The article considers a two-person zero-sum game in which a searcher with b bombs wishes to destroy a mobile hider. The players are restricted to move on a straight line with maximum speeds v and u satisfying v>u>0; neither player can see the other but each knows the other’s initial position. The bombs all have destructive radius R and there is a time lag T between the release of a bomb and the bomb exploding. The searcher gets 1 unit if the hider is destroyed and 0 if he survives. A solution is given for b=1, and extended to b>1 when the time lag is small. Various applications of the game are discussed.
