Question

There are 3 closed cartons in a room. One of the cartons contains cash. There is a printed message that is displayed outside each carton. Only one message is True and the other two messages are False. The first carton has the message: Cash is not in the Carton. The second carton has the message: No cash in the Carton. The third carton has the message: Cash is in the second carton. Which carton has the cash?

• A. First
• B. Second
• C. Third
• D. Cannot be determined

Answer 1

The Correct Option is A

Let's analyze the statements on each carton:
1. First Carton: "Cash is not in this carton."
2. Second Carton: "No cash in this carton."
3. Third Carton: "Cash is in the second carton."
We know that only one of these statements is true, and the other two are false. Let's examine each possibility.
Case 1: First Carton has Cash
- First Carton Statement: "Cash is not in this carton." (False)
- Second Carton Statement: "No cash in this carton." (True)
- Third Carton Statement: "Cash is in the second carton." (False)
This fits the requirement of one true and two false statements. Therefore, if the first carton has cash, only the second statement is true.
Case 2: Second Carton has Cash
- First Carton Statement: "Cash is not in this carton." (True)
- Second Carton Statement: "No cash in this carton." (False)
- Third Carton Statement: "Cash is in the second carton." (True)
This situation results in two true statements, which contradicts the condition that only one statement is true. Therefore, the second carton cannot have cash.
Case 3: Third Carton has Cash
- First Carton Statement: "Cash is not in this carton." (True)
- Second Carton Statement: "No cash in this carton." (True)
- Third Carton Statement: "Cash is in the second carton." (False)
This situation also results in two true statements, which contradicts the condition that only one statement is true. Therefore, the third carton cannot have cash.
Conclusion
The only consistent case with one true and two false statements is the first carton having cash.
Therefore, the correct answer is option A: First Carton.

Answer 2

Since exactly one of the three printed messages is true and the other two are false, it is often quicker to test each message for being the one true statement, rather than testing each carton for holding the cash.

Suppose the third carton's message is the true one, 'cash is in the second carton'. Then the cash is in the second carton, which would also make the first carton's message, 'cash is not in this carton', true, since the cash is not in the first carton either. That gives two true messages at once, which is not allowed, so the third message cannot be the true one.

Suppose instead the first carton's message is the true one, 'cash is not in this carton'. Then the cash is in either the second or the third carton. If it is in the second carton, the third carton's message would also be true, again giving two true messages. If it is in the third carton, the second carton's message, 'no cash in this carton', would also be true, once again giving two true messages. Either way this breaks the one-true-statement condition, so the first message cannot be the true one either.

That leaves the second carton's message as the only one that can be true, 'no cash in this carton', meaning the cash is not in the second carton. Since the third message is then false, the cash is not in the second carton, already established, and since the first message must also be false, the cash must be in the first carton.

1. Option A (First): This matches the only scenario where exactly one message, the second carton's, comes out true, so this is correct.
2. Option B (Second): This scenario was shown to force two true messages at once, so this is incorrect.
3. Option C (Third): This scenario was also shown to force two true messages at once, so this is incorrect.
4. Option D (Cannot be determined): Since exactly one consistent scenario was found, the carton can in fact be determined, so this is incorrect.

Only the scenario with the second message true is consistent, and in that scenario the cash sits in the first carton.

the correct answer is Option A: First.