Step 1: A patient with sudden one-sided facial droop, loss of forehead wrinkling and inability to close the eye has a peripheral facial weakness pattern.
Step 2: This presentation defines Bell's palsy, which is an idiopathic dysfunction of the nerve that motors all the muscles of facial expression - the facial nerve, numbered cranial nerve VII.
Step 3: Because cranial nerves XI, IX and III control trapezius/sternocleidomastoid, pharynx and eye movements respectively, none of them produces facial-expression palsy.
\[\boxed{\text{7th cranial nerve}}\]