Why don't you post solutions to (all) exercises on the tutorial program?
The main goal of the course is to acquire certain skills (e.g., you should acquire the skill to give proofs of properties using logically valid reasoning). In order to acquire those skills, you need to practice a lot. If you (can) look up the solution of an exercise as soon as you get stuck when trying to solve it, then you will probably learn how to solve the exercise at hand, but you will not learn the skill of solving similar exercises in general. A much better way to deal with the situation that you're stuck with an exercise, is to look up the solution to a similar exercise, and then try to replay and adapt it to the exercise you need to solve. If you manage to do that, you will actually learn the skill.
For those who want to learn from example solutions (or who simply disagree with the didactic approach sketched above), a complete [alternative exercise program], consisting of solved exercises only, is available. This program should also sufficiently prepare you for the weekly tests and the exam, provided that you do not look at the solution to an exercise before you have found a solution yourself, and only use it to confirm the correctness of your own.
I am trying to prepare for the tutorials on Fridays by making all the exercises on the schedule beforehand, but I don't seem to have enough time between the Wednesday lecture and the Friday tutorials to do them all. Is there a better strategy?
Yes, there is! Note that you can start earlier with making the exercises on the program. In fact, the exercises on the schedule for the tutorials are about material treated in the two preceding lectures. Suppose that you insist on having attended the lecture in which the corresponding part of the course material is discussed before starting to make exercises about that part. In the lecture on Friday (a week earlier), half of the relevant material has already been discussed, and so for about the first half of the exercises, you have a whole week. Then you have the time between the Wednesday lecture and the Friday tutorial to do the other half, which we admit is quite short if Thursday is full with other lectures. But note that the book also does a good job at explaining the material; maybe you do not need the lecture on Wednesday to do the exercises, or at least you can do some of them already? The general advice is to start doing exercises as soon as possible. Incidentally, note that you are expected to spend approximately 8 hours per week on studying the material outside the scheduled contact hours.