Two Prizes [Puzzle]

Suppose I offer you two prizes: prize A and prize B. You are to make a statement – any statement you like.

If the statement is clearly true, I will give you a prize. You will win either A or B, I am not saying which one.

And if your statement is false, you won’t get any prize.

It’s clear from this that you want to make a statement that is clearly true, because otherwise you won’t win any prize. You can say something like “One plus one equals two.” This is clearly true, and you will win either A or B.

However, let’s say you really would like to win prize A. The question is: what statement can you make that will ensure that you will win prize A?

[From Forever Undecided: A Puzzle Guide to Gödel]


5 responses to “Two Prizes [Puzzle]

  1. I’d say “I don’t want to win prize A”

  2. Sorry. I meant “I don’t want to win prize B”

    • Reuben,

      But how do I know if that’s a correct statement or not? I don’t know what your preference is. Not knowing what your preference is, I will have to make an assumption – either your statement is true or false. In both cases, the outcomes don’t guarantee that you will win prize A. If I assume that your statement is true, then I will give you either A or B. Let’s say I give you B. I assumed that you don’t want to win B, but hey life’s not fair sometimes. 🙂 On the other hand, if I assume that the statement is false, they you don’t win anything.

      Even if we assume that I am aware of your liking for prize A, it doesn’t work. If I am aware of your preference, then the statement you made is clearly false. Hence, you don’t win anything.

      • OK. So what do I have to do to win that prize? Nothing illegal or immoral I hope 😀

        • No, nothing immoral or illogical. 🙂

          Here’s the statement you should make: “You will not give me prize B.”

          Suppose I assume that this statement is false, and don’t give you anything. But then what you said becomes true. (As I did not give you prize B.) Hence, this statement can not be false; it must be true.

          Since it is a true statement, I will have to either give you A or B. Now I can’t give you B, because that would make the statement false. And we already established that the statement can’t be false.

          Hence, I must give you A.

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