More Puzzles of Love and Passion

Broken Resolutions

Tom, Dick and Harry, three carefree lads who shared a bachelor apartment, were the happiest fellows alive. Tom had Teresa, Dick had Doris, and Harry had Harriet: had them, in fact, every blessed night of the week.

Naturally, after a few months of this pleasant but exacting activity, signs of wear began to show themselves. In fact, Tom, Dick and Harry all manifested symptoms of exhaustion. Tom had pouches under his eyes of marsupial dimensions; Dick could not lift a highball to his lips without spilling half of it; and Harry felt so very weak in the small of his back, poor chap, that he needed help in climbing the stairs.

It was about midnight, not too long ago, when our three heroes returned to their diggings almost simultaneously. They stared at each other haggardly.

"How'd it go?" Dick asked shakily. "Have fun?"

"This can't go on," Tom whispered faintly. "This thing has got too big for me."

"Help me up the stairs, fellows," Harry said. "I have an idea I want to put to you."

When each was sprawled on his neck in an armchair, Harry put forward his idea, his voice barely audible. "Look at us. Wrecks. Shadows of our former selves. Hollow shells. Fellows, we gotta call a halt, or it'll be too late. We gotta stop this stuff."

"Stop?" Tom asked. "You mean -- stop?"

"And we need each other's moral support," Harry said.

"Harry's right," Dick said. "We all gotta lay off -- for a while."

"Lay off?" Tom asked. "For how long?"

"At least a month," Harry said firmly. "We need at least a month to regain our strength."

So the three agreed, with many protestations of good faith, to refrain and desist, "within the limits of human endurance," for at least a month, if possible.

Well, Tom was the first to break the compact. One Tuesday he walked into the room with an unmistakably guilty but satisfied smile on his face.

"You did it!" Dick exclaimed. "You traitor!"

"I guess I did," Tom said sheepishly. "My human endurance is sort of low. But it was nice."

"I'm ashamed of you," Dick said, with indignation. "We agreed on a month at the very minimum."

Despite his recriminations, however, Dick was the next one to capitulate. He lasted half again as long as Tom, but he finally fell, on a Wednesday, when he and Doris had a real ball, made all the more delightful by the enforced spell of abstinence.

"What, you too?" Harry cried. "And am I left alone? Where's my moral support?"

"Carry on, old boy," Dick said cheerfully, quite forgetting his indignation over Tom's defection. "We are still with you in spirit, though not in body, haha."

And Harry did carry on. He lasted twice as long as Tom, but eventually he too succumbed, on a Thursday, when he and Harriet made up for lost time and then some. "At least," he said, with justified pride, "I held out for more than the agreed month, which is more than either of you voluptuaries can say."

"Well, it's good to be back in the old routine, isn't it?" Dick said. "By the way, Harry, just how the hell many days was it?"

"You figure it out," Harry replied, "I'm tired." But so were his buddies, so we're asking you to do it.

The Sapphire Ring

"You have made an old man very happy," the lecherous old geezer said, patting the young lady in various delectable places. "Very happy, my child. And I intend to express my gratitude in tangible form."

So saying, he opened a box by his side and revealed 12 identical gold rings, each set with a gem the size of a plover's egg.

"Gee!" she exclaimed. "Lookit all them big sapphires!"

"No, my dear," he cackled, "only one of them is a sapphire -- all the rest are fakes. You may have one ring. Be sure you choose the genuine one."

"How'm I gonna do that?" she asked. "They all look alike."

"Yes," he said, "it would be difficult without this." And he took from its case a simple balance scale. "The true sapphire does not weigh quite the same as the imitations. With this scale, however -- and in no more than three weighings -- you should be able to pick out the right one."

"Well, does the sapphire weigh more or less than the others?" she asked.

"Ah, my dear," he said, "that you must find out for yourself. I shall be interested to learn whether your mind is as beautifully put together as your body."

"Gee!" she said, and set herself to the task of picking out the true ring from the pile of 12 by no more than three weighing operations with the balance scale.

"I have it!" she cried a moment later, slipping it on her finger.

"How did you do it so swiftly?" he asked, amazed at her brilliance.

"It was easy," she said. "I took two of the rings, see, and I weighed them against each other. Well, they wouldn't balance. So I took one of them and weighed it against a third ring, and they did balance. So I knew that the other one was the sapphire."

"Upon my word!" the old roue exclaimed. "I see that Nature decided not to give you a mind to match your figure, but gave you good fortune instead."

He was astonished, of course, because the young lady had not chosen the proper and infallible method of acquiring the sapphire, but had acquired it nevertheless. You, needless to say, can tell her how she should have gone about it.

