Trial in Wonderland III
The Dodo, the Gryphon, and the Mock Turtle were on trial for theft. Exactly one of the three was guilty. Each was allowed to make an accusation (they could accuse themselves).
- The Dodo said, "The Mock Turtle is Guilty!"
- The Gryphon said, "The Dodo is Guilty!"
- The Mock Turtle's statement was kept private.
In addition:
- The Queen of Hearts was told who the Mock Turtle accused and how many of the three statements were true.
- Alice was told how many of the three statements were true.
User her powers of deduction, the Queen of Hearts announced, "I know who is guilty!"
Alice replied, "I also know who is guilty!"
It is well-known that both the Alice and the Queen are very logical. Which defendant is guilty?
This problem is an easier version of this problem and this problem .
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1 solution
If the Mock Turtle accused the Gryphon, then no matter who was guilty, exactly 1 true statement would have been made. Then the Queen would not have been able to figure out which was the true statement. Therefore, the Mock Turtle did not accuse the Gryphon .
Alice knows that the Queen figured out who was guilty, so by the same logic we used, she knows that the Mock Turtle did not accuse the Gryphon. If she were told that 1 or 2 true statements were made, she would know that either the Dodo or the Mock Turtle was guilty, but not which. Therefore, she must have been told that 0 true statements were made . (Note: she can't have been told that 3 true statements were made, since we know that the Dodo and Gryphon accused different people.)
We know that 1 or 2 people accused the Dodo and 1 or 2 people accused the Mock Turtle, but 0 true statements were made. Therefore, the Gryphon is guilty .