Two Truths and A Lie

I just tweeted a very interesting two truths and a lie:

  • P=NP
  • All even numbers greater than 2 are sums of primes
  • The logical conjunction of the above two

I'll leave the solution to the reader. It occurred to me while lying in bed, however, that it should be possible to make a list such that any of the three can be the lie. After a little thought and some trial and error, the following fits the bill:

  • One of the following two statements is false
  • One of the other two statements is false
  • One of the previous two statements is false

Simple, but it works. Neat.

This reminds me of the riddle in Inside Man:

Which weighs more: all the trains that pass through Grand Central Station [in NYC] in a year - or the trees cut down to print all U.S. currency in circulation? Here's a hint: It's a trick question.

Once again, I leave the solution as an exercise to the reader... or you can watch the movie.

EDIT: here are a few more humorous Two Truths and A Lie's I came up with:

  • Water is wet
  • Fire is hot
  • The cake

"well, obviously, the cake is a lie."

  • You think this one is true
  • You think the last one is probably the lie
  • You're not sure anymore


  • Either you won't answer, or you'll answer correctly
  • Either you won't answer, or you'll answer incorrectly
  • You will answer

Interestingly, it's possible to correctly answer this last one. You can figure out how.

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