Flax-Golden Tales

unit eleven: Critical and Creative Thinking

The Stub-Book

Pedro Antonio de Alarcón
(Spain, 1833-1891)

The action begins in Rota. Rota is the smallest of those pretty towns that form the great semicircle of the bay of Cádiz. But despite its being the smallest, the grand duke of Osuna preferred it, building there his famous castle, which I could describe stone by stone. But now we are dealing with neither castles nor dukes, but with the fields surrounding Rota, and with a most humble gardener, whom we shall call Uncle Buscabeatas[1] though this was not his true name.

From the fertile fields of Rota, particularly its gardens, come the fruits and vegetables that fill the markets of Huelva and Seville. The quality of its tomatoes and pumpkins is such that in Andalusia the people of Rota are always referred to as pumpkin- and tomato-growers, titles which they accept with pride.

And, indeed, they have reason to be proud; for the fact is that the soil of Rota, which produces so much, that is to say, the soil of the gardens, that soil which yields three or four crops a year, is not soil, but sand, pure and clean, cast up by the ocean, blown by the furious west winds and thus scattered over the entire region of Rota.

But the ingratitude of nature is here more than compensated for by the constant diligence of man. I have never seen, nor do I believe there is in all the world, any farmer who works as hard as the farmer of Rota. Not even a tiny stream runs through those melancholy fields. No matter! The pumpkin-grower has made many wells from which he draws the precious liquid that is the lifeblood of his vegetables. The tomato-grower spends half his life seeking substances which may be used as fertilizer. And when he has both elements, water and fertilizer, the gardener of Rota begins to fertilize his tiny plots of ground, and in each of them sows a tomato-seed, or a pumpkin pip which he then waters by hand, like a person who gives a child a drink.

From then until harvest time, he attends daily, one by one, to the plants which grow there, treating them with a love only comparable to that of parents for children. One day he applies to such a plant a bit of fertilizer; on another he pours a pitcherful of water; today he kills the insects which are eating up the leaves; tomorrow he covers with reeds and dry leaves those plants which cannot bear the rays of the sun, or those which are too exposed to the sea winds. One day, he counts the stalks, the flowers, and even the fruits of the earliest ripeners; another day, he talks to them, pets them, kisses them, blesses them, and even gives them expressive names in order to tell them apart and individualize them in his imagination.

Without exaggerating, it is now a proverb (and I have often heard it repeated in Rota) that the gardener of that region touches with his own hands at least forty times a day every tomato plant growing in his garden. And this explains why the gardeners of that locality get to be so bent over that their knees almost touch their chins.

Well, now, Uncle Buscabeatas was one of those gardeners. He had begun to stoop at the time of the event which I am about to relate. He was already sixty years old . . . and had spent forty of them tilling a garden near the shore.

That year he had grown some enormous pumpkins that were already beginning to turn yellow, which meant it was the month of June. Uncle Buscabeatas knew them perfectly by color, shape, and even by name, especially the forty fattest and yellowest, which were already saying cook me.

“Soon we shall have to part,” he said tenderly, with a melancholy look.

Finally, one afternoon he made up his mind to the sacrifice and pronounced the dreadful sentence.

“Tomorrow,” he said, “I shall cut these forty and take them to the market at Cádiz. Happy is the man who eats them!” Then he returned home at a leisurely pace, and spent the night as anxiously as a father whose daughter is to be married the following day.

“My poor pumpkins!” he would occasionally sigh, unable to sleep. But then he reflected and concluded by saying, “What can I do but sell them? For that I raised them! They will be worth at least fifteen duros[2]!”

Imagine, then, how great was his astonishment, his fury and despair, when, as he went to the garden the next morning, he found that, during the night, he had been robbed of his forty pumpkins. He began calculating coldly, and knew that his pumpkins could not be in Rota, where it would be impossible to sell them without the risk of his recognizing them.

“They must be in Cádiz, I can almost see them!” he suddenly said to himself. “The thief who stole them from me last night at nine or ten o’clock, escaped on the freight boat .... I’ll leave for Cádiz this morning on the hour boat, and there I’ll catch the thief and recover the daughters of my toil!”

