On a square haystack game

A haystack game is a hider-seeker zero-sum game of locating a needle in a haystack. Baston and Bostock have obtained partial solutions to this game for the case of a square haystack. This paper supplements their results, thus confirming their belief that a complete solution is difficult.The author would like to thank a referee for his helpful comments, in particular for suggesting Lemma 2.1 which has led to a more concise and transparent treatment of Section 2.