The number hides game
V. J. Baston, F. A. Bostock, Thomas S. Ferguson · Proceedings of the American Mathematical Society · 1989
We solve the following two-person zero-sum game, introduced by Ruckle. Players I and II simultaneously choose sequences of m m and n n consecutive integers respectively from the integers 1 to p p inclusive. The payoff to I is the number of integers in the intersection of the two sequences. A continuous version of this game is also solved as well as the variations in which one of the players need not choose his integers consecutively.