Puzzle 2
by Ari Nieh

Among the words are the names of several integer sequences.  
If you number the words and look at what each sequence is saying, 
you get the following:

[capitalization and punctuation added to improve readability]

    Fibonacci numbers:  Warning!  You really shouldn't distrust
    primes.  Squares aren't genuine.

    Primes:  You really shouldn't doubt the primes.  Take last word of
    relevant sequences; first letter if honest, last otherwise.

    Squares:  Warning!  Both Fibonacci and cubes speak true.

    Cubes:  Warning!  Distrust Catalan!

    Catalan numbers:  Warning!  You shouldn't believe Bell.

    Bell numbers:  Warning!  You shouldn't believe anyone.

This is a truthtellers-and-liars logic puzzle.  After you've solved it, 
following the instructions of the prime numbers (who were telling the truth) 
yields the letters GOENBE in no particular order.

The first letters of the unused words spell out:

GET LOST SCRAM LEAVE VANISH EXIT

and so the correct answer is BEGONE.