Beer Jokes and Hat Puzzles

This is one of my favorite jokes:

Three logicians walk into a bar. The waitress asks, “Do you all want beer?”
The first logician answers, “I do not know.”
The second logician answers, “I do not know.”
The third logician answers, “Yes.”

This joke reminds me of hat puzzles. In the joke each logician knows whether or not s/he wants a beer, but doesn’t know what the others want to drink. In hat puzzles logicians know the colors of the hats on others’ heads, but not the color of their own hats.

This is a hat puzzle which has the same answers as in the beer joke. Three logicians walk into a bar. They know that the hats were placed on their heads from the set of hats below. The total number of available red hats was three, and the total number of available blue hats was two.

Red Hat Red Hat Red Hat Red Hat Red Hat

Three logicians walk into a bar. The waitress asks, “Do you know the color of your own hat?'”
The first logician answers, “I do not know.”
The second logician answers, “I do not know.”
The third logician answers, “Yes.”

The puzzle is, what is the color of the third logician’s hat?

This process of converting jokes to puzzles reminds me of the Langland’s Program, which tries to unite different parts of mathematics. I would like to unite jokes and puzzles. So here I announce my own program:

Tanya’s Program: Find a way to convert jokes into puzzles and puzzles into jokes.

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10 Comments

  1. adbge:

    Hi, Tanya. I love your blog. There’s something delightfully straightforward about it. (Or maybe the word I’m looking for is understated? Dunno.)

    Anyways, regarding puzzles and jokes, one characteristic they share is that they both often set up some scenario and put it together in an unexpected way.

    Example:

    A girl phoned me the other day and said, “Come on over, there’s nobody home.” I went over. Nobody was home.

  2. Tanya Khovanova:

    adbge. LOL

  3. George R.:

    Variation:
    5 logicians walk into a bar.
    The waitress asks, “Do you all want beer?
    1st: I don’t know
    2nd: I don’t know
    3rd: I don’t know
    4th: I don’t know
    5th: No, I do not!
    Whom should the waitress serve a beer? :-)

  4. George R.:

    About the hat puzzle: The third logician can figure out his color (red) even without having to actually LOOK at the colors of the other hats. :-)

  5. George R.:

    Pardon for not giving a complete answer at my previous post.
    If 1st had seen two blue hats, he would have
    guessed that his own hat was red. So he saw
    at least one red hat.
    If the 2nd had seen the third wearing a blue hat,
    he would have guessed that his own hat was red
    -since at least one of them had to have the red
    one that the 1st had seen-.

    So the 3rd already knows that he isn’t wearing
    a blue hat. Thus ,he has a red hat.

  6. George R.:

    Joke Puzzles
    1.If you ask someone “What time is it?” and she answers¨
    $π/arccsc(2φ)$ what is her name? And is it a.m or p.m?
    2.the derivative of a hen is an egg: (d/dx)(hen)=egg
    But the Integral of an egg is not a chicken. Why?
    3. What is the equation of the ΚΑΦΕΝΕΙΟΝ ?
    (this one is half mathematical,half linguistic) :-)

  7. peter:

    Humor and the sense (interpretation) of humor as mathematical objects… More generally, emotions as mathematical objects – love, hatred, shame etc. as math objects (models). It is going to be a hard project. Good luck!

  8. Alexander B.:

    I see arXiv didn’t censor your paper this time… what changed?

  9. Tanya Khovanova:

    Alexander B,

    I do have more citations. Plus, I sent them my blog post.:-)

  10. Roberto C.:

    Variation:

    Three logicians walk into a bar. The waitress asks, “Does anyone want beer?”
    The first logician answers, “I do not know.”
    The second logician answers, “I do not know.”
    The third logician answers, “No.”