Dr. Johnson’s Coin Challenge
The Setup
Dr. Johnson places three coins on the table: a gold coin, a silver coin, and a copper coin. He instructs his nurse to create a sentence. The rules are simple: if she states a truthful sentence, she will receive a coin of her choice. However, if her sentence is false, she will not receive any coin.
The Nurse’s Strategy
To ensure she receives a gold coin, the nurse should say: “You will give me neither a copper nor a silver coin.”
Analyzing the Statement
If her statement is true, she will receive the gold coin. Conversely, if the statement is false, it implies she would receive both the copper and silver coins. This scenario contradicts the initial rules, which state that she would get nothing for a false statement. Therefore, her statement must be true, guaranteeing her the gold coin.