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AW.4. DIVIDING AN L-TROMINO INTO CONGRUENT PARTS



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6.AW.4. DIVIDING AN L-TROMINO INTO CONGRUENT PARTS
See also 6.F.4.
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?

Editorial comment -- The L-shaped dissection problem. JRM 23:1 (1991) 69-70. Refers to Gardner.

Comments and partial solution by Michael Beeler. JRM 24:1 (1992) 64-69.

Martin Gardner. Tiling the bent tromino with n congruent shapes. JRM 22:3 (1990) 185 191.


6.AX. THE PACKER'S SECRET
This requires placing 12 unit discs snugly into a circular dish of radius 1 + 2 3 = 4.464.
Tissandier. Récréations Scientifiques. 5th ed., 1888, Le secret d'un emballeur, pp. 227-229. Not in the 2nd ed. of 1881 nor the 3rd ed. of 1883. Illustration by Poyet. He shows the solution and how to get the pieces into that pattern. No dimensions given. = Popular Scientific Recreations; [c1890]; Supplement: The packer's secret, pp. 855 856.

Hoffmann. 1893. Chap. X, no. 48: The packer's secret, pp. 356 & 394 = Hoffmann-Hordern, p. 255. Says the problem is of French origin. Gives dimensions 3½ and ¾, giving a ratio of 14/3 = 4.667. "The whole are now securely wedged together ...." [I think this would be a bit loose.]

"Toymaker". The Japanese Tray and Blocks Puzzle. Work, No. 1447 (9 Dec 1916) 168. Says to make the dish of radius 7 and the discs of radius 1½, again giving a ratio of 14/3 = 4.667. Makes "a firm immovable job ...."


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