Hi, i need help with one interesting exercise.

So, i have 100 meters long rod and there are 100 walking robots. Every robot moves with speed 1 m/s. When two robots meet, they turn round and continue from each other. When a robot gets at the end of the rod, it will turn round too. The robots are located and directed on the rod randomly and independently.

In the middle of the rod, there is also robot R and it is directed to the right side. His behavior is same as the others. What is the probability, that the robot R will be after 100 s exactly in the middle of the rod.

Thank you for your advices.