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Coins


rookie1ja
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  • 3 weeks later...
  • 2 weeks later...
They would just give you one coin, the least expensive one

That would REALLY be a paradox!

Assume you said "I will not get any coins".

If you then get any coin, you have been lying, and therefor deserve no coin. But not getting a coin would mean you told the truth and thus deserve to get a coin. Which brings you back to getting a coin for a lie, and so on, and so forth, ad infinitum.

But I've thought of two possible ideas:

1: Say "You won't give me anything but the gold coin".

-----------------------------------------------------

Now, IF they give you anything but the gold coin, you would have lied, and therefor deserve no coin at all.

And if they give you no coin at all, you had been saying the truth and thus deserved a coin.

The only way they can avoid paradox, is by giving you the gold coin.

2: Say "IF you give me ANY coin, it can ONLY be the gold one".

-------------------------------------------------------------

This is actually the same statement in a somewhat different form. Thus it would result in exactly the same situation as above: they can ONLY give you the gold coin to avoid a conflict of terms.

Happy puzzling,

CollectingCoins.

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"There is a gold coin on the table; silver is another coin on the table; and copper is the last coin on the table."

Three true statements in one sentence. Each true statement gains you one coin, so you'll gain all three coins.

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  • 2 weeks later...

This is an easy one for simple thought. A true statement will get you the gold coin.. a false will get you none. Nothing is said about what the statement has to be about, only that you must be truthful. Lets assume the statement must concern the exercise...here is a garaunteed statement

"There are 3 coins on the table"

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  • 2 weeks later...

well these make alot of sense when you read the answer but if you dont i would NEVER had thought of the answer so i have no idea but i do get it only when i read the answer

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  • 2 weeks later...
I was trying to stump my girlfriend with this and she came up with a situation i believe works... does it??

If you give me a coin, then it will be the gold coin.

Doesn't work. The person in charge of giving out coins can easily declare that sentence false and say that if he would have given you a coin it would have been the copper one.

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  • 2 weeks later...
  • 2 weeks later...

The two correct answers, both given on the first page, are

"You will give me neither the silver coin nor the copper coin."

and

"You will give me either the gold coin or nothing."

Note that these are exactly equivalent statements; saying one is the same thing as saying the other.

Let 'G', 'S', and 'C' represent the respective statements "You will give me the gold coin," "You will give me the silver coin," and "You will give me the copper coin." Then '!G', '!S', and '!C' represent the respective statements "You will not give me the gold coin," "You will not give me the silver coin," and "You will not give me the copper coin."

Using this notation, the first correct answer can be represented as

I. !S AND !C [or, equivalently, !(S OR C)]

while the second correct answer can be represented as

II. G OR (!G AND !S AND !C)

These two statements are exactly equivalent. For convenience, let's define N to mean "You will give me nothing" (i.e. N is !G AND !S AND !C). Then II, the second correct answer, can be written as

III. G OR N

This can be rewritten as

IV. (!S AND !C AND !N) OR (!G AND !S AND !C)

Since !S and !C are both common to both conditions, we can say

V. !S AND !C AND (!N OR !G)

Since N is (!G AND !S AND !C), then !N is (G OR S OR C). So we have

VI. !S AND !C AND (G OR S OR C OR !G)

Since we have already established !S AND !C as a condition, we can get rid of the possibility S OR C. This reduces to

VII. !S AND !C AND (G OR !G)

But (G OR !G) is a trivially true identity, so we can simply omit it (it's always true so it's like multiplying by one). So this becomes

VIII. !S AND !C

which is identical to I, the first correct answer.

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  • 2 weeks later...
Guest Guest_mojobrain_*

You ensure you get the gold coin, by getting all of them.

Just say the following sentences:

-The gold coin is the most valuble of the 3.

-The silver coin is less valuble than the gold.

-The copper coin is the least valuble coin.

All sentences are true, and there is no limit specified on the statements :unsure: you can make or how many coins you can have.

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I agreed with the 2 correct answers and tried to find my own, what about:

"You will give me the gold coin unless this statement is false"

Either it is true and he gives you the gold coin, or it is false and he doesn't give you any coin, which makes it true. The counterargument is that it is false because he could give me any coin, but then the statement is false so that he won't give me a coin which makes the statement true. It is a bit more confusing than the other answers, but I think it should still work.

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  • 2 weeks later...
What about "there is a gold coin and I want it." wouldn't that work?

Being as that is a true statement, but does not force a decision on which coin they will give you, no.

You do want the gold coin, but that dosen't mean they have to give it to you to make your statement true.

So, you'll keep on wanting the gold coin, but you'll have the copper.

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