Classic....

 You are hopefully familiar with knight/knave logic problems (made famous by Raymond Smullyan) — knights are truthtellers who always tell the truth, while knaves always lie. The following is a nice, interesting one (in which Leon & Larry are liars, and Tim a truthteller), originally from Smullyan, but quoted in Jason Rosenhouse’s current volume “Games For Your Mind”:

“You meet triplets named Leon, Larry, and Tim. They are visibly indistinguishable, but Leon and Larry are knaves, while Tim is a knight… What one question  could you direct to one of the brothers to determine whether or not he is Larry?”

answer below:

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ANSWER:

Suppose you simply randomly ask one of the brothers, “Are you Larry?” This does no good. Both Tim and Larry will say “no,” and Leon will say “yes.” A yes answer would identify Leon, but a no answer could come from either Tim or Larry, and fails to ID which is which.

If instead we ask, “Are you Tim?” then everyone will simply respond “yes” and we gain nothing. 

The intriguing part is that if we ask, “Are you Leon?” the responder will give away whether he is or is not Larry. Larry will lie and answer “yes.” Tim will tell the truth and say “no,” and Leon will lie, also saying “no.” We know anyone answering “no” is not Larry, and anyone replying “yes” must be Larry.