The article considers a two-person zero-sum game in which the movement of the players is constrained to integer points...,¸-1,0,1,...of a line L. Initially the searcher (hider) is at point x=0 (x=d,d>0). The searcher and the hider perform simple motion on L with maximum speeds w and u, respectively, where w>u>0. Each of the players knows the other’s initial position but not the other’s subsequent positions. The searcher has a bomb which he can drop at any time during his search. Between the dropping of the bomb and the bomb exploding there is a T time lag. If the bomb explodes at point i and the hider is at point i-1, or i, or i+1, then the destruction probability is equal to P, or 1, or P, respectively, where 0<P<1. d,w,u, and T are integer constants. The searcher can drop the bomb at integer moments of time t=0,1,.... The aim of the searcher is to maximize the probability of the destruction of the hider.
