Can You Solve the Three Gods Riddle?

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In this TED-Ed riddle, we explore a classic logic puzzle invented by logician Raymond Smullyan. As the video tells us, it has been called the hardest logic puzzle ever. They're not kidding.

So here's the situation. You have crash-landed on a mysterious planet. The only way to escape is to appease three alien overlords (they were "gods" in the original telling, hence its name).

You know that the three aliens are named Tee, Eff, and Arr. There are also three artifacts on the planet, each of which matches a single alien (for the sake of simplicity, let's assume they are labeled "Tee," "Eff," and "Arr"). To appease the aliens, you need to match up the artifacts with their aliens—but you don't know which of the aliens is which!

You are allowed to ask three yes-or-no questions, each addressed to any one alien. (You can address multiple questions to the same alien, but you don't have to.)

To further complicate things, each alien has a specific behavior with regard to telling the truth. Tee's answers are always true. Eff's answers are always false. Arr's answers are random.

Yet another problem is that while you know the alien words "ozo" and "ulu" somehow correspond to "yes" and "no," but you don't know which is which. (I know, this situation just keeps getting worse!) So while you can communicate enough of the alien language to ask questions, they will respond only with "ozo" or "ulu." You may ask the questions one at a time, building on each response if you wish—meaning you have time to think about the next question based on what you have learned.

So your task is to ask three yes-or-no questions, while not knowing which answering words correspond to "yes" and "no," of three aliens whose identity is unknown, but whose behavior is predictable...if you knew their identity. How can you figure out which alien is which, so you can hand the right objects to the aliens? Put your thinking caps on, then roll the video explanation (which includes the answer, after a suitable pause):

For more on this puzzle, check out this TED-Ed page. For some flavor on logician Raymond Smullyan, check out his interview with Johnny Carson.