So saying, he lingered for some twenty minutes more at the scene of the catastrophe, counting the pumpkins that were missing, until, at about eight o’clock, he left for the wharf.

Now the hour boat was ready to leave. It was a small craft which carries passengers to Cádiz every morning at nine o’clock, just as the freight boat leaves every night at twelve, laden with fruit and vegetables.

The former is called the hour boat because in an hour, and occasionally in less time, it cruises the thirty-eight kilometers separating Rota from Cádiz.

It was, then, ten-thirty in the morning when Uncle Buscabeatas stopped before a vegetable stand in the Cádiz market, and said to a policeman who accompanied him:

“These are my pumpkins! Arrest that man!” and pointed to the vendor,

“Arrest me?” cried, the latter, astonished and enraged. “These pumpkins are mine; I bought them.”

“You can tell that to the judge,” answered Uncle Buscabeatas.

“No, I won’t!”

“Yes, you will!”

“You old thief!”

“You old scoundrel!”

“Keep a civil tongue. Men shouldn’t insult each other like that,” said the policeman very calmly, giving them each a punch in the chest.

By this time several people had gathered, among them the inspector of public markets. When the policeman had informed the inspector of all that was going on, the latter asked the vendor in accents majestic:

“From whom did you buy these pumpkins?”

“From Uncle Fulano, near Rota,” answered the vendor.

“He would be the one,” cried Uncle Buscabeatas. “When his own garden, which is very poor, yields next to nothing, he robs from his neighbors’.”

“But, supposing your forty pumpkins were stolen last night,” said the inspector, addressing the gardener, “how do you know that these, and not some others, are yours?”

Well,” replied Uncle Buscabeatas, “because I know them as well as you know your daughters, if you have any. Don’t you see that I raised them? Look here, this one’s name is Fatty; this one, Plumpy Cheeks; this one, Pot Belly; this one, Little Blush Bottom; and this one, Manuela, because it reminds me so much of my youngest daughter.”

And the poor old man started weeping like a child.

“That is all very well,” said the inspector, “but it is not enough for the law that you recognize your pumpkins. You must identify them with incontrovertible proof. Gentlemen, this is no laughing matter. I am a lawyer!”

“Then you’ll soon see me prove to everyone’s satisfaction, without stirring from this spot, that these pumpkins were raised in my garden,” said Uncle Buscabeatas.

And throwing on the ground a sack he was holding in his hand, he kneeled, and quietly began to untie it. The curiosity of those around him was overwhelming.

“What’s he going to pull out of there?” they all wondered.

At the same time another person came to see what was going on in that group and when the vendor saw him, he exclaimed:

“I’m glad you have come, Uncle Fulano. This man says that the pumpkins you sold me last night were stolen. Answer ...”

The newcomer turned yellower than wax, and tried to escape, but the others prevented him, and the inspector himself ordered him to stay.

As for Uncle Buscabeatas, he had already faced the supposed thief, saying:

“Now you will see something good!”

Uncle Fulano, recovering his presence of mind, replied:

“You are the one who should be careful about what you say, because if you don’t prove your accusation, and I know you can’t, you will go to jail. Those pumpkins were mine; I raised them in my garden, like all the others I brought to Cádiz this year, and no one could prove I didn’t.”

“Now you shall see!” repeated Uncle Buscabeatas, as he finished untying the sack.

A multitude of green stems rolled on the ground, while the old gardener, seated on his heels, addressed the gathering as follows:

“Gentlemen, have you never paid taxes? And haven’t you seen that green book the tax-collector has, from which he cuts receipts, always leaving a stub in the book so he can prove afterwards whether the receipt is counterfeit or not?”

“What you are talking about is called the stub-book,” said the inspector gravely.

“Well, that’s what I have here: the stub-book of my garden; that is, the stems to which these pumpkins were attached before this thief stole them from me. Look here: this stem belongs to this pumpkin. No one can deny it . . . this other one . . . now you’re getting the idea . . . belongs to this one . . . this thicker one . . . belongs to that one . . . exactly! And this one to that one . . . that one, to that one over there . . .”

