Four Lives
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Four Lives

A Celebration of Raymond Smullyan

Jason Rosenhouse, Raymond M. Smullyan

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eBook - ePub

Four Lives

A Celebration of Raymond Smullyan

Jason Rosenhouse, Raymond M. Smullyan

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This `best of` collection of works by Raymond Smullyan features excerpts from his published writings, including logic puzzles, explorations of mathematical logic and paradoxes, retrograde analysis chess problems, jokes and anecdotes, and meditations on the philosophy of religion. In addition, numerous personal tributes salute this celebrated professor, author, and logic scholar who is also a magician and musician.

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Year
2014
ISBN
9780486782942
Part III
A Smullyan Sampler
5
King Arthur in Search of His Dog
Though puzzles about liars and truthtellers have a long history, today the genre is all but synonymous with Raymond Smullyan. His creativity and depth of thought, coupled with his brilliant use of such puzzles to illuminate difficult ideas in modern logic, have made him justly famous among those who enjoy mathematical reasoning. I can think of no better introduction to Raymond’s contributions in this area than a series of puzzles that first appeared in his delightful book, King Arthur in Search of His Dog and Other Curious Puzzles. The book was published in 2010, when Raymond was just a kid of ninety-one.
1. Merlin’s Plan
Wonderful, indeed, as is the well-known story of King Arthur’s search for the Holy Grail, the lesser-known tale of Arthur’s search for his missing dog is at least as remarkable. As you will see, it explains the true secret of Merlin’s well-deserved fame as a magician—how his marvelous skill at the art of logical deduction enabled him to solve mysteries beyond the ken of most persons of his time.
The story begins on the day that King Arthur’s favorite dog was missing. All Camelot was in an uproar!
"How could he ever have jumped over the palace fence?" asked King Arthur in amazement. "It seems like a miracle!"
"Perhaps one of the guards carelessly let him by," suggested Merlin.
"Well, can’t you use your magic to bring him back?"
"Alas, no," replied Merlin. "My magic works only on wolves, not on dogs."
"Then I guess it is hopeless for me to find my dog again," said Arthur mournfully.
"I wouldn’t say hopeless," replied Merlin, "but, the matter will be very difficult!"
"What hope is there?" asked King Arthur eagerly.
"Well," replied Merlin, "there is Klug, the Dog Wizard."
"Klug?" asked Arthur. "I have never heard of him. What does he do?"
"Why, Klug has the power to change any dog into a wolf. If you meet Klug, all you have to do is pronounce the name of your dog. Then Klug will utter his magic incantations, and wherever in the land your dog may be, he will instantly be transformed into a wolf."
"What good will that do me?" cried Arthur. "I don’t want my dog to be a wolf; I want him as a dog!"
"Ah!" said Merlin, "the whole point is that once your dog has become a wolf, I will have magic power over him. Then I can easily call him back to the castle!"
King Arthur thought this over for a moment.
"Still, said Arthur, "I will have him back only as a wolf, and I want him back as a dog!"
"Oh, that’s no problem," replied Merlin. "Once we have him back as a wolf, I can easily change him back to his former shape. Remember, I have complete magic power over all wolves!"
"Great! Great!" cried King Arthur, clapping his hands in joy. "Now our problem is completely solved! It only remains to find Klug!"
"That only is more than a little," replied Merlin gravely. "Unfortunately, Klug is extremely difficult to find!"
"Where is he?" asked Arthur.
"Well you see, in recent months, Klug has become pretty much of a hermit. He has gotten extremely interested in a branch of knowledge he is developing called "Dog-logic." He is doing strenuous research in this area and does not wish to be disturbed. Hence, he has hidden himself from the world and has become a hermit living in a cave."
"Good grief!" said Arthur. "No one knows where he lives?"
"Yes, there is one person in the land—only one—who knows his whereabouts. His name is Gunter. Gunter is also a wizard. If you can find Gunter, then you can find Klug. But you cannot find Klug without first finding Gunter."
"How do I find Gunter?"
"Unfortunately, Gunter is also very difficult to find," replied Merlin.
"Then the case is hopeless!" cried Arthur.
"No," replied Merlin, "I said that Gunter is very difficult to find; I did not say it was impossible. I wish you’d listen more carefully to what I say!"
"I am listening!" cried Arthur in despair. "Just tell me what to do!"
"Well, you see," replied Merlin "one difficulty is that Gunter goes under an assumed name. He is now living in a small hamlet named Caxton. There are thirty people living in this hamlet, and five of them are wizards. One of the five wizards is Gunter.
"Now comes the difficult part," continued Merlin. "The trouble is that all of the people in Caxton, as well as in the surrounding region, are either dishonest and always lie, or are honest and always tell the truth. The dishonest ones never tell the truth, and the honest ones never lie. This makes it very difficult to evaluate the truth of anything they say!"
"What about the five wizards?" asked Arthur. "Are they honest or dishonest?"
