Sources page biographical material

6.G.2. DISSECTION OF 6³ INTO 3³, 4³ AND 5³, ETC.
H. W. Richmond. Note 1672: A geometrical problem. MG 27 (No. 275) (Jul 1943) 142. AND Note 1704: Solution of a geometrical problem (Note 1672). MG 28 (No. 278) (Feb 1944) 31 32. Poses the problem of making such a dissection, then gives a solution in 12 pieces: three 1 x 3 x 3; 4 x 4 x 4; four 1 x 5 x 5; 1 x 4 x 4; two 1 x 1 x 2 and a V pentacube.

Anon. [= John Leech, according to Gardner, below]. Two dissection problems, no. 2. Eureka 13 (Oct 1950) 6 & 14 (Oct 1951) 23. Asks for such a dissection using at most 10 pieces. Gives an 8 piece solution due to R. F. Wheeler. [Cundy & Rollett; Mathematical Models; 2nd ed., pp. 203 205, say Eureka is the first appearance they know of this problem. See Gardner, below, for the identity of Leech.]

Richard K. Guy. Loc. cit. in 5.H.2, 1960. Mentions the 8 piece solution.

J. H. Cadwell. Some dissection problems involving sums of cubes. MG 48 (No. 366) (Dec 1964) 391 396. Notes an error in Cundy & Rollett's account of the Eureka problem. Finds examples for 12³ + 1³ = 10³ + 9³ with 9 pieces and 9³ = 8³ + 6³ + 1³ with 9 pieces.

J. H. Cadwell. Note 3278: A three way dissection based on Ramanujan's number. MG 54 (No. 390) (Dec 1970) 385 387. 7 x 13 x 19 to 10³ + 9³ and 12³ + 1³ using 12 pieces.

M. Gardner. SA (Oct 1973) c= Knotted, chap. 16. He says that the problem was posed by John Leech. He gives Wheeler's initials as E. H. ?? He says that J. H. Thewlis found a simpler 8 piece solution, further simplified by T. H. O'Beirne, which keeps the 4 x 4 x 4 cube intact. This is shown in Gardner. Gardner also shows an 8 piece solution which keeps the 5 x 5 x 5 intact, due to E. J. Duffy, 1970. O'Beirne showed that an 8 piece dissection into blocks is impossible and found a 9 block solution in 1971, also shown in Gardner.

Harry Lindgren. Geometric Dissections. Van Nostrand, Princeton, 1984. Section 24.1, pp. 118 120 gives Wheeler's solution and admires it.

Richard K. Guy, proposer; editors & Charles H. Jepson [should be Jepsen], partial solvers. Problem 1122. CM 12 (1987) 50 & 13 (1987) 197 198. Asks for such dissections under various conditions, of which (b) is the form given in Eureka. Eight pieces is minimal in one case and seems minimal in two other cases. Eleven pieces is best known for the first case, where the pieces must be blocks, but this appears to be the problem solved by O'Beirne in 1971, reported in Gardner, above.

Charles H. Jepsen. Additional comment on Problem 1122. CM 14 (1988) 204 206. Gives a ten piece solution of the first case.

Chris Pile. Cube dissection. M500 134 (Aug 1993) 2-3. He feels the 1 x 1 x 2 piece occurring in Cundy & Rollett is too small and he provides another solution with 8 pieces, the smallest of which contains 8 unit cubes. Asks how uniform the piece sizes can be.