This is my solution, I think it is simpler than the one proposed by Jason Dyer (which rises the question asked by Siva Budaraju):

The chest with the treasure is the one that opens if I say a true statement.

If this statement is true, the chest with the treasure opens, because it is the one that opens if the statement is true. If this statement is false, the chest with the treasure opens, because it is the one that opens if the statement is false. So, in any case, the chest with the treasure will open.

Before giving the answer, note that a statement in the form

If A, then B.

is false if and only if the hypothesis (A) is true and the conclusion (B) is false. Given this fact, only one statement is needed:

"If the truth-opening chest opens, then the treasure is inside it."

First, note that truth-opening chest cannot stay shut given the above statement.

If it did, then the hypothesis of the if-then statement (the truth-opening chest opens) would be false. However, if the hypothesis of an if-then statement is false, then the entire if-then statement is TRUE. So this is a contradiction! The truth-opening chest has to open. In addition, when this happens, the if-then statement forces the inevitable conclusion that the chest must contain the treasure. (If it contained the gas, the if-then statement would be false, yet the truth-opening chest opened meaning the if-then statement is true; this is a contradiction.)

Second, the false-opening chest cannot open given the above statement.

Suppose the false-opening chest did open. Then it would mean the if-then statement is false. The only way for it to be false is if the hypothesis is true and the conclusion is false. The hypothesis being true means the truth-opening chest opened, which also implies the original if-then statement is true. So the if-then statement is both true and false, which is a contradiction. Hence, the false-opening chest must stay shut.

How about if you say "The deadly gas is in the chest that opens if I lie." ?

I would make the statement, “The truthful chest has the treasure”.

All you need to say, I believe, is "The treasure is in the truth chest." If its true then the truth chest opens and you win. If the statement is false, the false box opens with the treasure inside.

A simple statement: "Truth will be rewarded."

This is a particular instance of the knights and knaves puzzle. We could reformulate it in predicate form as follows. Let $T_1(x)$ and $T_2(x)$ denote the boxes that evaluate our statement as truthful or not. Then the rules for each box can be written as: $\\ T_1(x)\Leftrightarrow false \\T_2(x)\Leftrightarrow\neg false$

The goal is to find a statement that leads to the same outcome for both rules. So our solution is to force the one box to evaluate the outcome of the other box like so: $\\ T_1(T_2(x))\Leftrightarrow\neg false \\ T_2(T_1(x))\Leftrightarrow\neg false$

Notice how, no matter which box evaluates the statement, the outcome is the same. This approach generalises the form a statement might take to solve the puzzle instead of providing one particular example.

I think Michele's solution is better, but would you accept this solution? The sentence is the whole text between the quotes:

"The sentence <The chest that contains the treasure opens for true statements.> is not a paradox in this case."

link text

Quite simply say that "the gas is in the box that opens when you're statement is false." If the above is true the box which opens you make a true statement will open this box must by definition contain the treasure are the gas is in the other box. If the above is false the gas is in the box that opens when a statement is true and the box that opens when the statement is false opens which must contain the treasure.

"If I say, 'The other chest has the treasure,' then the other chest will remain closed."

Case 1 : The chest that opens when you give a true statement has the treasure, and the chest that opens when you give a false statement has the poisonous gas.

Saying "The other chest has the treasure" will keep the truth chest closed because it is not true that the other chest has the treasure, and it will also keep the false chest closed because it is true that the other chest has the treasure. Saying "If I say, 'The other chest has the treasure,' then the other chest will remain closed" will then be true for both chests, so that the truth chest with the treasure opens but the false chest with the poisonous gas stays closed.

Case 2 : The chest that opens when you give a true statement has the poisonous, and the chest that opens when you give a false statement has the treasure.

Saying "The other chest has the treasure" will open the truth chest because it is true that the other chest has the treasure, and it will also open the false chest because it is not true that the other chest has the treasure. Saying "If I say, 'The other chest has the treasure,' then the other chest will remain closed" will then be false for both chests, so that the truth chest with the poisonous gas remains closed but the false chest with the treasure opens.

Here is Leon’s solution:

The false chest has the poisonous gas in it.

So if it is true, then we open the true chest. If it is false, we open the false chest. Both outcome would bring us the treasure.

"The poisonous gas is not in the chest that opens upon uttering a true statement." If this is true then the "true" chest will open to reveal the treasure. If this is false, then the poisonous gas is indeed in the "true" chest and the "false" chest will open to reveal the treasure.

You have to say a false statement that won't kill you. Saying something like, the chest which opens with a false statement has gas in it can't open the chest with the false statement and gas because it would mean that it was true. So it has to open the chest with the true statement.

