Dr. Johnson’s Challenge to Anna
The Setup
Dr. Johnson wanted to assess the intelligence of his physician assistant, Anna. To do this, he devised a challenge involving three envelopes. He placed a cheque for $100 inside one of the envelopes and labeled them as follows:
1. The first envelope stated, “This envelope does not have the cheque.”
2. The second envelope claimed, “This envelope has the cheque.”
3. The third envelope read, “The second envelope does not have the cheque.”
The Challenge
Dr. Johnson instructed Anna to determine which envelope contained the cheque solely by reading the statements on the envelopes. He emphasized that only one of the statements was true, while the other two were false.
Finding the Solution
To solve the puzzle, Anna must analyze the statements carefully. If the statement on the second envelope is true, then it implies that the second envelope contains the cheque. However, this would mean that the statements on the first and third envelopes are false.
If the first envelope’s statement is false, it would indicate that the first envelope actually contains the cheque. This creates a contradiction since we initially assumed the cheque was in the second envelope.
Therefore, the conclusion is that the statement on the second envelope must be false, which means the second envelope does not contain the cheque. This outcome confirms that the statement on the third envelope is true, implying that the first envelope’s statement is false.
Thus, the only logical conclusion is that the first envelope contains the cheque.
Conclusion
In summary, Anna should select the first envelope to successfully retrieve the cheque.