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Dave Winer serves coffee to four logicians

From Dave Winer:

Four logicians are having breakfast. Waitress asks — Will you all be having coffee? The first logician says “I don’t know.” Second says “I don’t know.” Third says “I don’t know.” Fourth says “No.” The waitress returns with their coffees. Who gets coffee?

It does have a solution. The solution is not a cheat or wordplay or a sort of “lightbulb” joke anything extraneous to the puzzle. For example, it’s not “None of them, because logicians drink tea” or “None, because the first three were saying, “I don’t. No.” or “None, because coffee isn’t axiomatic.”

[HINT:]: Think about how each of the logicians would answer the question if she were going to order coffee or not order coffee.

I’ll put the answer in the first comment. [Actually, I changed my mind. I’ll post the answer in a comment if no one else comments.]

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21 Responses to “Dave Winer serves coffee to four logicians”

  1. 1, 2, and 3 get coffee. The waitress didn’t ask if they EACH would be having coffee, she asked if “you all” will be having coffee — i.e. will the _whole group_ be having coffee. Thus the ones that wanted coffee couldn’t answer “yes”, because they didn’t know how the _others_ would order until all the orders were in. So they say “I don’t know.”

  2. Sigh! I was coming in here to post the answer, and then got upset that I was beaten, and then was excited that I knew the person who beat me to it. Hi, Jason!

  3. And I’m excited because I figured it out before my engineer hubby did. But I actually noticed the key word in the question while reading it aloud to him. I hadn’t read your hint, but when I did it confirmed my solution.

  4. Just to make explicit what’s implicit in the first answer: Anyone who didn’t want coffee would know that the conjunct was false, as would anyone preceded by someone who didn’t want it. So only someone who did want it (and hadn’t heard from anyone else who didn’t yet) would be ignorant of the answer to the collective question.

  5. I was excited because I got it right also, without even a hint from my brother! It didn’t strike me at first, but in reviewing the statement I realized the importance of the waitress’s phrasing of the question.

  6. It’s a good job that the first 3 did want coffee though; if the first one hadn’t (or the subsequent 2) all the following answers would have been no and there would have been no way of telling them apart ;)

  7. Yes, Rachel has a nice catch. But in the particular case it is clear that 3 coffees were served nd the last philosopher didn’t get any.

    (Haven’t commented here in a long time, so I am willing to be redundant.]

  8. The fourth ‘logician’ is an impostor.

    Even he or she cannot be certain that they won’t all be having coffee.

    The waitress may have simply abandoned the attempt to deduce the order and decided to get 4 coffees anyway.

    No logician can foretell the future.

    Therefore, if the waitress was a logician she would probably have brought 4 coffees simply to teach the 4th a lesson.

    If she had instead asked “Do you all want coffee?”, then perhaps the 4th could speak in the negative with more certainty.

    The waitress had instead asked for a prophecy – which no logician would dare answer except with “I don’t know”.

  9. I don’t get it. Can anybody explain it to me?

  10. Fit Gizmos-

    My take was that when the waitress asked “Will you all be having coffee,” the key word is “all,” covering the entire group, not each person separately.

    If the 1st customer knew he was not going to have coffee, he would have said “No,” meaning we are not ALL having coffee, because I am not going to have coffee. If he wanted coffee, he would have to say “I don’t know” if we are ALL having coffee, because he does not know what the other three want.

    The second and third logicians are in a similar predicament, so they give the same answer. If the second or third did not want coffee, they would have said “No” because their refusal would mean that not ALL were having coffee.

    The fourth logician knew she was not having coffee so that she said “NO” we are not all having coffee, meaning that was the case because she was not having coffee. The clever waitress then determined that the other three wanted coffee as none of them had said “No.”

    I hope that is a little more clear.

  11. So the question ISN’T will you be having coffee, but will you all be having coffee. Three say they don’t know, meaning they don’t know if all four are having coffee. The last says no meaning he knows that all won’t be. The only reason he could know this is that he is not having coffee. The others could have said no, too, if they weren’t having coffee, too. So therefore the original three must have wanted coffee, so the waitress brings three coffees.

    (I promise I didn’t look at the other answers until I finished.)

  12. the question was wrongly asked. it should have been: Four logicians, etc, etc. WHERE WAS THE RESTAURANT?

    If it had been in the South, the question Will y’all be having coffee? would have been addressed simultaneously to each of the four. The meaning that has been tortured out of the example in the comments would have required the waitress to ask “Will ALL Y’ALL be having coffee?” Of course she would not have asked the same question about grits, she would just bring everybody grits regardless.

  13. I like grits, so please tell me where this restaurant is so I can get some! I like coffee too, but if asking for it causes this kind of commotion or need for thought, I’ll just have the grits.

  14. All wrong.

    The logicians were asked if they were going to have coffee, they were not asked if the WANTED coffee.

    Until they actually received the coffee, they could not be sure that it would in fact arrive. A terrorist bomb may have blown up the restaurant or they may, individually or collectively, died, had a change of mind etc.

    So they could not predict with certainty that they would in fact have the coffee.

    So the only logical answer is that they don’t know.

    The fourth, however, DOES know, he has decided not to have coffee and can prevent its arrival simply by saying no.

    Three coffees for the “don’t knows” please

  15. What fun!

    Well, the question is a bit of a cheat because modifies the pragmatics of the question; unless the waitress was a PhD student in a university math department, specifically hired to amuse the faculty.

    If you think about the question in terms of conversational pragmatics, that is “what is the question doing in this situation?”, I think you’ll agree that the waitress was in fact asking each one of them if they, individually, were having coffee.

    In fact, the waitress must have come from the math department, certainly not Philosophy or English, otherwise she would not have returned at all.

  16. I think it’s time the correct answer was given.

    1) We’re privileged to know who the waitress is. It’s Dave Winer (in drag, disguised as a waitress).

    2) All four ‘logicians’ end up having coffees. Even the question reveals that ‘she’ brings back at least two coffees, but the article informs us that coffee is served to all four ‘logicians’.

    3) None of the logicians could know how many coffees they would be having, but we at least, with our knowledge, know that the fourth person was not a very good logician – either that, or they were a poor linguist. They ended up having a coffee despite prophesying that they wouldn’t – simply due to Dave Winer’s mischief.

    4) We can suppose that if the 4th ‘logician’ had said they will be having coffee, that Dave Winer wouldn’t have served it to them, but then that’s a different situation, not the one we’ve been invited to consider.

    5) The logic problem is a red herring designed to lure the unwary into concluding that coffee was served to only three logicians, despite already being informed that it was served to four. It is demonstrably a red herring as David Kamenetz has observed – it is highly unlikely that a waitress would take instruction by inference (unless Dave Winer in drag and not feeling contrary).

    6) The icing on the cake is that all four ‘logicians’ were female students in the breakfast room of a women’s dormitory at a prestigious college that Dave Winer once attended, and this is part of an anecdote of his, relating one of the merry escapades of his youth. It also explains why he was in drag.

  17. This assumes that the waitress understood their logical meanderings, and is also a good enough waitress to get all of the orders right even if she did understand them, and also doesn’t hate them enough to intentionally get their orders wrong. You really have to establish your axioms better.

  18. It took me a bit, and it was just wordplay from the waitresses question.

  19. No Texan (whose use of Y’all in every possible context is well known) would ever guess that answer.

  20. Great, now we’re being spammed..

  21. (I removed the spam… unless, of course, spiral of hope is spam.)

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