# Which offer is better?

You are to make a statement.
Of these two offers you have to choose one; which one is more profitable to you, and why?

1. If the statement is true, you get exactly 10 dollars. If the statement is false, you get either less than or more than 10 dollars but not exactly 10.
2. Regardless of whether the statement is true or false, you get more than 10 dollars.
• This isn't a logic puzzle since it doesn't involve formal logical deduction. I've added the tag "liars", but there's probably a better one.
– Deusovi
Commented Jan 31, 2016 at 23:03
• @Deusovi thanks for the re-tag. Please add another suitable tag :-) Commented Feb 1, 2016 at 15:15

## 9 Answers

Take the

first

offer, and then state:

"The reward for making this statement is less than [insert large value here] dollars, but not exactly 10".

If you get 10 dollars, that makes your statement false, so you shouldn't have gotten 10 dollars.
If you get less than [large value] dollars but not 10, that makes your statement true, so you should have gotten 10 dollars.
So the only way for the offer to be fulfilled correctly is if you get at least [large value] dollars.

• @user1717828 When the statement is about the reward, whether it's true or not depends on the amount of the reward. This statement makes it so that the offer can only be satisfied by making the reward a very large amount.
– f''
Commented Jan 31, 2016 at 22:34
• If I state as fact that something will occur that I have no knowledge or control over, isn't that a falsehood at the moment it is uttered whether the prediction ultimately proves correct or not? Commented Feb 1, 2016 at 2:41
• @robert: You know, often logic puzzles are poorly worded for this very reason! But in this case, the offer was stated to be dependent on the statement being true or false, not you being honest or not. Commented Feb 1, 2016 at 2:51
• @Robert, I think you just worded perfectly what I've been thinking about four the past hour: The 73rd president of the United States will be Theresa Jones. That statement, as of right now, is neither true nor false. The logic puzzle is flawed. Commented Feb 1, 2016 at 3:01
• What if you pick a number so large that it would be impossible to satisfy? E.g.: "I will get less than one septillion dollars but not exactly 10." That's several orders of magnitude more money than exists in the world, and thus the offer cannot be fulfilled, which makes it true, so I'd get exactly 10, which makes it false, etc. Commented Feb 1, 2016 at 14:32

Sounds like you just found a true Oracle, that's amazing. You can make good money with online bets.

Choose the first offer and pick a statement like:

The team X will win against the team Y in the match Z.

• If you get 10 dollars, team X will win.
• If you get a different amount of money, team X will tie or lose.

Bet any amount of dollars you have on the outcome of the match, and collect your prize.

• Aah, what an interesting answer, and the use of "Oracle". Morpheus will be happy ^_^ Commented Feb 1, 2016 at 13:00
• The question doesn't say anything about how long it will take the payer to pay you. The payer could simply wait until the game finishes to pay you. Commented Feb 1, 2016 at 19:27
• @user2023861 Agreed, that's a loophole in this! (paying the money). Commented Feb 3, 2016 at 5:41

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 dollars nor 1000 dollars."

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 dollars. But since you cannot receive 10 dollars if the statement is false, you must receive 1000 dollars. note: Of course you can use any amount in place of “$1000.”

• Why is this community wiki?
– Tim
Commented Feb 2, 2016 at 17:27
• @Tim I felt it would be better this way. Isn't it right to do so? Commented Feb 2, 2016 at 17:32

The question confuses causality and effect. I would choose option 1 and my statement would be;

You are not going to give me 10 dollars

This causes a paradox. If I get 10 dollars then it infers my statement is true, but it is false. If I don't get 10 dollars it infers my statement is false, but it is true.

• that's really a great observation. Commented Feb 1, 2016 at 17:41
• You can create a paradox, but why should that result in you getting any money? Why is that more profitable? Commented Feb 2, 2016 at 16:10

The most profitable is (without looking at any answers):

The first option

Because:

You make a statement like:

I won't get either 10 or 1,000,000,000,000 dollars for this statement.

Now you can't get 10 dollars because that would make the statement false
and you only ever get exactly 10 bucks for a true statement.
So you must he paid a trillion dollars as that's the only other way that statement can be false.
If you're paid anything else the statement is true but you're not
getting the mandatory exact 10 dollars for it.

Edit:
Ouch! Should have stipulated the currency!
Got a trillion Monopoly dollars - not even worth a single cent!!! :(

• Assuming that it comes in a proper assortment of denominations, it sells for about \$7 per \$15140 pack (sold as replacement money), so conservatively still worth about $400,000,000. Going to be a hassle to sell it all, though. Commented Feb 3, 2016 at 20:46 • @JoelRondeau Yeah, but they're virtual AND non-transferable :( ( Commented Feb 3, 2016 at 21:25 Option 2. You are guaranteed more than 10 dollars no matter what you say. Also note that puzzle doesn't state that the statement has to be related to your winnings. It could be "the sun is hot". • Not necessarily; look at the accepted answer. – Deusovi Commented Feb 2, 2016 at 15:44 I'll go with First Option and the statement is I'll get less than 10 dollars. Simple and Sober. The first! Because I just have a 50% chance to fail, without even reading. • But the second statement gives you a 0% chance to fail. Commented Feb 3, 2016 at 18:54 I'd take option 2, because there's only 9 amounts below \$10 whereas there's infinite above, so the odds of getting more than \\$10 is higher.

• There's no rule that amount must be integer. And that cannot go below zero (=you owe money instead) either. Commented Feb 2, 2016 at 13:53