Solution To: A Penny For Your Thoughts

Here was the original problem:

A penny and a quarter are on a table. You are told:

"If you tell me a true statement, I will give you one of the coins. If you tell me a false statement, you will get none."

What statement can you make that will guarantee that you will receive the quarter? Explain.

Here is the solution:

The statement you need to make is "You won't give me the penny."

Here is why:

1.  Suppose you are not given either coin.  Then the statement you made was true and (by the rules given in the original problem), you should have received a coin since your statement was true.

2.  Suppose you are given the penny.  Then the statement you made was false and you should not have been given either of the coins.

Since both scenarios lead to a logical contradiction, the only choice remaining is that you are given the quarter.


I'm willing to bet (and I don't mean this to sound rude) that half of you are still scratching your heads and the other half of you are kicking yourselves right now.  I have to admit that I'm not sure I could have solved the problem if I had to.  Fortunately, when I encountered it a few years back, I didn't have to!  :)

Sincerely,
The Math Freak