Three boxes are on a table. One box contains gold and the other two are empty. Each box has a printed message, and exactly one message is true while the other two are false. Box 1 says The gold is not here. Box 2 says The gold is not here. Box 3 says The gold is in the second box. Which box contains the gold?

Introduction / Context:
This is a classic logical puzzle about three boxes, one of which contains gold while the other two are empty. Each box carries a message, but only one of these messages is true and the other two are false. The challenge is to determine which box contains the gold by analyzing the truth values of the statements. Such puzzles train your skills in logical deduction, consistency checking, and reasoning about exactly one true statement conditions, which are common in analytical reasoning tests.

Given Data / Assumptions:

- There are three boxes: Box 1, Box 2, and Box 3. - Exactly one box contains gold; the other two are empty. - Box 1 message: The gold is not here. - Box 2 message: The gold is not here. - Box 3 message: The gold is in the second box. - Exactly one of these three statements is true; the other two are false.

Concept / Approach:
We treat each possible location of the gold as a case and then determine which messages would be true or false in that case. Because exactly one statement is true, any case that yields zero or more than one true statement must be rejected. By checking each possible box systematically, we can find the only arrangement that satisfies the condition of having exactly one true message. This is a straightforward application of case analysis in logic puzzles.

Step-by-Step Solution:
Step 1: Assume first that the gold is in Box 1. Step 2: If the gold is in Box 1, then the statement on Box 1, The gold is not here, is false. Step 3: Under the same assumption, the statement on Box 2, The gold is not here, is true, because the gold is indeed not in Box 2. Step 4: The statement on Box 3, The gold is in the second box, is false because the gold is in Box 1, not Box 2. Step 5: In this case, exactly one statement, the one on Box 2, is true, and the other two are false, satisfying the condition. Step 6: For completeness, consider the case where the gold is in Box 2. Then Box 1, The gold is not here, is true, and Box 2, The gold is not here, is false. Box 3, The gold is in the second box, is true. That gives two true statements, which violates the exactly one true statement condition. Step 7: Finally, consider the case where the gold is in Box 3. Then Box 1 and Box 2 both say the gold is not here, which is true for each, resulting in at least two true statements. Box 3 says the gold is in the second box, which is false. Again, more than one statement is true, so this case is invalid. Step 8: Therefore, the only scenario where exactly one statement is true is the case where the gold is in Box 1.

Verification / Alternative check:
We can also reason more quickly by observing that statements on Box 2 and Box 3 are direct opposites: Box 2 says the gold is not in Box 2, and Box 3 says the gold is in the second box. With exactly one true statement overall, exactly one of these two must be true and the other false. If Box 3 were true, the gold would be in Box 2, which would make Box 2 false, but then Box 1, The gold is not here, would also be true, giving two true statements. Thus Box 3 cannot be true. Therefore Box 2 must be the one with the true statement, implying the gold is not in Box 2. With gold not in Box 2 and Box 3 proven false, the gold must be in Box 1.

Why Other Options Are Wrong:
Box 2 cannot contain the gold because that would make both Box 1 and Box 3 correct, violating the exactly one true statement rule. Box 3 cannot contain the gold because both Box 1 and Box 2 would then have true statements. The option None of the boxes contradicts the given condition that one box does contain gold, and Cannot be determined ignores the clear logical deduction that isolates Box 1 as the only consistent location.

Common Pitfalls:
People sometimes miscount how many statements are true in each scenario or assume that exactly one statement in total must be true without checking all cases thoroughly. Another pitfall is overlooking the direct contradiction between Box 2 and Box 3 or forgetting that exactly one true statement applies to the set of all three statements. Carefully listing the truth values in each case and counting true statements helps avoid these errors.

Final Answer:
The gold must be in Box 1 to satisfy the condition that exactly one message is true.