# Heron Suit Problem

Here is another logic problem from Ian Stewart.

1. No cat that wears a heron suit is unsociable.
2. No cat without a tail will play with a gorilla.
3. Cats with whiskers always wear heron suits.
4. No sociable cat has blunt claws.
5. No cats have tails unless they have whiskers.

Therefore:

No cat with blunt claws will play with a gorilla.

Is the deduction logically correct?

I confess I don’t know what a heron suit is.  Google showed various garments with herons imprinted on the cloth, so maybe that is what it is.

See the Heron Suit Problem for a solution.

# Puzzle of the Purloined Papers

Ian Stewart has a nice logic problem in his Casebook of Mathematical Mysteries, which includes a pastiche of Sherlock Holmes in the form of Herlock Soames and Dr. Watsup, along with brother Spycraft and nemesis Dr. Mogiarty.

“An important document was accidentally mislaid, and then stolen,” Spycraft said. “It is essential to the security of the British Empire that it be recovered without delay. If it gets into the hands of our enemies, careers will be ruined and parts of the Empire may fall. Fortunately, a local constable caught a glimpse of the thief, enough to narrow it down to precisely one of four men.”

“Petty thieves?”

“No, all four are gentlemen of high repute. Admiral Arbuthnot, Bishop Burlington, Captain Charlesworth, and Doctor Dashingham.”

Soames sat bolt upright. “Mogiarty has a hand in this, then.”

Not following his reasoning, I asked him to explain.

“All four are spies, Watsup. Working for Mogiarty.”

“Then … Spycraft must be engaged in counter-espionage!” I cried.

“Yes.” He glanced at his brother. “But you did not hear that from me.”

“Have these traitors been questioned?” I asked.

Spycraft handed me a dossier, and I read it aloud for Soames’s benefit. “Under interrogation Arbuthnot said ‘Burlington did it.’ Burlington said ‘Arbuthnot is lying.’ Charlesworth said ‘It was not I.’ Dashingham said ‘Arbuthnot did it.’ That is all.”

“Not quite all. We know from another source that exactly one of them was telling the truth.”

“You have an informer in Mogiarty’s inner circle, Spycraft?”

“We had an informer, Hemlock. He was garrotted with his own necktie before he could tell us the actual name. Very sad—it was an Old Etonian tie, totally ruined. However, all is not lost. If we can deduce who was the thief, we can obtain a search warrant and recover the document. All four men are being watched; they will have no opportunity to pass the document to Mogiarty. But our hands are tied; we must stick to the letter of the law. Moreover, if we raid the wrong premises, Mogiarty’s lawyers will publicise the mistake and cause irreparable damage.”

Which man was the thief?

See the Purloined Papers Puzzle for solutions.

# Do I Avoid Kangaroos?

This is a fun logic puzzle from one of Ian Stewart’s many math collections.  I discovered that the problem actually is basically one of Lewis Carroll’s examples from an 1896 book:

1. The only animals in this house are cats.
2. Every animal that loves to gaze at the moon is suitable for a pet.
3. When I detest an animal, I avoid it.
4. No animals are meat-eaters, unless they prowl by night.
5. No cat fails to kill mice.
6. No Animals ever take to me, except those in this house.
7. Kangaroos are not suitable for pets.
8. Only meat-eaters kill mice.
9. I detest animals that do not take to me.
10. Animals that prowl at night love to gaze at the moon.

If all these statements are correct, do I avoid kangaroos, or not?

See Do I Avoid Kangaroos? for solutions.

# Swallowing Elephants

This is a simple logic puzzle from one of Ian Stewart’s many math collections.

1. Elephants always wear pink trousers.
2. Every creature that eats honey can play the bagpipes.
3. Anything that is easy to swallow eats honey.
4. No creature that wears pink trousers can play the bagpipes.

Therefore:

Elephants are easy to swallow.

Is the deduction correct, or not?

See Swallowing Elephants for a solution.