The Tale of the Generous Rajah
by Stan Smith
An armchair in the reading room of the Baskerville Public Library proved too comfortable a place for Thomas P Stanwick at four o’clock on a warm afternoon. His eyes slid closed, his head slumped to his chest, and the book slipped from his fingers to the floor.
The head librarian, who had seen these symptoms before, walked quietly over to the amateur logician and gently shook his shoulder.
“Mr. Stanwick! You haven’t fallen asleep, have you, sir?” she asked.
Stanwick snapped to alertness.
“What?” he said. “Oh, hello, Mrs. Mitten. Good Lord, I wasn’t snoring, was I?”
“No, no. I caught you in time.”
“Thank you.” Stanwick sheepishly picked up the book. “It’s no reflection on what I was reading. Have you seen the memoirs of Morton Henry Stanley? He was a British explorer who traveled from Bombay across the Thar Desert to the northern reaches of India in the early 1800’s.”
“No, I don’t think I’ve heard the name.” Intrigued, the librarian sat down in the chair beside Stanwick’s and examined the book closely.
“Stanley had many interesting adventures,” Stanwick went on. “In one, he missed an excellent chance of gaining a large fortune in precious stones.”
“Do go on,” the librarian said.
Stanwick settled back in his chair and toyed with the tip of his droopy mustache.
“Well, as you probably know,” he recounted, “India in those days had many independent kingdoms, or raji, each ruled by a fierce rajah. During one of his journeys, Stanley was captured by one of these rajahs. The rajah found his prisoner to be a fascinating conversationalist. (Stanley was a gifted linguist and knew several Indian dialects.) They discussed local politics and world events, and played many games of chess.
“That night the rajah presided over an elaborate dinner, which was, according to his custom, to have been followed by the execution of the trespasser. The rajah, however, announced that he would give Stanley an opportunity to leave the raj unharmed and even wealthy.
“Three large chests were brought in to the center of the dining hall. Each was lavishly bound and secured by a huge lock. A besotted servant then stumbled in carrying three signs, one picturing a diamond, another picturing a ruby, and the third picturing an emerald. The fellow first put the emerald sign on the first trunk. After a confused pause, he then took that sign off the first trunk and put it on the second trunk. Finally, after some fumbling, he put the diamond sign on the first trunk and the ruby sign on the third trunk. Then he staggered out.
“’You must forgive my servant,’ laughed the rajah, turning to his guest of honor. ‘He has taken a little to much hashish today. I am afraid that in none of his attempts did he succeed in putting the correct sign on the correct chest. Nevertheless, one chest does contain diamonds, another contains rubies, and another emeralds.
‘’’Each chest has a rather complicated lock. Here is a golden lockpick. I will give you five minutes to open one of the chests. Seeing its contents should enable you to divine the contents of all three chests. If you succeed in divining this, you may have all three chests and their contents, and safe passage to the border. If you fail, I fear I must proceed with the execution. You may begin.’
“Stanley needed no further prompting. Snatching up the lockpick, he hurried over to the three chests, paused briefly, and then began furiously picking at the lock of the middle chest, the one with the emerald sign. As the rajah chuckled quietly, Stanley muttered to himself and wrestled with the lock. Beads of sweat glistened on his forehead as the rajah called time. With a curse, Stanley flung the pick to the ground and glared at the still impregnable lock.
“The rajah laughed heartily at the spectacle of the explorer’s fury and frustration.
‘’’Such a pity!’ he exclaimed. ‘I fear that the lock was too stubborn for you.’
‘’’Just tell me what is in one of these chests, good rajah,’ said Stanley, ‘and I will indeed tell you what is in the other two.’ ‘’’I am sure you could, my friend,’ replied the rajah. ‘But fear not. You have entertained me well today, so I will spare your life and reward you for your company. The rajah then made good on this word by giving our relieved hero a small bagful of precious stones and a mounted escort to the border of the raj.”
Stanwick grinned slyly. Mrs. Mitten, who had a weakness for tales of adventure in exotic lands, remained lost in thought for a moment.
“It’s a shame that he couldn’t open the lock,” she said at last. “I think I see how he could then have deduced the contents of all three chests, if all the signs were wrong.”
“Quite true!” said Stanwick with a laugh. “Poor Stanley, however, was not quite astute enough to guess the real cause of the rajah’s amusement. If only the brave explorer had been a little more alert, he might have realized that he had the power to ‘divine’ the contents of all three chests without touching the lockpick at all.”
How could Stanley have done this?
Answer below.
The Tale of the Generous Rajah
Morton Henry Stanley was correct in asserting that, if he could know what was in one chest, all of which were mislabeled, he could deduce what was in the other two. Suppose he had succeeded in opening the middle chest, the one with the emerald sign. It would have contained either diamonds or rubies. If it had contained diamonds, then the rubies would have been in the chest with the diamond sign and the emeralds would have been in the chest with the ruby sign. If it had instead contained rubies, then the diamonds would have been in the chest with the ruby sign and the emeralds would have been in the chest with the diamond sign. Only by these combinations could all three chests have the wrong signs. Had he chosen and opened one of the other two chests, similar reasoning would have revealed the contents of all three.
Unfortunately for the good explorer, he failed to notice that the rajah had said that the befuddled servant had failed in each of his attempts to match a sign to the right chest. As Stanwick noticed, there were in fact four such attempts, the first being when the servant put the emerald sign on the first trunk. Only after that did he arrange the signs in their final order (diamond-emerald-ruby). This meant that the first trunk contained neither emeralds nor diamonds. It therefore contained the rubies. Since the second chest had the emerald sign, the emeralds must have been in the third chest, and the diamonds must have been in the second. The offer of a lockpick was therefore an unnecessary ruse. Stanwick knew this, but Morton Henry Stanley never suspected it.