One question for the mixed-up oracle

Question

You stand before an oracle who answers only yes/no questions. The oracle is one of two fixed types: an honest one that always answers truthfully, or a deceiver that always answers falsely. You do not know which type you are facing.

You get to ask exactly one yes/no question, and you want to find out whether it will rain tomorrow.

What single question guarantees you learn the truth about tomorrow's rain, whichever type the oracle is?

Accepted Answer

Ask this nested question: "If I asked you whether it will rain tomorrow, would you answer 'yes'?" Then treat a "yes" as "it will rain" and a "no" as "it won't." Here is why that works for both types. Honest oracle. It reports exactly what it would say. It would say "yes" to "will it rain?" precisely when it rains. So its answer to the nested question is "yes" exactly when it rains. Correct. Deceiver. Work from the inside out. To the plain question "will it rain?" the deceiver lies, so it would answer "yes" exactly when it won't rain. Now the nested question asks it to report that behavior, "w…

One question for the mixed-up oracle

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