114

Three logicians walk into a bar. The barman says, 'Does everybody want a drink?'

The first logician says, 'I don't know.'

The second logician says, 'I don't know.'

What does the third logician say?

Please provide a clear explanation of why each of the logicians reply in the way they do.

Bob
  • 4,253
  • 2
  • 21
  • 45
  • i saw this somewhere – Abr001am Apr 19 '15 at 12:18
  • 5
    I think this is a very old joke/puzzle. It appears various places in a variety of forms. – Bob Apr 19 '15 at 12:31
  • very smart aspects can be remarked from these memes, that helps you behave vigilant and lively minded – Abr001am Apr 19 '15 at 12:40
  • 58
    As a former logician, I would like to point out that, in reality, the first logician would say "no." There is at least one person in the world who does not want a drink. – David Richerby Apr 19 '15 at 20:26
  • 3
    http://spikedmath.com/445.html – Abr001am Apr 19 '15 at 22:29
  • @Agawa001 also http://mrburkemath.blogspot.com/2011/05/coffee-logic.html – geometrian Apr 19 '15 at 23:43
  • @DavidRicherby Depends on the timeframe, I'd say. – No. 7892142 Apr 20 '15 at 13:19
  • Pretty sure this already exists in this site, making this a dupe, but I can't find it. – Adam Davis Apr 20 '15 at 14:00
  • 12
    @DavidRicherby As another former logician, I would like to point out that, in reality, although the odds would definitely be in the favor of at least one person in the world not wanting a drink, it would still be an assumption unless he indeed knows at least one person in the world who does not want a drink... – Warlord 099 Apr 20 '15 at 14:16
  • You'd think one of them would have seen it. –  Apr 20 '15 at 17:46
  • "Hey, did you do those chores?" Explanation: Someone is bound to ask "What chores?" to which the 3rd logician will smile and name his preferred drink. – cuddlyable3 Apr 19 '15 at 21:48
  • @Warlord099 I know lots of people that don't drink, so I don't think that would be too much of an assumption. – reirab Apr 20 '15 at 18:46
  • 5
    @reirab I would love to know one person who has never ever in their life drank some water... There is nothing to imply that the drink has to be alcoholic (which I am assuming is your premise). I don't drink alcohol and I have been to bars with friends where I have had food and water. – Warlord 099 Apr 20 '15 at 20:47
  • A better phrasing would be "Do all of you want a drink?" That excludes the pedantic interpretations of "everybody" by people like @DavidRicherby. – Rand al'Thor Apr 26 '15 at 21:12
  • @randal'thor Excluding pedantry from a discussion about logicians being pedantic would be... something. – David Richerby Apr 26 '15 at 21:34
  • @DavidRicherby True, but only some pedantry is meant to be allowed for this puzzle! :-) – Rand al'Thor Apr 26 '15 at 21:35
  • If the first logician said no the second one would have said: "Abuse of the universe of discourse can falsify any claim and is therefor not constructive." Logicians can get testy when they're thirsty. – candied_orange Jan 10 '16 at 21:51
  • As a logician myself, I would like to offer the point that if any of the mentioned logicians were Irish by blood, they would without any doubt have answered "yes" because there is no way he could imagine that anybody wouldn't. Since the first two were unsure, then they could not have been Irish. However, it is possible, since we don't know what he said, that the third one was Irish, in which case he would have said "yes" most emphatically after seeing two people who were unsure. – bgmCoder Jan 30 '16 at 17:22
  • Three logicians walk into a bar. Ouch. –  Aug 29 '16 at 15:30
  • @Warlord099, “the odds would definitely be in the favor of at least one person in the world not wanting a drink”—now that's a statement put so precisely! :) Reminded me of another one: “there is at least one sheep in Scotland such that at least one of its sides is black.” – kkm -still wary of SE promises Jul 27 '20 at 16:20

2 Answers2

125

Question:

Does everybody want a drink?

The third logician answers:

"YES" if he wants a drink, "NO" if doesn't want it.

Reason:

The first says "I don't know" because he wants a drink, but doesn't know if everybody wants one. If the first didn't want a drink, he would have answered "No".
Same for the second, he wants a drink but doesn't know if the third wants one. So, the third answers "Yes" if he wants a drink, "No" if he doesn't.

leoll2
  • 12,590
  • 3
  • 39
  • 83
  • 65
    He might also say "I don't know" if he interprets "everybody" as more than just the three logicians. – Ian MacDonald Apr 19 '15 at 12:05
  • 8
    Actually, if "everybody" meant more than the logicians, the first one could safely answer "No", as the barman is not allowed to drink on the job. – Nigralbus Apr 21 '15 at 12:19
  • 18
    @Nigralbus Not being allowed doesn't mean he doesn't want one! The logician would have to be aware of someone who never wants a drink, which seems trivial -- assuming a newborn doesn't want alcohol is a safe bet. – Matthew Read Apr 21 '15 at 12:31
  • 4
    @MatthewRead But there is no reason to think that the drink has to be alcoholic... – Warlord 099 Apr 21 '15 at 13:14
  • 4
    If the first one really wants a drink, he will say "Yes", knowing that if the premise of all three being logicians is true, then their answers will not contradict. In that situation, either the premise is false or all three say "Yes" and the first one gets the drink he wanted.. – Anon May 20 '15 at 22:23
13

We'll name the logicians A, B, and C to simplify.

If A wants a drink, A doesn't yet know whether B and C want a drink. Thus A cannot answer "yes".

If A does not want a drink, A would say "no" because at least one of A, B, and C don't want a drink, making "does everybody want a drink" false.

By saying "I don't know" A indicates their personal desire for a drink, but his lack of knowledge about the other two.

B is essentially in the same situation. B can deduce that A wants a drink, but still doesn't know the preference of C, therefore must answer "no" if B doesn't want a drink, and must answer "I don't know" if B wants a drink.

C, however, can now deduce that A and B both want drinks.

So if the third logician wants a drink, they say:

Yes, everybody wants a drink.

If the third logician doesn't want a drink, they say:

No, not everyone wants a drink.

Bailey M
  • 16,973
  • 2
  • 69
  • 119
Adam Davis
  • 1,587
  • 1
  • 11
  • 16