Sources page biographical material

6.AW. DIVISION INTO CONGRUENT PIECES
Polyomino versions occur in 6.F.4.

Quadrisecting a square is 6.AR.

See also: 6.AS.1, 6.AT.6.a, 6.AY, 6.BG.

For solid problems, see: 6.G.3, 6.G.4, 6.AP, 6.AZ?, 6.BC.

See: Charades, Enigmas, and Riddles, 1862, in 6.AW.2 for a quadrisection with pieces not congruent to the original.
6.AW.1. MITRE PUZZLE
Take a square and cut from two corners to the centre to leave ¾ of the square. The problem is to quadrisect this into four congruent parts.
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 The Philosophy of Analysis -- unpublished collection of MSS in the BM as Add.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.F.4, 6.AQ, 6.AY -- so it seems clear that he knew this problem.

Jackson. Rational Amusement. 1821. Geometrical Puzzles.

No. 15, pp. 26 & 86 & plate II, fig. 11. 2 squares, one double the size of the other, to be cut into four pieces to make a mitre. Just cut each along the diagonal.

No. 18, pp. 27 & 87 & plate II, fig. 14. Six equal squares to form a mitre. Cut each diagonally. [Actually you only need to cut three of the squares.]

Endless Amusement II. 1826? Prob. 5, pp. 192-193. Mitre puzzle -- says the pieces are not precisely equal. = New Sphinx, c1840, pp. 131-132.

Magician's Own Book. 1857.

Prob. 12: The quarto puzzle, pp. 269 & 294. Solution is a bit crudely drawn, but the parts are numbered to make it clear how they are combined. = Illustrated Boy's Own Treasury, 1860, No. 41, pp. 403 & 442.

Prob. 28: Puzzle of the two fathers, pp. 275-276 & 298. One father has L tromino (see 6.F.4), the other has the mitre. Solution carefully drawn and shaded. c= Landells, Boy's Own Toy-Maker, 1858, pp. 148-149.

Book of 500 Puzzles. 1859.

Prob. 12: The quarto puzzle, pp. 83 & 108. Identical to Magician's Own Book.

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

Boy's Own Conjuring Book. 1860.

Prob. 11: The quarto puzzle, pp. 231 & 257. Identical with Magician's Own Book.

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

Hanky Panky. 1872. The one quarterless square, p. 132

Hoffmann. 1893. Chap. X, no. 29: The mitre puzzle, pp. 347 & 386 = Hoffmann-Hordern, pp. 243 & 247. Photo on p. 247 shows Enoch Morgan's Sons Sapolio Color-Puzzle. This says to arrange the blocks 'in four equal parts so that each part will be the same size color and shape.' It appears that the blocks are isosceles right triangles with legs equal to a quarter of the original square. There are 6 blue triangles, 6 yellow triangles and 12 red triangles. I think there were originally 6 red and 6 orange, but the colors have faded, and I think one wants each of the four parts having one color.

Brandreth Puzzle Book. Brandreth's Pills (The Porous Plaster Co., NY), nd [1895]. P. 5: The mitre puzzle. Similar to Hoffmann. No solution.

Loyd. Origin of a famous puzzle -- No. 19: The mitre puzzle. Tit Bits 31 (13 Feb & 6 Mar 1897) 363 & 419. Nearly 50 years ago someone told him to quadrisect ¾ of a square into congruent figures. The L tromino was intended, but young Loyd drew the mitre shape instead. He says it took him nearly a year to solve it. But see Dudeney's comments below.

Clark. Mental Nuts. 1904, no. 31. Dividing the land. Quadrisect an L tromino and a mitre.

Pearson. 1907. Part II, no. 87: Loyd's mitre puzzle, pp. 87 & 178.

Dudeney. The world's best puzzles. Op. cit. in 2. 1908. He says he has traced it back to 1835 (Loyd was born in 1841) and that "strictly speaking, it is impossible of solution, but I will give the answer that is always presented, and that seems to satisfy most people." See also the solution to AM, prob. 150, discussed in 6.AY. Can anyone say what the 1835 source might be -- a version of Endless Amusement??

Wehman. New Book of 200 Puzzles. 1908.

P. 43: Puzzle of the two fathers. c= Magician's Own Book, with cruder solution.

P. 47: The quarto puzzle. c= Magician's Own Book, without the numbering of parts.

Loyd. Cyclopedia. 1914. A tailor's problem, pp. 311 & 381. Quadrisect half of a mitre. This has a solution with each piece similar to to the half mitre.

Loyd Jr. SLAHP. 1928. Wrangling heirs, pp. 35 & 96. Divide mitre into 8 congruent parts -- uses the pattern of Loyd Sr.

Putnam. Puzzle Fun. 1978. No. 106: Divide the shape, pp. 16 & 39. "Divide the given shape into four pieces, such that each and every piece is the same area." This is much easier than the usual version. Put two half-size mitres on the bottom edge and two trapeziums are left.