Defeating The Logical Billionaire
Take the first offer
You meet a billionaire known for his logic. He makes two offers:
You make any statement you want. If the statement is true, you get exactly 10 dollars. If the statement is false, you get either less than or greater than 10 dollars, but not exactly 10 dollars.
You make any statement you want. Whether your statement is true or false, you get more than 10 dollars.
Which offer should you take?
Take the first offer and make the statement “you will neither give me exactly ten dollars nor exactly one billion dollars”
The statement “you will neither give me exactly ten dollars nor exactly one billion dollars” is true or false.
If the statement is true, the billionaire will not pay exactly $10. But the billionaire will pay exactly $10 if the statement is true, a contradiction.
On the other hand, if the statement is false, then either the billionaire will pay exactly $10 or the billionaire will pay exactly $1 billion. But we know the billionaire will not pay exactly $10 if the statement is false, so he must pay exactly $1 billion.