Here are my estimated scores for each problem

problem 1 - 1 (~100% chance)

problem 2 - 5 or 6 (most likely 6)

problem 3 - 0 (100% chance)

problem 4 - 7 (~100% chance)

problem 5 - 7 (~100% chance)

problem 6 - 6 or 7 (most likely 7)