We are given that he says he does know and have no reason to doubt it. It is possible that Peter and Sandy know one another and already know that they are perfect at figuring out maths/logic puzzles.
The puzzle doesn't state whether Sandy has figured it out because that information is not necessary to figure out the solution. We can infer that she has (under that implicit assumption that she is a perfect logician) by the fact that we know less than she does and still have enough information, though. As for that last part: we also don't truly know that Peter isn't lying just to mess with the puzzle, I guess. That is another implicit assumption.
