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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 The Philosophy of Analysis -- unpublished collection of MSS in the BM as Add.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.]