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F.3. DISSECTING A CROSS INTO Zs AND Ls



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 The Philosophy of Analysis -- unpublished collection of MSS in the BM as Add.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


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