Deterministic physics vs Master-Server, what do you suggest?

Hi, I would like to make a question.
I'm programming a 2D racing game, the clients are selecting the path, then they send the path to the server, which syncs all the clients.
The physical race is happening on the clients (local). This is perfect apart from the fact that physics is random, so the results are slightly changing within the clients I'm holding the server on a free AWS EC2 instance.

Solutions
1) Finding a way to have a deterministic physics on the clients such that the racings are all the same
2) Simulating on sub-servers with a master server controlling them, but I really don't know how to put all this mess up on a remote linux AWS instance

What do you suggest?