And as he spoke, he fitted the stem to the pumpkins, one by one. The spectators were amazed to see that the stems really fitted the pumpkins exactly, and delighted by such strange proof, they all began to help Uncle Buscabeatas, exclaiming:

“He’s right! He’s right! No doubt about it. Look: this one belongs here . . . That one goes there . . . That one there belongs to this one . . . This one goes there . . .”

The laughter of the men mingled with the catcalls of the boys, the insults of the women, the joyous and triumphant tears of the old gardener, and the shoves the policemen were giving the convicted thief.

Needless to say, besides going to jail, the thief was compelled to return to the vendor the fifteen duros he had received, and the latter handed the money to Uncle Buscabeatas, who left for Rota very pleased with himself, saying, on his way home:

“How beautiful they looked in the market! I should have brought back Manuela to eat tonight and kept the seeds.”

Mr. Know-All

W. Somerset Maugham (England, 1874-1965)

I was prepared to dislike Max Kelada even before I knew him. The war1 had just finished and the passenger traffic in the ocean going liners was heavy. Accommodation was very hard to get and you had to put up with whatever the agents chose to offer you. You could not hope for a cabin to yourself and I was thankful to be given one in which there were only two berths. But when I was told the name of my companion my heart sank. It suggested closed portholes2 and the night air rigidly excluded. It was bad enough to share a cabin for fourteen days with anyone (I was going from San Francisco to Yokohama), but I should have looked upon it with less dismay if my fellow passenger’s name had been Smith or Brown.

When I went on board I found Mr. Kelada’s luggage already below. I did not like the look of it; there were too many labels on the suitcases, and the wardrobe trunk was too big. He had unpacked his toilet things, and I observed that he was a patron of the excellent Monsieur Coty;3 for I saw on the
washing-stand his scent, his hairwash and his brilliantine.4 Mr. Kelada’s brushes, ebony with his monogram in gold, would have been all the better for a scrub. I did not at all like Mr. Kelada. I made my way into the smoking-room. I called for a pack of cards and began to play patience.5 I had scarcely started before a man came up to me and asked me if he was right in thinking my name was so and so.

“I am Mr. Kelada,” he added, with a smile that showed a row of flashing teeth, and sat down.

“Oh, yes, we’re sharing a cabin, I think.”

“Bit of luck, I call it. You never know who you’re going to be put in with. I was jolly glad when I heard you were English. I’m all for us English sticking together when we’re abroad, if you understand what I mean.”

I blinked.

“Are you English?” I asked, perhaps tactlessly.

“Rather. You don’t think I look like an American, do you? British to the backbone, that’s what I am.”

To prove it, Mr. Kelada took out of his pocket a passport and airily waved it under my nose.

King George6 has many strange subjects. Mr. Kelada was short and of a sturdy build, clean-shaven and dark skinned, with a fleshy, hooked nose and very large lustrous and liquid eyes. His long black hair was sleek and curly. He spoke with a fluency in which there was nothing English and his gestures were exuberant. I felt pretty sure that a closer inspection of that British passport would have betrayed the fact that Mr. Kelada was born under a bluer sky7 than is generally seen in England.

“What will you have?” he asked me.

I looked at him doubtfully. Prohibition was in force and to all appearances the ship was bone dry. When I am not thirsty I do not know which I dislike more, ginger ale or lemon squash. But Mr. Kelada flashed an oriental smile at me.

“Whisky and soda or a dry martini, you have only to say the word.”

From each of his hip pockets he furnished a flask and laid it on the table before me. I chose the martini, and calling the steward he ordered a tumbler of ice and a couple of glasses.

“A very good cocktail,” I said.

“Well, there are plenty more where that came from, and if you’ve got any friends on board, you tell them you’ve got a pal who’s got all the liquor in the world.”

Mr. Kelada was chatty. He talked of New York and of San Francisco. He discussed plays, pictures, and politics. He was patriotic. The Union Jack is an impressive piece of drapery, but when it is flourished by a gentleman from Alexandria or Beirut, I cannot but feel that it loses somewhat in dignity. Mr. Kelada was familiar. I do not wish to put on airs, but I cannot help feeling that it is seemly in a total stranger to put mister before my name when he addresses me. Mr. Kelada, doubtless to set me at my ease, used no such formality. I did not like Mr. Kelada. I had put aside the cards when he sat down, but now, thinking that for this first occasion our conversation had lasted long enough, I went on with my game.

