Dr. Johnson’s Coin Challenge

Scenario Overview

Dr. Johnson presents three coins on the table: a gold coin, a silver coin, and a copper coin. He instructs his nurse to speak a sentence, establishing rules for her reward based on the truthfulness of her statement.

Rules of the Game

If the nurse utters a truthful sentence, she will receive one of the coins, regardless of which one it is. Conversely, if her sentence is false, she does not receive any coins.

The Strategic Sentence

To ensure she receives the gold coin, the nurse should say, “You will give me neither a copper nor a silver coin.”

Analysis of the Statement

If her statement is true, she will indeed be awarded the gold coin. However, if her statement is false, it implies that she would receive both the copper and silver coins. This outcome contradicts the initial conditions, which state that she should receive nothing for a false statement.

Conclusion

Therefore, the nurse’s statement must be true, guaranteeing her a gold coin as a reward.