# Question:

Which offer is better?

`1) You are to make a statement. If the statement is true, you get exactly \$10. If the statement is false, you get either less than or more than \$10 but not exactly \$10.2) You are to make a statement. Regardless of whether the statement is true or false, you get more than \$10.`

# Solution: Offer 1

`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.”`

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