Sources page biographical material

6.G.3. DISSECTION OF A DIE INTO NINE 1 x 1 x 3
Hoffmann. 1893. Chap. III, no. 17: The "Spots" puzzle, pp. 98 99 & 130 131 = Hoffmann Hordern, pp. 90-91, with photo. Says it is made by Wolff & Son. Photo on p. 91 shows an example made by E. Wolff & Son, London.

Benson. 1904. The spots puzzle, pp. 203 204. As in Hoffmann.

Collins. Book of Puzzles. 1927. Pp. 131 134: The dissected die puzzle. The solution is different than Hoffmann's.

Rohrbough. Puzzle Craft. 1932. P. 21 shows a dissected die, but with no text. The picture is the same as in Hoffmann's solution.

Slocum. Compendium. Shows Diabolical Dice from Johnson Smith catalogue, 1935.

Harold Cataquet. The Spots puzzle revisited. CFF 33 (Feb 1994) 20-21. Brief discussion of two versions.

David Singmaster. Comment on the "Spots" puzzle. 29 Sep 1994, 2pp. Letter in response to the above. I note that there is no standard pattern for a die other than the opposite sides adding to seven. There are 2³ = 8 ways to orient the spots forming 2, 3, and 6. There are two handednesses, so there are 16 dice altogether. (This was pointed out to me perhaps 10 years before by Richard Guy and Ray Bathke. I have since collected examples of all 16 dice.) However, Ray Bathke showed me Oriental dice with the two spots of the 2 placed horizontal or vertically rather than diagonally, giving another 16 dice (I have 5 types), making 32 dice in all. A die can be dissected into 9 1 x 1 x 3 pieces in 6 ways if the layers have to alternate in direction, or in 21 ways in general. I then pose a number of questions about such dissections.