This is a solution to problem 19 on the hard interview questions node. If you have not read the question, the following will make no sense to you:

You should take offer #1, because you can guarantee yourself an arbitrarily large amount of money, simply by using the following as your statement:

"I will receive neither $10 nor $1000."

If we assume the statement is true, this leads to a contradiction because you would receive $10, by the rules.

If we assume the statement is false, then to satisfy the falsity of the statement, you must receive either $10 or $1000. But since you cannot receive $10 if the statement is false, you must receive $1000.

Of course you can use any amount in place of "$1000."