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Why is the answer what it is? I made my selection and I was wrong. Why is the correct answer, the right answer?

If Cell 3 holds worthless brass, Cell 2 holds the gold key.
If Cell 1 holds the gold key, Cell 3 holds worthless brass.
If Cell 2 holds worthless brass, Cell 1 holds the gold key.

Knowing this brave fool, and knowing that all that is said cannot be true, which cell contains the gold key?

I think it's basically a matter of eliminating the impossible answers to get the right answer.

What if Cell 1 holds the gold key?
Then, by statement 2, Cell 3 must hold worthless brass.
Furthermore, Cell 2 would also hold worthless brass, so statement 3 is okay.
On the other hand, statement 1 could not be true, since it would follow that Cell 2 must hold the gold key, which conflicts with the supposition that Cell 1 holds the gold key.

What if Cell 2 holds the gold key?
Then Cell 3 would hold worthless brass, so statement 1 is okay.
Furthermore, Cell 1 would also hold worthless brass, so statement 2 could be ignored, since Cell 1 would not hold the gold key.
And statement 3 could also be ignored, since Cell 2 would not hold worthless brass.

What if Cell 3 holds the gold key?
Then Cell 3 would not hold worthless brass, so statement 1 could be ignored.
Furthermore, Cell 1 would not hold the gold key, so statement 2 could be ignored.
On the other hand, statement 3 could not be true, since it would follow that Cell 1 must hold the gold key, which conflicts with the supposition that Cell 3 holds the gold key.

Thus, the only choice which doesn't create a conflict is that Cell 2 holds the gold key.

Cool!

Okay that makes sense to me. I got hung up on the later sentence that states; "...and knowing that all that is said cannot be true...". I was starting with an assumption that at least one of them must be "FALSE".

(Pause)
I also must have made some other assumptions, because now that you've explained it, every time I try to write out what I was originally thinking, I keep finding faulty logic. I thought I had figured that one option would make only one statement FALSE, but now it doesn't seem to work out that way.

Thanks.