The Inspector decides the best thing to do is interview the doctors in charge of the asylum.
“They should know about these peculiar people,” the Inspector mutters.
“What makes a person peculiar?” you ask.
“Anyone who thinks they’re a patient is peculiar,” replies the Inspector. “And if all the patients believe that a person is peculiar—but none of the doctors do—that person is special.”
“What’s more, every person in this asylum has a best friend here. And between any two people, A and B, if A believes B is special, then A’s best friend believes B is a patient. What do you think of that?”
You shake your head. “I couldn’t tell you…”
The two of you meet the first head doctor, Doctor Tarr.
“Tell me, Doctor Tarr,” asks the Inspector. “Are all the doctors in this asylum sane?”
“Of course they are!” yells the doctor.
“What about the patients,” you put in. “Are they all insane?”
“At least one of them is. If you’ll excuse me—” and he runs off to deal with a patient.
“That wasn’t much of an answer,” you remark.
“No it wasn’t. Let’s talk to the other head doctor.”
You find Professor Fether, the doctor in question, and buttonhole him.
“Doctor Tarr said that at least one patient here is insane,” announces the Inspector. “That’s true, isn’t it?”
“Of course it’s true!” shouts Professor Fether. “All the patients are insane! What kind of an asylum do you think this is?”
“What about the doctors?” you ask. “Are they all sane?”
“At least one of them is,” he responds.
“And Doctor Tarr—is he sane?”
“Of course! How dare you ask such a question.” Professor Fether storms off in a huff. You and the Inspector sit down to work out the situation at the asylum.
Explain the situation by submitting a solution…