The ‘Gunport Problem’ was originated by Bill Sands and popularised by Martin Gardner in his long-running Mathematical Games column for Scientific American. The original paper by Sands is available online at JSTOR and an extract from Gardner's article is reprinted in ‘The Colossal Book of Short Puzzles and Problems’. We introduce the problem by way of the following quote from Sands' paper. If one places 2×1 dominoes on an m×n board (each domino covering exactly two unit squares of the board) until no more dominoes can be accommodated, one notices that there may be a number of 1×1 squares, or ‘holes’ left vacant. How can this number be maximised?
