Solution to Which box has the gold?

How to decide based on the statements on the boxes?

Once upon a time, in a far away kingdom, there lived a king who was a mathematician. He wanted to find a suitable friend with whom to discuss mathematics. He invited the best mathematicians in his kingdom to come and solve some riddles that he posed to them. The first one of these was to determine which of the above two boxes has the gold.

Can you solve it?

Solution: You can argue as follows: The statement on box B can either be true or false. If it is true, then the statement on box A must be false. On the other hand, if the statement on box B is false, then either both statements are false or both are true. But since we have assumed that the statement on box B is false, then both statements must be false. In either case, the statement on box A is false. So you conclude that the gold must be in box A. Alas, when you open box A you do not find the gold. The gold is in fact in box B.

Why is the logic above incorrect? The reason is that the statement on box B is self referential and therefore cannot be used to make any conclusions. It is like the statement: “This statement is false”. Hence the only valid statement in the problem is the statement on box A, which says the gold is in the other box - box B. As indeed it is.