The Gunport Problem

The "Gunport Problem" was originated by Bill Sands (1971) and popularised by Martin Gardner in his longrunning Mathematical Games column for Scientific American (April 1974). The original paper by Sands is available online (1) 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 2x1 dominoes on an mxn 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 1x1 squares, or "holes" left vacant.