So last time, I posted a puzzle:
Two men, Jack and John, stand at an intersection. You know that one of them always tells the truth, and the other always lies. But you don’t know which one is Jack and which one is John, nor do you know whether Jack is the liar or if John is the liar. Asking only one of the men only one question, how do you determine whether Jack or John is the liar? In the same situation, again using only one question, how do you determine which of them is Jack? And one final catch: your question in each case must be three words or less.
As promised, here’s the answer! But in case you want to think about it some more, here’s a picture of a couple of owls to scroll past.
OK so now the answers for real.
For the first part, to determine whether Jack or John is the liar, the question to ask is “Are you Jack?” If he says yes, then John is the liar. If he says no, then Jack is the liar.
This sounds ridiculous, but it works! Let’s say John is the liar, so Jack is the truth-teller. If you ask Jack the question, he’ll truthfully say yes, he’s Jack. If you ask John the question, he’ll lie and say yes, he’s Jack. Now let’s say Jack is the liar. If you ask Jack the question, he’ll lie and say no, he’s not Jack. If you ask John the question, he’ll truthfully say no, he’s not Jack.
Of course, similar variations of the question also work. “Are you John?” “Is he Jack?” “Is he John?” all work as well, if you work out the logic.
Now the second part, figuring out which one is Jack. This time, the question is “Does Jack lie?” If he says yes, you’re talking to John. If he says no, you’re talking to Jack.
This works too, believe it or not. Let’s say you’re talking to John. If Jack is the liar, then John will truthfully say yes, that Jack lies. If John is the liar, he’ll lie and say yes, Jack lies. Now let’s say you’re talking to Jack. If Jack is the liar, then he’ll lie and say no, he doesn’t lie. If John is the liar, then Jack will tell the truth and say no, he doesn’t lie.
You can also ask “Does John lie?” and reverse the logic, of course. And if there were a way to say “to tell the truth” in one word, you could ask if Jack does that, too.
The two parts of the question have this strange, unexpected (at least to me) symmetry: the question you would naturally think to ask for one situation is the correct question to ask for the other, in this messed up world where there’s a guy who always lies.