Summary: This paper considers a three-person rendezvous problem on the line which was introduced earlier by the authors. Three agents are placed at three consecutive integer value points on the real line, say 1, 2, and 3. Each agent is randomly faced towards the right or left. Agents are blind and have a maximum speed of 1. Their common aim is to gather at a common location as quickly as possible. The main result is the proof that a strategy given by V. Baston is the unique minimax strategy. Baston’s strategy ensures a three way rendezvous in time at most 3.5 for any of the \(3!2^3= 48\) possible initial configurations corresponding to positions and directions of each agent. A connection is established between the above rendezvous problem and a search problem of L. Thomas in which two parents search separately to find their lost child and then meet again.