“Who ya gonna vote for? None of the above!”

Here’s one of my favourite little logic problems, courtesy of Faron. It’s about time I got this off my noticeboard and onto my interwebs.

Which of the following is true?

  1. All of the below.
  2. None of the below.
  3. All of the above.
  4. One of the above.
  5. None of the above.
  6. None of the above.

Solutions involving exhaustive analysis of the 2^6 possibilities are forbidden, although elegant code doing so will at least be admired for its cleverness, especially if it’s in Haskell. ;-)

3 Responses to ““Who ya gonna vote for? None of the above!””

  1. February 26th, 2008 | 6:34 pm

    Looks like a SAT problem to me.

    Unfortunately my attempt to convert it to CNF and put it through my (slow, probably very buggy) SAT solver failed miserably…

  2. February 27th, 2008 | 12:55 am

    SAT!? But there are only 64 possibilities to check – I hope you were joking! :-) Anyway, it’s much more fun to do it by hand: a nice little exercise in propositional logic; it’s quite easy, although you need to be careful to avoid handwaving or dodgy proofs by contradiction at the end.

  3. February 27th, 2008 | 3:03 pm

    Well yes, I did solve it by hand first :)

    … using contradictions. Is that disallowed now?