Why not try to accuse that one of the chest contained the treasure? Something like " The treasure is in the chest that will open if i tell a true statement". If im correct, then the truth chess will open. If im wrong, the false chest will open, containing the treasure.

"the treasure is in the truthful chest" should work. True if the treasure is in the truthful chest, therefore that opens. False if poison is the truthful, opening the treasure again

My proposed statement:

If I make a false statement, the chest with the deadly gas will open. <br>

If it's true, then the chest with the treasure will open. If it's false, then that means that the chest holding the deadly gas only opens if I say a true statement, so the chest with the treasure should also open.

well if you say "the true box contains the treasure" if it has the treasure you would get it because the statement would be true and if it doesn't the statement would be false so you would open the false box witch would have to contain the treasure.

Another statement can be, If this statement is false then the chest with the poisonous gas opens

Say the box on the left has the treasure if it is true the left box opens with treasure. if it is false the box on the right opens with the treasure

Just say: "The treasure is in the truth-telling chest" . If the treasure is in the truth-telling chest, it will open. If the treasure is in the false-telling chest, this false-telling chest will open then.

One of the chests contains the deadly gas

One possible answer is, " I will live if the true chest opens. " If the treasure is in the true chest, then you will live when it opens. If the gas is in the true chest, then the false chest will open with the treasure inside it.

My solution was slightly different that the common if then argument.

Mine was "This statement is true and the box with the treasure will open" My reasoning is that the entire statement is true only if both substatments are true. thus if the statement is true then the treasure box opens and I get it. If the statement is false, it would be because the treasure is in the lying box(hence You cannot both tell the truth and get the treasure) but if the statement is false, the lying box opens and I get the treasure

"One of these chests contains treasure" is a true statement.

Say "2+2=4"

Or "2 is even no."

Or "1=1"

If I say The chest that'll open if I say a true statement contains treasure then the chest with treasure will open

Say 'the chest with the treasure opens if what I said is true

"The left box contains the treasure". If it does it opens, if not, the other box, which must contain the treasure, opens.

We first convert both chest to "True chest".

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Consider "If i say A, u will open."

When A is true, both chest will open.

When A is false, both chest will close.

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Eg: plug in A=(earth is round) which is true.

"If i say (earth is round), u will open."

It is easy to understand that True chest will open. But saying (earth is round), False chest will close, so say the statement "If i say A, u will open" is false, False chest will open.

Conclusion: both chest will open.

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When A is false, similar argument deduce that both chest will close.

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Now Plug in A=(u contain treasure)

"If i say (u contain treasure) then u will open."

Only for treasure chest, A is true to it. Only it will open.

I got the same answer as Michele Chiminazzo. “The box with the treasure opens for true statements.” The key is to refer to the box with the treasure since truth or falsity depends only on the opening rule. Stating the opening rule as true makes the truth or falsity of the statement correspond to the opening rule. In addition, the other box will not open since it must have the opposite opening rule.

Notice that identities like 2+2=4 or statements like "One chest has the treasure" are true (the problem itself says that in one chest there's the treasure, but you don't know in wich). True statements will open the truth-opening chest; but the treasure can be in the other one, so you'll die.

Conditional statements ( if ... then ... ) or statements which refers to future events (like "it will open ...") may be correct, but so logically tricky.

There's a much simpler (and elegant) way to win: "the treasure is in the truth-opening chest" (equivalent to Sean McCloskey answer).
If true, then the treasure is actually in the truth-opening chest and, since I said a true statement, it will open. If false, then the treasure is in the false-opening chest and, since I said a false statement, it will open.

The statement I propose is the following. The box that opens when one says the Truth contains the treasure. 1) If this is true, then the "truth" box will open and the treasure will be inside. 2) If it is false, then it means the treasure is in the "false" box. In that case the "false" box will open which will contain the treasure.

I have another question of the same sort, "There are 2 ways one to heaven and another to hell" ( You want to go to heaven ), and there's a man on each of the gates, ( one always tells the truth, another man always lies ), they both know each other that( if I'm the truth teller, the other is a lier and the lier knows that the other guy is truth teller), You can make only one statement, ( either by asking one of them or by involving both of them to answer your question), Can you guarantee that you go to heaven?

Bonus : If no, then why?!... If yes then how?!

Post your answer in the comments!

My solution: the earth is round

Dab on dem flat earthers

"One of the chests contains the treasure. "

Just say "2 + 2 is 4"

"One of the two boxes contains a treasure"

Where can I find the exact solution for this problem????

“The gas is contained in the chest that will open to a false statement” If the gas is in the false chest, then the statement is true this the other chest (with the treasure) will open. If the gas is in the true chest, then the statement is false and the false chest (with the treasure) will open.

what about: " one of the two chests contains the treasure "?