What is the only crainial nerve that enters and leaves the skull?

The correct answer is indeed the

accessory nerve

The fibers that make up the accessory nerve enter the skull through the foramen magnum and proceed to exit the jugular foramen with cranial nerves IX and X. Due to its unusual course, the accessory nerve is the only nerve that enters and exits the skull.

The answer is the accessory nerve.

Explanation:

We have 12 pairs of cranial nerves, the accessory nerve is the XI pair. This is responsible for the innervation of the sternocleidomastoid and trapezius muscles.

The fibers of the accessory nerve originate from neurons that are located in the upper spinal cord. These fibers join together forming roots and once the nerve is constituted, it enters the skull through the great hole that is located at the base of the skull.

Then, the nerve continues its path along the inside of the skull in the direction of the jugular hole and then leaves the skull next to the glossopharyngeal nerve (IX) and the vagus (X).

Thus, the accessory nerve enters and leaves the skull again, characterized by being the only cranial nerve which has this behavior.