The Getaway

She was the wife of the Resident Physician and he was but a lowly interne. The fact that they were in a private sanatorium for the insane lent an exciting note to their illicit romance. The trouble was that with the place crawling with nuts it was extremely difficult for them to steal their golden moments without detection. It was so difficult, in fact, that they decided to bust out of the place together and seek an unencumbered life on some faraway isle. To hell with the dedicated life, the distinguished husband, the Hippocratic oath, and all that stuff. They wanted out.

But how to get out? She put it to him squarely on one of their furtive visits to the laundry room.

"You know how my husband runs this place," she whispered. "Like a jail. The only exit is through the front gate, which is just past the front office. And you can't keep track of him long enough to be sure he won't be right there, watching all comings and goings."

"There's always one patient or another wandering around in the front hall," he suggested. "We could ask him whether the doctor was in the office."

"But George," she answered, stamping her little foot, "you know the patients we have here. Only two sorts. The paraploops with their Messianic complex, whose obsession is that they can only speak the truth, and the schizobleeps with their persecution complex, who are incapable of anything but a lie."

"Of course," he said. "How stupid of me. And there's no way of telling them apart."

"So, don't you see? We can't know, when we ask the patient, whether he is lying or telling the truth."

"Then," he said firmly, "we must devise a question so phrased that, whether or not the patient is lying, we gain the information we need."

"OK, devise," she said. "This I have to see."

He pondered a moment. "I have it!" he exclaimed. "Pack a bag and meet me in the main hall tomorrow at three."

Together, the next day, they made their way toward the main gate. Sure enough, a patient was in the hall. Was he a truth-teller or a liar? It didn't matter.

"Tell me, my good man," the interne began -- and then he asked whether the Resident Physician was up front there in the office -- but in such a form that the patient, in his reply, would have to convey the correct information, whether he was telling the absolute truth or an absolute lie.

As it happened, the good doctor was out in Ward III, giving an audience to Catherine the Great. Our happy couple made their escape and are now blissfully established in Tahiti, selling Equanil and Serutan to the natives.

How did he phrase the question? Well now, surely you're as smart as that interne.

Answers on Page 79

Answers to Puzzles on Page 54

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The Broken Resolutions. If Harry held out twice as long as Tom, and was the only one to last longer than a month, Tom must have abstained for at least 16 days, but no more than 20 (if more than 20, Dick would have lasted more than a month). Tom gave up on a Tuesday and Dick gave up on a Wednesday, or what must have been 8 days later. Since Dick lasted half again as long as Tom, 8 must be half of Tom's time. Tom=16, Dick=24, Harry=32.

The Sapphire Ring. Number the rings from 1 to 12.

First weighing: 1, 2, 3, 4 on the left, 5, 6, 7, 8 on the right. Either they will balance or one side will sink. In the latter case, let us assume that it is the left side that sinks. This means that the true ring is either on the left and is heavier than the others, or is on the right and is lighter. Second weighing: 2, 3, 4, 5 vs. 1, 9, 10, 11. If the scale now balances, we know that the true ring is either 6, 7 or 8 and that it is lighter than the others. Third weighing: 6 vs. 7. Whichever rises is the true ring; if they balance, 8 is the true ring.

If, in the second weighing, the scale continues to be heavy on the left side, 1 and 5 are eliminated as possible candidates (since interchanging them had no effect), and 2, 3 or 4 must be the true ring, and be heavier. Third weighing: 2 vs. 3. Whichever sinks is the true ring; if they balance, 4 is.

If, in the second weighing, the scale now rises on the left and sinks on the right, either 5 is too light or 1 is too heavy. Third weighing: 5 vs. any other except 1. If it balances, 1 is the true ring; if it does not balance, 5 is.

If, in the first weighing, the scale balances, the true ring is either 9, 10, 11 or 12. Second weighing: 9, 10, 11 vs. any other three except 12. If the scale balances, 12 is the one. If it does not balance, 9, 10 or 11 is the true ring, and is either lighter or heavier than the others, depending on whether that side rose or sank. The third weighing will discover it, by the same process as above.

The Getaway. "Tell me, my good man," the interne said, "what would you say if I asked whether the boss doctor is up front there in that office?"

If the patient is a truth-teller, he answers, of course, "I would say no."

If the patient is a compulsive liar, he must lie about what he would say. If he had been asked, "Is the doctor there?" he would have had to tell a lie and say yes. But, being asked whether he would say yes, he must lie again and say no.

In either case -- truth-teller or liar -- our couple gets the correct information.