“The three on the four,” said Mr. Kelada.

There is nothing more exasperating when you are playing patience than to be told where to put the card you have turned up before you have a chance to look for yourself.

“It’s coming out, it’s coming out,” he cried. “The ten on the knave.”

With rage and hatred in my heart I finished.

Then he seized the pack.

“Do you like card tricks?”

“No, I hate card tricks,” I answered.

“Well, I’ll just show you this one.”

He showed me three. Then I said I would go down to the dining-room and get my seat at the table.

“Oh, that’s all right,” he said, “I’ve already taken a seat for you. I thought that as we were in the same stateroom we might just as well sit at the same table.”

I did not like Mr. Kelada.

I not only shared a cabin with him and ate three meals a day at the same table, but I could not walk round the deck without his joining me. It was impossible to snub8 him. It never occurred to him that he was not wanted. He was certain that you were as glad to see him as he was to see you. In your own house you might have kicked him downstairs and slammed the door in his face without the suspicion dawning on him that he was not a welcome visitor. He was a good mixer, and in three days knew everyone on board. He ran everything. He managed the sweeps,9 conducted the auctions, collected money for prizes at the sports, got up quoit and golf matches, organized the concert and arranged the fancy-dress ball. He was everywhere and always. He was certainly the best hated man in the ship. We called him Mr. Know-All, even to his face. He took it as a compliment. But it was at mealtimes that he was most intolerable. For the better part of an hour then he had us at his mercy. He was hearty, jovial, loquacious and argumentative. He knew everything better than anybody else, and it was an affront to his overweening10 vanity that you should disagree with him. He would not drop a subject, however unimportant, till he had brought you round to his way of thinking. The possibility that he could be mistaken never occurred to him. He was the chap who knew. We sat at the doctor’s table. Mr. Kelada would certainly have had it all his own way, for the doctor was lazy and I was frigidly indifferent, except for a man called Ramsay who sat there also. He was as dogmatic as Mr. Kelada and resented bitterly the Levantine’s cocksureness. The discussions they had were acrimonious and interminable.

Ramsay was in the American Consular Service and was stationed at Kobe. He was a great heavy fellow from the Middle West, with loose fat under a tight skin, and he bulged out of his ready-made clothes. He was on his way back to resume his post, having been on a flying visit to New York to fetch his wife who had been spending a year at home. Mrs. Ramsay was a very pretty little thing, with pleasant manners and a sense of humour. The Consular Service is ill paid, and she was dressed always very simply; but she knew how to wear her clothes. She achieved an effect of quiet distinction. I should not have paid any particular attention to her but that she possessed a quality that may be common enough in women, but nowadays is not obvious in their demeanour. It shone in her like a flower on a coat.

One evening at dinner the conversation by chance drifted to the subject of pearls. There had been in the papers a good deal of talk about the cultured pearls which the cunning Japanese were making, and the doctor remarked that they must inevitably diminish the value of real ones. They were very good already; they would soon be perfect. Mr. Kelada, as was his habit, rushed the new topic. He told us all that was to be known about pearls. I do not believe Ramsay knew anything about them at all, but he could not resist the opportunity to have a fling at the Levantine, and in five minutes we were in the middle of a heated argument. I had seen Mr. Kelada vehement and voluble before, but never so voluble and vehement as now. At last something that Ramsay said stung him, for he thumped the table and shouted.

“Well, I ought to know what I am talking about, I’m going to Japan just to look into this Japanese pearl business. I’m in the trade and there’s not a man in it who won’t tell you that what I say about pearls goes. I know all the best pearls in the world, and what I don’t know about pearls isn’t worth knowing.”

Here was news for us, for Mr. Kelada, with all his loquacity, had never told anyone what his business was. We only knew vaguely that he was going to Japan on some commercial errand. He looked around the table triumphantly.

“They’ll never be able to get a cultured pearl that an expert like me can’t tell with half an eye.” He pointed to a chain that Mrs. Ramsay wore. “You take my word for it, Mrs. Ramsay, that chain you’re wearing will never be worth a cent less than it is now.”

