Sources page biographical material

6.F.2. COVERING DELETED CHESSBOARD WITH DOMINOES
See also 6.U.2.

There is nothing on this in Murray.

Pál Révész. Op. cit. in 5.I.1. 1969. On p. 22, he says this problem comes from John [von] Neumann, but gives no details.

Max Black. Critical Thinking, op. cit. in 5.T. 1946 ed., pp. 142 & 394, ??NYS. 2nd ed., 1952, pp. 157 & 433. He simply gives it as a problem, with no indication that he invented it.

H. D. Grossman. Fun with lattice points: 14 -- A chessboard puzzle. SM 14 (1948) 160. (The problem is described with 'his clever solution' from M. Black, Critical Thinking, pp. 142 & 394.)

S. Golomb. 1954. Op. cit. in 6.F.

M. Gardner. The mutilated chessboard. SA (Feb 1957) = 1st Book, pp. 24 & 28.

Gamow & Stern. 1958. Domino game. Pp. 87 90.

Robert S. Raven, proposer; Walter P. Targoff, solver. Problem 85 -- Deleted checkerboard. In: L. A. Graham; Ingenious Mathematical Problems and Methods; Dover, 1959, pp. 52 & 227.

R. E. Gomory. (Solution for deletion of any two squares of opposite colour.) In: M. Gardner, SA (Nov 1962) = Unexpected, pp. 186 187. Solution based on a rook's tour. (I don't know if this was ever published elsewhere.)

Michael Holt. What is the New Maths? Anthony Blond, London, 1967. Pp. 68 & 97. Gives the 4 x 4 case as a problem, but doesn't mention that it works on other boards. (I include this as I haven't seen earlier examples in the educational literature.)

David Singmaster. Covering deleted chessboards with dominoes. MM 48 (1975) 59 66. Optimum extension to n dimensions. For an n-dimensional board, each dimension must be  2. If the board has an even number of cells, then one can delete any n-1 white cells and any n-1 black cells and still cover the board with dominoes (i.e. 2 x 1 x 1 x ... x 1 blocks). If the board has an odd number of cells, then let the corner cells be coloured black. One can then delete any n black cells and any n-1 white cells and still cover the board with dominoes.

I-Ping Chu & Richard Johnsonbaugh. Tiling deficient boards with trominoes. MM 59:1 (1986) 34-40. (3,n) = 1 and n  5 imply that an n x n board with one cell deleted can be covered with L trominoes. Some 5 x 5 boards with one cell deleted can be tiled, but not all can.