Pinocchio always lies -- says, "All my hats are green."

[henh...@gmail.com]

The 17th annual Brazilian Olympiad featured an incredibly tricky logic puzzle that went viral on social media. <------ Recently ? on Twitter ?



Here's an interesting logic puzzle from MindYourDecisions:



Assume that both of the following sentences are true:

------- Pinocchio always lies
------- Pinocchio says, "All my hats are green."

What can we conclude from the above two statements:

(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.

[Pancho]

(A). I don't understand why this is difficult? If he had no hats, the
statement would be vacuously true. So he must have at least one hat that
is not green.

[henh...@gmail.com]

i understand that many Non-puzzle fans can never grok the [vacuously true] concept -- maybe it's related to the birth of modal logic.

in the actual test conditions, you have to get this right within 10 seconds (?) or so, so it's not super-easy.



https://en.wikipedia.org/wiki/American_Mathematics_Competitions
i can't quite figure out how this system (of selection, competition) changed from when i was young.