Thursday, June 12, 2008

Pants or No Pants Today

You have stepped across the border into a strange new nation. After studying the inhabitants for a while, you make the following observations.
  1. All bearded Capricorns have jobs.
  2. All Capricorns with jobs can do magic tricks.
  3. All Capricorns who can do magic tricks are double-jointed.
  4. All double-jointed people who wear pants have beards.
  5. All unemployed, clean-shaven people can do magic tricks.
  6. Nobody who has a beard and can do magic tricks wears pants.

Which of the following statements is true based on your observations?
  1. Nobody with a beard wears pants.
  2. No double-jointed people wear pants.
  3. No one who can do magic tricks wears pants.
  4. No Capricorns wear pants.
  5. None of the above.


  1. ...except "none of the above", obviously...

  2. Suppose you have a Capricorn that wears pants and does magic. Then he doesn't have a beard (6) and he is double-jointed (3) -> But that means he has a beard (4). That doesn't work.

    Suppose you have a Capricorn that wears pants and does not do magic. Then he's unemployed (2), which means he doesn't have a beard (1) -> Which means he does magic tricks. That doesn't work.

    Suppose there was a Capricorn who wore pants. Either he doesn't do magic tricks or he does; suppose he does. Then by (6) he doesn't have a beard, then by (3) he is double-jointed - but by (4), he has a beard. This is a contradiction, so he can't do magic tricks. Then by (2) he's unemployed, then by (1) he doesn't have a beard, then by (5) he does magic tricks - another contradiction. Therefore, such a Capricorn doesn't exist.

    And so the answer is no capricorns can wear pants!

    I'm not going to go through the rest of them, but for instance 1) A bearded person who wears pants can exist, as long as he/she doesn't do magic tricks.


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