 square, with 12 trees in the corners, centres of sides and four at the centre of the square, to be divided into 4 congruent parts each with 3 trees. Solution uses 4 L-tetrominoes. The same problem is repeated as Puzzle 17 -- Twelve-hole puzzle in (1855) 339 with solution in (1856) 28.

Magician's Own Book. 1857. Prob. 14: The square and circle puzzle, pp. 270 & 295. Same as Family Friend. = Book of 500 Puzzles, 1859, prob. 14, pp. 84 & 109. = Boy's Own Conjuring book, 1860, prob. 13, pp. 231-232 & 257. c= Illustrated Boy's Own Treasury, 1860, prob. 8, pp. 396 & 437. c= Hanky Panky, 1872, A square of four pieces, p. 117.

Landells. Boy's Own Toy-Maker. 1858. Pp. 146-147. Identical to Family Friend.

Leske. Illustriertes Spielbuch für Mädchen. 1864?

Prob. 584-2, pp. 286 & 404. 4  Z pentominoes to make a Greek cross. (Also entered in 6.F.3.)

Prob. 584-3, pp. 286 & 404. 4 L-tetrominoes to make a square.

Prob. 584-5, pp. 286 & 404. 8  L pentominoes and 4  L hexominoes make a 8 x 8 square. Same as Catel, but diagram is inverted.

Prob. 584-7, pp. 287 & 405. 4 Z pentominoes and 4  L tetrominoes make a 6 x 6 square. Same as Catel, but diagram is inverted.

Mittenzwey. 1880.

Prob. 174, pp. 33 & 85; 1895?: 199, pp. 38 & 87; 1917: 199, pp. 35 & 84. 4  Z pentominoes to make a (Greek) cross. (Also entered in 6.F.5.)

Prob. 186, pp. 35 & 88; 1895?: 211, pp. 40 & 90; 1917: 211, pp. 36 & 87. 4 x 4 square into 4 L-tetrominoes.

Prob. 187, pp. 35 & 88; 1895?: 212, pp. 40 & 90; 1917: 212, pp. 36 & 87. 6 x 6 square into 4 Z pentominoes and 4  L tetrominoes, as in Catel, p. 10.

Prob. 215, pp. 38 & 90; 1895?: 240, pp. 42 & 92; 1917: 240, pp. 39 & 88. Square garden with 12 trees quadrisected into four L-tetrominoes.

S&B, p. 20, shows a 7 piece cross dissection into 3 Zs, 2 Ls and 2 straights, from c1890.

Hoffmann. 1893. Chap. X, no. 37: The orchard puzzle, pp. 350 & 390 = Hoffmann-Hordern, pp. 247, with photo. Same as Family Friend 3. Photo on p. 247 shows St. Nicholas Puzzle Card, © 1892 in the USA.

Tom Tit, vol 3. 1893. Les quatre Z et des quatre L, pp. 181-182. = K, No. 27: The four Z's and the four L's, pp. 70 71. = R&A, Squaring the L's and Z's, p. 102. 6 x 6 square as in Catel, p. 10.

Sphinx. 1895. The Maltese cross, no. 181, pp. 28 & 103. Make a Maltese cross (actually a Greek cross of five equal squares) from 4 P-pentominoes. Also: quadrisect a P pentomino.

Wehman. New Book of 200 Puzzles. 1908. The square and circle puzzle, p. 5. = Family Friend.

Burren Loughlin & L. L. Flood. Bright-Wits Prince of Mogador. H. M. Caldwell Co., NY, 1909. The Zoltan's orchard, pp. 24-28 & 64. = Family Friend.

Anon. Prob. 84. Hobbies 31 (No. 799) (4 Feb 1911) 443. Use at least one each of: domino; L-tetromino; P and X pentominoes to make the smallest possible square Due to ending of this puzzle series, no solution ever appeared. I find numerous solutions for 5 x 5, 6 x 6, 8 x 8, of which the first is easily seen to be the smallest possibility.

A. Neely Hall. Carpentry & Mechanics for Boys. Lothrop, Lee & Shepard, Boston, nd [1918]. The square puzzle, pp. 20 21. 7 x 7 square cut into 1 straight tromino, 1  L tetromino and 7 L hexominoes.

Collins. Book of Puzzles. 1927. The surveyor's puzzle, pp. 2-3. Quadrisect 3/4 of a square, except the deleted 1/4 is in the centre, so we are quadrisecting a hollow square.

Arthur Mee's Children's Encyclopedia 'Wonder Box'. The Children's Encyclopedia appeared in 1908, but versions continued until the 1950s. This looks like 1930s?? 4  Z pentominoes and 4  L tetrominoes make a 6 x 6 square and a 4 x 9 rectangle.

W. Leslie Prout. Think Again. Frederick Warne & Co., London, 1958. All square, pp. 42 & 129. Make a 6 x 6 square from the staircase hexomino, 2 Y-pentominoes, an N tetromino, an L-tetromino and 3 T-tetrominoes. None of the pieces is turned over in the solution, though this restriction is not stated.