Summary: Two players are placed on the real line at a distance \(d\) with a distribution \(F\) known to both. Neither knows the direction of the other, nor do they have a common notion of a positive direction on the line. We seek the least expected rendezvous time \(R= R(F)\) in which they can meet, given maximum speeds of one. We consider the cases where \(F\) is a bounded, point, discrete, or finite mean distribution. We obtain upper bounds or exact values for \(R\) and in one case an optimality condition for search strategies. A connection with Beck’s linear search problem is established.