Answer to

old chestnut: true/false boxes:

The intended answer to this old brainteaser is that the gold is in box B.

This is arrived at as follows:

Assume the sign on A is true. Then the gold is in box A and the sign on box B is true. But the sign on box B says the sign on box A is false. We've arrived at a contradiction, so we take a step back and scrap our assumption; the sign on A must be false.

So now assume the sign on B is true. The first part is already true; we've found that the sign on A is false. The second part says that the gold is in box A. However, we've reached another contradiction. If the sign on B is true and the gold is in box A, then the sign on A is true!

So assume both signs are false. Then the first part of the sign on B is true, so the second part must be false -- the gold is in box B. Then the sign on A is false as well -- doubly false, in fact.

However, there's a general problem with such problems: we assumed that each statement was either true or false. It is possible to write a statement that cannot be called true or false without creating an inconsistency; the classic example is the Liar's Paradox: "This statement is false." Note that this is exactly what the signs fall into is you put the gold into box A. With those parts being true, the signs reduce to A:"B is true" and B:"A is false". This is a general problem with statements that make claims of truth or falsity of other statements in the same group, and should generally be looked out for in such problems.