"Some of them are honest, and some of them are dishonest," replied Merlin, "and this further complicates matters."
Arthur thought about this for a while. "Exactly what do you suggest we do?"
"We had best go immediately to Caxton," replied Merlin. "When we get there, we will try to ferret out the five wizards and bring them back to Camelot. When we have them here, I will devise further strategies to find out which one is Gunter. Then, as I have explained, once we have found Gunter, we can find Klug. Once we have Klug, we get him to turn your dog into a wolf. Then I use my magic power over the wolf to bring him back to the castle, and then I turn him back into a dog."
This sounded like an excellent plan, so after making a few hasty preparations, the two set out on their journey. Little did they realize what strange adventures awaited them!
2. Two Unexpected Obstacles
Towards late afternoon, Arthur and Merlin found themselves in a rather heavily wooded region.
"We are not far from Caxton," said Merlin, "and have already entered the region where everyone is either honest and always tells the truth or is dishonest and always lies. We must now be very careful!"
At this point, they came to a fork in the road, but the sign to Caxton had been blown down by a storm.
"Zounds!" said Merlin. "I don’t remember whether the left road or the right road is the one that leads to Caxton!"
Just then, they spied two inhabitants standing under a tree. "Let us ask them," suggested Arthur. They probably know."
"I have no doubt that they know," replied Merlin. "My only doubt is about their honesty!"
Well, they approached the two inhabitants. "Which road leads to Caxton?" asked Arthur.
"The left one," said the first inhabitant.
"Is he honest?" Arthur asked the second inhabitant.
"No, he is not," was the reply.
"At least one of us is honest," said the first inhabitant, with a strange smile.
At this point, Merlin knew which road to take. Did they take the left road or the right road? The solution follows.
* * *
"How did you know which road to take?" asked Arthur, after they were well on their way.
"Oh, that was easy," replied Merlin. "That was about the simplest case I ever came across. If only our remaining adventures turn out to be that simple!"
"You still haven’t told me," remarked Arthur.
"Oh," replied Merlin, "I hardly thought it needed explanation. The second one said that the first one was dishonest. This means that one of the two is honest and the other is dishonest, because if the second one is honest, his claim is true, which means the first one is dishonest. On the other hand, if the second one is dishonest, then he lied about the first one, which means that the first one is honest. Therefore, the two are of opposite types—one is honest and the other is dishonest."
"But which is the honest one?" asked Arthur.
"I wouldn’t have known," replied Merlin, "if the first one hadn’t made a second statement, but fortunately he said that at least one of the two was honest, and what he said was true. Since he told the truth, he is honest; therefore he also told the truth when he said that the left road leads to Caxton. That is why we took the left road."
* * *
Well, the next obstacle proved more difficult. Arthur and Merlin soon came across another fork in the road, and again the sign to Caxton had been blown down by the storm.
"Zounds!" said Arthur. "Again we are foiled!"
"Not necessarily," replied Merlin thoughtfully. "Do you not spy yonder three damsels resting under the tree?"
"In sooth, I do," replied Arthur, "and fairer damsels have I rarely spied, but are they honest?"
"They are the three Cornwall sisters," replied Merlin. "Their names are Helen, Lynette, and Vivian. I have heard many wondrous tales about them, but I do not know which of them are honest and which of them are dishonest."
Arthur and Merlin soon came up to the three sisters. "Which road leads to Caxton?" asked Arthur.
Helen then named either the left road or the right road, but she said it too indistinctly for either Arthur of Merlin to make out what she said.
"What did she say?" Merlin asked Lynette.
"She said the left road," replied Lynette.
"She did not!" said Vivian.
Arthur did not know what to make of any of this. Then Merlin asked, "Exactly how many of you three are honest?"
Helen then either said one, or she said two, or she said three, but she said it too softly for either Arthur or Merlin to make out.
"What did she say?" Merlin asked Lynette.
"She said one," Lynette replied.
"Did she answer truthfully?" Merlin asked Lynette.
"Yes, she did," Lynette replied.
At this, Merlin stood for a while in thought. "Come," he said finally to Arthur, "I know which road we should take."
Which road did they take? The solution follows.
* * *
"This seems much more difficult than our last problem," Arthur said to Merlin when they were well on the road. "How did you ever solve this one?"
"To begin with," said Merlin, "Lynette and Vivian made contradictory claims; Lynette said that Helen said, ‘left,’ and Vivian said that Helen didn’t. Therefore, one of these two lied, and the other told the truth. So one of them—Lynette or Vivian—is honest, and the other dishonest."
"All well and good," said Arthur, "but how do we know which of them is the honest one?"
"By considering Lynette’s second statement," replied Merlin. "Lynette said that Helen said that exactly one of the three is honest. Mind you, Lynette never said that exactly one of the three is honest; she onl...

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