Was pleasantly surprised to encounter the following logic puzzle in the latest edition of NPR’s Sunday Puzzle Podcast, which is mostly about word puzzles.

A waitress approaches a breakfast table with five logicians, and asks “Do all of you want a coffee?” The first logician says, “I don’t know.” The second, third and fourth also say (in that order), “I don’t know.” The fifth says, “No!” Who does the waitress give coffee to, and why?

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If I had to guess: the waitress gives coffee to no one, because she isn’t going to formulate a logic puzzle and solve it.

Your answer is more interesting than the usual one! Since there is no assumption that the waitress is also a logician, anything can happen! (As far as I know, the world is not teeming with logicians who haven’t managed to find a university position, so it’s also perhaps implausible that the waitress is a logician!)

Yes, the problem is poorly phrased :-)

In a related, but less silly, spirit, see also this comment on the infamous Boy-Girl probability question.

So what is the actual solution?

I think the waitress could take revenge and give coffee just to the guy who said he didn’t want it.

(At least, that is what I’d like to do in her place!)

The solution is that she would give coffee to the first four, and not to the fifth. Here’s why &hellip

Suppose the first logician had not wanted coffee. Then of course he knows that at least one of them doesn’t want coffee. In other words, he would know that the answer to the waitress’s question is “No&rdquo. Since he said “I don’t know&rdquo, it means that he wants coffee. He says that he doesn’t know because there could be others who don’t want coffee. One can similarly show that the next three also want coffee.

The fifth logician, on the other hand, knows by this time that everyone else wants coffee. So she can answer “Yes&rdquo or “No” depending on whether she wants it or not. Since she says “No”, it means that she doesn’t want it.