Mrs. Ramsay in her modest way flushed a little and slipped the chain inside her dress. Ramsay leaned forward. He gave us all a look and a smile flickered in his eyes.

“That’s a pretty chain of Mrs. Ramsay’s, isn’t it?”

“I noticed it at once,” answered Mr. Kelada. “Gee, I said to myself, those are pearls all right.”

“I didn’t buy it myself, of course. I’d be interested to know how much you think it cost.”

“Oh, in the trade somewhere round fifteen thousand dollars. But if it was bought on Fifth Avenue I shouldn’t be surprised to hear anything up to thirty thousand was paid for it.”

Ramsay smiled grimly.

“You’ll be surprised to hear that Mrs. Ramsay bought that string at a department store the day before we left New York, for eighteen dollars.”

Mr. Kelada flushed.

“Rot. It’s not only real, but it’s as fine a string for its size as I’ve ever seen.”

“Will you bet on it? I’ll bet you a hundred dollars it’s imitation.”

“Done.”

“Oh, Elmer, you can’t bet on a certainty,” said Mrs. Ramsay.

She had a little smile on her lips and her tone was gently deprecating.

“Can’t I? If I get a chance of easy money like that I should be all sorts of a fool not to take it.”

“But how can it be proved?” she continued. “It’s only my word against Mr. Kelada’s.”

“Let me look at the chain, and if it’s imitation I’ll tell you quickly enough. I can afford to lose a hundred dollars,” said Mr. Kelada.

“Take it off, dear. Let the gentleman look at it as much as he wants.”

Mrs. Ramsay hesitated a moment. She put her hands to the clasp.

“I can’t undo it,” she said, “Mr. Kelada will just have to take my word for it.”

I had a sudden suspicion that something unfortunate was about to occur, but I could think of nothing to say.

Ramsay jumped up.

“I’ll undo it.”

He handed the chain to Mr. Kelada. The Levantine took a magnifying glass from his pocket and closely examined it. A smile of triumph spread over his smooth and swarthy face. He handed back the chain. He was about to speak. Suddenly he caught sight of Mrs. Ramsay’s face. It was so white that she looked as though she were about to faint. She was staring at him with wide and terrified eyes. They held a desperate appeal; it was so clear that I wondered why her husband did not see it.

Mr. Kelada stopped with his mouth open. He flushed deeply. You could almost see the effort he was making over himself.

“I was mistaken,” he said. “It’s very good imitation, but of course as soon as I looked through my glass I saw that it wasn’t real. I think eighteen dollars is just about as much as the damned thing’s worth.”

He took out his pocketbook and from it a hundred dollar note. He handed it to Ramsay without a word.

“Perhaps that’ll teach you not to be so cocksure another time, my young friend,” said Ramsay as he took the note.

I noticed that Mr. Kelada’s hands were trembling.

The story spread over the ship as stories do, and he had to put up with a good deal of chaff that evening. It was a fine joke that Mr. Know-All had been caught out. But Mrs. Ramsay retired to her stateroom with a headache.

Next morning I got up and began to shave. Mr. Kelada lay on his bed smoking a cigarette. Suddenly there was a small scraping sound and I saw a letter pushed under the door. I opened the door and looked out. There was nobody there. I picked up the letter and saw it was addressed to Max Kelada. The name was written in block letters. I handed it to him.

“Who’s this from?” He opened it. “Oh!”

He took out of the envelope, not a letter, but a hundred-dollar note. He looked at me and again he reddened. He tore the envelope into little bits and gave them to me.

“Do you mind just throwing them out of the porthole?”

I did as he asked, and then I looked at him with a smile.

“No one likes being made to look a perfect damned fool,” he said.

“Were the pearls real?”

“If I had a pretty little wife I shouldn’t let her spend a year in New York while I stayed at Kobe,” said he.

At that moment I did not entirely dislike Mr. Kelada. He reached out for his pocketbook and carefully put in it the hundred-dollar note.

Keeping Errors at Bay

Bertrand Russell (England, 1872-1970)

To avoid the various foolish opinions to which mankind are prone, no superhuman genius is required. A few simple rules will keep you, not from all error, but from silly error.

