Answer: Subarachnoid hemorrhage (SAH).
Step 1: The combination of SUDDEN onset, very severe headache (the classic thunderclap or worst headache of my life) plus neck rigidity is the textbook presentation of SAH, usually from a ruptured berry aneurysm.
Step 2: Blood in the subarachnoid space irritates the meninges, producing meningismus (neck stiffness, photophobia), nausea, vomiting and sometimes brief loss of consciousness or seizures.
Step 3: Why not the others. Intraparenchymal hemorrhage usually gives focal neurological deficits that build up, not isolated thunderclap headache with meningism. Meningitis causes neck rigidity too, but it evolves over hours to days with fever, not as an instant sudden-onset event. The pattern of abrupt headache plus stiff neck is most specific for SAH.
Hence SAH is correct.
Ref: Harrison's Principles of Internal Medicine, 20e.