The hardest logic puzzle ever
Three gods are labeled A, B, and C. You know their types are Truth, Lie, and Random, but not which label has which type.
- Truth always tells the truth.
- Lie always lies.
- Random flips a mental coin each time and answers either truthfully or falsely at random.
Your task: identify the type of A, B, and C using exactly three yes/no questions. You may ask only one god per question, and later questions may depend on earlier answers.
The gods understand your language but answer only da or ja. One means “yes” and one means “no”—you do not know which is which.
How should the three questions be designed?
(This is George Boolos’s “hardest logic puzzle ever”, adapted from Raymond Smullyan’s knights-and-knaves puzzles.)
See Wikipedia: The hardest logic puzzle ever.