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?
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?
Updated On: Sep 2, 2024
- First
- Second
- Third
- Cannot be determined
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The Correct Option is A
Solution and Explanation
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.
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.
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