36

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.
ABcDexter
  • 7,262
  • 4
  • 42
  • 84
  • 6
    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 Jan 31 '16 at 23:03
  • @Deusovi thanks for the re-tag. Please add another suitable tag :-) – ABcDexter Feb 01 '16 at 15:15

9 Answers9

68

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.

Hugh Meyers
  • 23,712
  • 1
  • 52
  • 171
f''
  • 33,665
  • 4
  • 120
  • 165
  • 1
    Wait, what? Can you ELI5? The reward doesn't change the statement's truthiness. – user1717828 Jan 31 '16 at 22:30
  • 7
    @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'' Jan 31 '16 at 22:34
  • 5
    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? – Robert Feb 01 '16 at 02:41
  • 4
    @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. – deep thought Feb 01 '16 at 02:51
  • @deepthought Good point. How about this: the offer only specifies outcomes if the statement is true or false. For a statement that is neither, no outcome is guaranteed. – Robert Feb 01 '16 at 02:55
  • 2
    @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. – user1717828 Feb 01 '16 at 03:01
  • 2
    If we're being picky it says "more profitable" not "guarantee yourself the most" or some such thing. Well the second offer doesn't say you'll get 10.05 dollars, it just says "more than 10 dollars", the possibility of getting a bazillion dollars under the second offer wasn't excluded. Therefore, you can't actually answer... But let's give OP a break :-) – deep thought Feb 01 '16 at 03:18
  • 1
    @user1717828 That statement is either true or false. We just don't know which yet. – Jon Kiparsky Feb 01 '16 at 04:05
  • 1
    Whether it has a truth value or not is a matter of philosophy. For the purposes of this answer I've chosen the interpretation that I believe the questioner intended. – f'' Feb 01 '16 at 04:09
  • How is this any better than offer 2? They have the same results – Justin Feb 01 '16 at 04:22
  • @f'' Your answer is probably right, please explain the usage of word 'correct' in the last line "the only way for the offer to be correct..." – ABcDexter Feb 01 '16 at 05:20
  • @deepthought The term "more profitable" itself implies that we're talking in terms of money, at least here :-) – ABcDexter Feb 01 '16 at 07:35
  • @user1717828 That vague statement of yours, which is neither true nor false, doesn't help you get any dollars! – ABcDexter Feb 01 '16 at 07:36
  • 1
    What if I state a fact: "The moon revolves around the earth". For Option1: I may get <10 or >10 with 50% probability while for Option 2: I will certainly get >10. Why isn't Option 2 not the best option? – thepace Feb 01 '16 at 08:50
  • 6
    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. – Darrel Hoffman Feb 01 '16 at 14:32
  • 1
    I'd choose the second option just because it would obviate the possibility of the payor interpreting my statement in a way to avoid giving me the money. – question_asker Feb 01 '16 at 18:37
  • 1
    Hm... "I will either get exactly 10 dollars and become emperor of the world or I will not get exactly 10 dollars." – Milo Brandt Feb 02 '16 at 00:45
  • @DarrelHoffman I'd say you had a chance to make some cash and you picked a huge number knowing the asker couldn't pay ;) – Insane Feb 02 '16 at 12:39
  • @DarrelHoffman You actually have a valid point, but then it wouldn't be nice of anyone to ask for every penny on Earth. – ABcDexter Feb 02 '16 at 17:40
  • 1
    The problem with this is that there's no maximum statement on statement 2. So regardless of what amount you use here, statement 2 could have still returned you more money, just because the amount is COMPLETELY random. – Khale_Kitha Apr 15 '16 at 21:44
  • @Khale_Kitha Statement 2 says the amount is "more than 10 dollars", but it doesn't say anywhere that the amount is random. Besides, using this method you can guarantee whatever amount you want, rather than relying on randomness. – f'' Apr 15 '16 at 21:51
  • 1
    But "more than 10 dollars" is an undefined amount, by definition. Even with your answer, it's an undefined amount, over a certain amount, right? Sure, it gives a higher chance of profitability, but I couldn't say that it "is more profitable." Maybe it's just semantics, but it doesn't seem like there's an actual valid answer to the logic. – Khale_Kitha Apr 15 '16 at 21:52
  • @Khale_Kitha The question isn't defined in a mathematically rigorous way. However, I'm pretty sure people generally consider "as much money as you want" to be more profitable than an unspecified amount greater than 10 dollars. – f'' Apr 15 '16 at 21:56
  • 1
    Perhaps so. But if we're taking this as an opinion question, then I would consider that there are amounts that are more than I could want. Excess over that could be given away if it was a issue. But I still posit that there's not enough info to do something without assuming. I appreciate your reply, though, as I was curious. – Khale_Kitha Apr 15 '16 at 22:01
23

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.

ABcDexter
  • 7,262
  • 4
  • 42
  • 84
GOTO 0
  • 13,549
  • 6
  • 47
  • 92
9

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.”

ABcDexter
  • 7,262
  • 4
  • 42
  • 84
7

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.

Qwerky
  • 231
  • 1
  • 4
6

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!!! :(

Paul Evans
  • 9,431
  • 2
  • 25
  • 49
  • 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. – Joel Rondeau Feb 03 '16 at 20:46
  • @JoelRondeau Yeah, but they're virtual AND non-transferable :( ( – Paul Evans Feb 03 '16 at 21:25
3

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".

Larry Troxler
  • 31
  • 3
3

I'll go with

First Option

and the statement is

I'll get less than 10 dollars.

Simple and Sober.

Laschet Jain
  • 416
  • 2
  • 8
2

The first!

Because I just have a 50% chance to fail, without even reading.

Zaibis
  • 121
  • 4
2

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.

question_asker
  • 9,631
  • 1
  • 37
  • 64
Mark Farrell
  • 21
  • 1
  • 3
    There's no rule that amount must be integer. And that cannot go below zero (=you owe money instead) either. – Trang Oul Feb 02 '16 at 13:53