On Friday I posted this puzzle…..

A man places three coins in front of you – a bronze coin, a silver coin and a gold coin.

The man says “If you tell me a true statement, you will be given one of the coins.  But if your statement proves to be false, you will be given nothing”.

What should you say to guarantee being given the gold coin?

If you haven’t tried to solve it, have a go now.  For everyone else the answer is after the break.

You should say ‘You will not give me the bronze or the silver coin’.  If this is true, you get the gold coin.  It cannot be a lie, because if it were a lie, it would have to come true!

Did you solve it?  Any other answers?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

55 comments

    1. I think that this fails because the guy can give you a copper coin in response to this because he doesn’t want to give you the gold one. ( nothing says he can’t give you a coin in order not to give you the gold one). Or he could *give* you a pat on the back, or a smile 🙂

  1. My alternative (equivalent I think ?) was “you will give me either the gold coin or you will give me nothing.”

    1. ‘either … or’ is clearer than just ‘or’. It makes it clearer that it is an exclusive or. Pedantic Semantic. It is also fairly impossible to give someone something or nothing at the same time so that makes it clear I think.

  2. I rejected that idea because I thought the man could make the statement wrong by giving him the copper ad silver coins.

    1. Not sure he could… he says “If you tell me a true statement, you will be given ONE of the coins”

    2. I am with bill, he did not say “will give you exactly one coin”… and if he gives you two coins, it is the same as giving one coin twice…

      I thought of the right solution was “i will not accept a silver and/or copper coin from you”…

  3. Surely, that statement does not ‘guarantee’ getting the gold coin? It’ll more than likely get you nothing, as it will be false. The set-up should ask ‘What true statement should you say to guarantee being given the gold coin?’.

  4. Took me a little under a minute but my nephew barely even had to think about it! Some guys at work suggested “if you give me a coin, it will be gold” but I felt he could still have been given nothing as the statement would be ambiguous in that case.

  5. What about “you will give me no coins”, then wait until his brain seizes up and he implodes in a puff of logical smoke, then you can take any of the coins you like!

  6. Many possible answers, since the question doesn’t specify that the statement needs to be regarding the coins 🙂 Could have just as easily answered with something like “I am a man” or “I am speaking to you”.

    1. Initially thought so also, but that type of statement doesn’t guarantee you the *gold* coin. The man could give either the silver or bronze coin.

  7. I did think of this (or in fact one of the equivalent ststements posters have mentioned), but I was also aware that with deeper analysis it is not an adequate solition. The man with the coins can keep his coins and reply as follows:

    “The truth is that I had decided to give you the bronze coin if you said a true statement. So in fact your statement is false and I will give you nothing. The fact that your statement correctly describes the fact that I have given you nothing is not sufficient to make it true, because it is false in other regards.”

    In general these logical problems are not part of the real world, because in the real world we do not dichotomise statements into true and false, it is much more messy. We also have (much more often) “sometimes true”, “true in part”, “true, subject to certain caveats”, “incomplete”, “statements based upon assumptions I don’t necessarily agree with”, “ambiguous statements”, “statements whose truth cannot be determined”, “inconsistent statements”, etc.

    1. Yeah, these puzzles aren’t really “real world” considerations. They are puzzles. And it’s okay to just say you couldn’t figure out. Or NOT say you couldn’t figure it out.

    2. “The fact that your statement correctly describes the fact that I have given you nothing is not sufficient to make it true, because it is false in other regards.”

      In what regards is it false?

    1. To elaborate, you might aswell say “bachelors aren’t married and you will give me the gold coin”. The first statement makes sure it can’t be false, and the second statement secures the gold coin.

    2. “you might aswell say “bachelors aren’t married and you will give me the gold coin”. The first statement makes sure it can’t be false”

      That part of what you say is true doesn’t guarantee that your whole statement is true. Consider:

      ‘bachelors aren’t married and Paris is the capital of Germany’.

      That sentence is clearly false, even though part of it is true.

  8. Yep, got it. But I knew you this one: you are sentenced to die. Before you’re executed, you may state one last wish. If your wish is granted, you are beheaded, if it is denied, you are hanged. What do you have to wish for, so you won’t die?

    1. If the execution’s in public and you’re allowed a visit beforehand, opt for hanging (“I wish for my sentence to be annulled” would probably do!) and arrange for a marksman friend to shoot the rope at the vital moment 😀

      Probably not the answer you’re looking for though…

    2. You say “I wish to be hanged.” It forces a paradox, because if they grant it, then they have to behead you, but then they aren’t really granting it.

  9. I would like to ask your opinion about “Photoreading”. Is it an illusion? Does it really work?
    Thank you in advance,
    Pat

    1. While the statement “The sun rises in the East” is a valid statement, it only guarantees you one of the coins – not necessarily the gold one.

  10. Is there any statement that could be used to procure the gold coin that didn’t rely on future events? The awkward thing about the given answer is that it requires the asker to work out the consequences of each decision, and only works if the statement is taken as meaning what will happen in reality (the intended interpretation), rather than the asker’s intentions (which is what Ivan was driving at).

  11. It is unrelated to gold coins, but I just found out, and thought it might be of interest to other visitors to Richard’s blog, that ‘Eleven plus two’ is an anagram of ‘Twelve plus one’. Kinda cool.

  12. “You will not give me the bronze or the silver coin.”

    “Yes I will.” (Gives bronze coin, wins.)

    1. But if he gives you the bronze coin, he proves your statement wrong in doing so. This violates the rules, since they stipulate that an incorrect statement means you get none of the coins.

  13. I don’t get this answer. If you just give him a bronze or silver coin, then you are just proving that his statement is false. Right? so He only gets a bronze or silver coin, doesn’t he???

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