Sources page biographical material

6.U.2. PACKING BRICKS IN BOXES
In two dimensions, it is not hard to show that a x b packs A x B if and only if a  divides either A or B; b divides either A or B; A and B are both linear combinations of a and b. E.g. 2 x 3 bricks pack a 5 x 6 box.

See also 6.G.1.

Anon. Prob. 52. Hobbies 30 (No. 767) (25 Jun 1910) 268 & 283 & (No. 770) (16 Jul 1910) 328. Use at least one of each of 5 x 7, 5 x 10, 6 x 10 to make the smallest possible square. Solution says to use 4, 4, 1, but doesn't show how. There are lots of ways to make the assembly.

Manuel H. Greenblatt ( -1972, see JRM 6:1 (Winter 1973) 69). Mathematical Entertainments. Crowell, NY, 1965. Construction of a cube, pp. 80 81. Can 1 x 2 x 4 fill 6 x 6 x 6? He asserts this was invented by R. Milburn of Tufts Univ.

N. G. de Bruijn. Filling boxes with bricks. AMM 76 (1969) 37 40. If a₁ x ... x a_n fills A₁ x ... x A_n and b divides k of the a_i, then b divides at least k of the A_i. He previously presented the results, in Hungarian, as problems in Mat. Lapok 12, pp. 110 112, prob. 109 and 13, pp. 314 317, prob. 119. ??NYS.

D. A. Klarner. Brick packing puzzles. JRM 6 (1973) 112 117. General survey. In this he mentions a result that I gave him -- that 2 x 3 x 7 fills a 8 x 11 x 21, but that the box cannot be divided into two packable boxes. However, I gave him the case 1 x 3 x 4 in 5 x 5 x 12 which is the smallest example of this type. Tom Lensch makes fine examples of these packing puzzles.

T. H. Foregger, proposer; Michael Mather, solver. Problem E2524 -- A brick packing problem. AMM 82:3 (Mar 1975) 300 & 83:9 (Nov 1976) 741-742. Pack 41  1 x 2 x 4 bricks in a 7 x 7 x 7 box. One cannot get 42 such bricks into the box.