I'm not sure how to do this problem...Can someone who has done or know how to do this help me?

This is turning into a Manhattan Project without a reason. There are two ways to push the "center" pin out. A cam action (see the attached), the problem is, the pin would also rotate because it is round and does not have a keyway to stop its rotation.
The other way would be to have a cam action between one of the lock housing surfaces that when turning the key it would push the pin out. This would not be allowed because on paragraph one they state, "collision between lock and key must not happen".
The two most possible ways are not possible because of restrictions.
I have posted this comment before:
"Reading the fifth paragraph, it says, "Assume that the 3D model of the lock is a perfect representation of reality." It shows the side view but not the top view, since we are "assuming" who is not to say that the top view shows the pin is off center. I believe it is the only way you can push that pin out when the key is turned."

Under the "assumed" requirements, I believe it is the only way to do it, and it would allow for the end of the key to have a radial guide with the lock and stability for the pin contact. Your design does not have a radial guide on the front of the back of the lock.