Trial in Wonderland II
While chasing the White Rabbit, Alice again met the White Knight.
"Hello again," bellowed the knight. "I've just witnessed the most marvelous trial at the courthouse. The Jabberwocky, the Caterpillar, and the Mad Hatter were all on trial. Exactly one of them was guilty, but I don't recall whom. They each accused exactly one of the other two - no one admitted his own guilt, but I don't recall what any of them said. Also, I don't recall how many of them lied."
Exasperated, Alice sighed, "Surely, you must remember more than that!"
"Well," said the White Knight, "I told the Queen of Hearts everything I've told you so far, but I also told her who each of the defendants accused. She was unable to determine the number of true statements the defendants made."
"Then," he continued, "I told the March Hare everything I've told you so far, but I also told him who the Jabberwocky and the Caterpillar each accused. The March Hare couldn't determine who the Mad Hatter accused."
The White Knight went on, "Finally, I met the Dormouse and told him everything I've told you so far, but I also told him who the Jabberwocky accused and the number of true statements made by the three defendants. After that, the Dormouse knew who was guilty."
Given that it is widely known that everyone in Wonderland is highly logical, who is guilty?
If you're stuck, try this problem first.
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1 solution
Since the Queen of Hearts knew who each of the defendants accused but did not know the number of true statements, the defendants could not all have accused distinct people. Moreover, no one admitted their own guilt, so they could not have all accused the same person. Therefore, two accused the third person, and the third accused one of the other two.
If exactly one of the Jabberwocky and the Caterpillar accused the Mad Hatter, then the March Hare would have known that the Mad Hatter accused the other person they accused. Therefore, either the Jabberwocky and the Caterpillar both accused the Mad Hatter; or the Jabberwocky accused the Caterpillar and the Caterpillar accused the Jabberwocky.
The Dormouse was told who the Jabberwocky accused, so he knew who the Caterpillar accused but not who the Mad Hatter accused. If the Dormouse was told that the Jabberwocky accused the Mad Hatter and that 0 or 1 statements were true, then could not have determined who was guilty. If the Dormouse was told that the Jabberwocky accused the Caterpillar and 1 or 2 statements were true, then he could not have determined who was guilty. Thus, we are left with one of two possible situations:
In either case, the Mad Hatter must be guilty.