Heisenberg's gold

Let's say Third box is True $\Longrightarrow$ Second box is Lie (Gold is in it) $\Longrightarrow$ First box is True.

It contradicts to the statement "One of the messages is true and the other two are lies."

However, if Third box is Lie $\Longrightarrow$ Second box is True $\Longrightarrow$ First box is Lie (Gold is in it).

Answer: First Box has the Gold!

Only 1 of the 3 statements is true would imply that 2 statements are false.

Statements 1 and 2 can't be both false because it would imply that there is a gold in first and second box.

Statements 2 and 3 can't be both false because it would imply that there is a gold in second box AND there's no gold in second box.

Therefore, statement 2 is true.

Following that statement 2 is true, we can conclude that statement:

1. The gold is here.

2. The gold is not here.

3. The gold is not in the 2nd box.

Therefore, the gold is in the first box.

As the message contains one truth, the third says that the gold is in the second box, if it is to be true, then the first box message will also become true. So Gold cannot be in second and third boxes. Gold is in the first box.

Situation 1: message 1 is true (the gold is not in the first box). Therefore, messages 2 and 3 are false, but they send out conflicting messages-message 2 being false means the gold is in the second box, but message 3 being false means the gold is NOT in the second box. Therefore, situation 1 doesn't work.

Situation 2: message 2 is true (the gold is not in the second box). Therefore, messages 1 and 3 are false, which means the gold is not in the second box and is in the first box.

Now, we already have our answer (the first box) but we'll do the last situation to check. Situation 3: message 3 is true (the gold is in the second box). Therefore, messages 1 and 2 are false, but they also send out conflicting messages-message 1 being false means the gold is in the first box, but message 2 being false means the gold is in the second box. Therefore, situation 3 doesn't work, so our only option is situation 2.

There are two lies and one true statement. If the first box tells the truth, then the Gold must be either in the second or third box. If the second box lies, then the Gold is in the second box, then the third box tells the true. And there are two true statements, which is unacceptable. If the Gold is in the third box and the third box lies, but then the second box tells truth. Again, two truth statements which is unacceptable. Therefore, the first box must have lied and the Gold is in it, the second box tells the truth and the third lies.

Suppose first box message is false. "Gold is not here" then implies a double negation, meaning gold is in the first box.

Second box says "gold is not here". This must be true. Because gold is in first box now.

Third box must have a false message. It says "gold is in the second box". This is false and hence is consistent.

Thus gold is in the first box.