# Justin Li

## Two Truths and A Lie

2010-06-29

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

What?