This problem in logic from Presh Talwalkar recalled an article I wrote a while ago but did not publish.  So I thought I would post it as part of the solution.

“Assume that both of the following sentences are true:

1. Pinocchio always lies;
2. Pinocchio says, “All my hats are green.”

We can conclude from these two sentences that:

• (A) Pinocchio has at least one hat.
• (B) Pinocchio has only one green hat.
• (C) Pinocchio has no hats.
• (D) Pinocchio has at least one green hat.
• (E) Pinocchio has no green hats.”

Actually, the question is which, none or more, of statements (A) – (E) follow from the two sentences?

Answer.

See Pinocchio’s Hats for solutions.