If the matter is one that can be settled by observation, make the observation yourself. Aristotle could have avoided the mistake of thinking that women have fewer teeth than men by the simple device of asking Mrs. Aristotle to keep her mouth open while he counted. He did not do so because he thought he knew. Thinking that you know when in fact you don't is a fatal mistake, to which we are all prone. I believe myself that hedgehogs eat black beetles, because I have been told that they do; but if I were writing a book on the habits of hedgehogs, I should not commit myself until I had seen one enjoying this unappetizing diet. Aristotle, however, was less cautious. Ancient and medieval authors knew all about unicorns and salamanders; not one of them thought it necessary to avoid dogmatic statements about them because he had never seen one of them.

Many matters, however, are less easily brought to the test of experience. If, like most of mankind, you have passionate convictions on many such matters, there are ways in which you can make yourself aware of your own bias. If an opinion contrary to your own makes you angry, that is a sign that you are subconsciously aware of having no good reason for thinking as you do. If someone maintains that two and two are five, or that Iceland is on the equator, you feel pity rather than anger, unless you know so little of arithmetic or geography that his opinion shakes your own contrary conviction. The most savage controversies are those about matters as to which there is no good evidence either way. Persecution is used in theology, not in arithmetic, because in arithmetic there is knowledge, but in theology there is only opinion. So whenever you find yourself getting angry about a difference of opinion, be on your guard; you will probably find, on examination, that your belief is going beyond what the evidence warrants.

A good way of ridding yourself of certain kinds of dogmatism is to become aware of opinions held in social circles different from your own. When I was young, I lived much outside my own country—in France, Germany, Italy, and the United States. I found this very profitable in diminishing the intensity of insular prejudice. If you cannot travel, seek out people with whom you disagree, and read a newspaper belonging to a party that is not yours. If the people and the newspaper seem mad, perverse, and wicked, remind yourself that you seem so to them. In this opinion both parties may be right, but they cannot both be wrong. This reflection should generate a certain caution.

Becoming aware of foreign customs, however, does not always have a beneficial effect. In the seventeenth century, when the Manchus conquered China, it was the custom among the Chinese for the women to have small feet, and among the Manchus for the men to wear pigtails. Instead of each dropping their own foolish custom, they each adopted the foolish custom of the other, and the Chinese continued to wear pigtails until they shook off the dominion of the Manchus in the revolution of 1911.

For those who have enough psychological imagination, it is a good plan to imagine an argument with a person having a different bias. This has one advantage, and only one, as compared with actual conversation with opponents; this one advantage is that the method is not subject to the same limitations of time and space. Mahatma Gandhi deplored railways and steamboats and machinery; he would have liked to undo the whole of the industrial revolution. You may never have an opportunity of actually meeting anyone who holds this opinion, because in Western countries most people take the advantage of modern technique for granted. But if you want to make sure that you are right in agreeing with the prevailing opinion, you will find it a good plan to test the arguments that occur to you by considering what Gandhi might have said in refutation of them. I have sometimes been led actually to change my mind as a result of this kind of imaginary dialogue, and, short of this, I have frequently found myself growing less dogmatic and cocksure through realizing the possible reasonableness of a hypothetical opponent.

Be very wary of opinions that flatter your self‑esteem. Both men and women, nine times out of ten, are firmly convinced of the superior excellence of their own sex. There is abundant evidence on both sides. If you are a man, you can point out that most poets and men of science are male; if you are a woman, you can retort that so are most criminals. The question is inherently insoluble, but self‑esteem conceals this from most people. We are all, whatever part of the world we come from, persuaded that our own nation is superior to all others. Seeing that each nation has its characteristic merits and demerits, we adjust our standard of values so as to make out that the merits possessed by our nation are the really important ones, while its demerits are comparatively trivial. Here, again, the rational man will admit that the question is one to which there is no demonstrably right answer. It is more difficult to deal with the self‑esteem of man as man, because we cannot argue out the matter with some non‑human mind. The only way I know of dealing with this general human conceit is to remind ourselves that man is a brief episode in the life of a small planet in a little corner of the universe, and that, for aught we know, other parts of the cosmos may contain beings as superior to ourselves as we are to jelly‑fish.

Other passions besides self‑esteem are common sources of error; of these perhaps the most important is fear. Fear sometimes operates directly, by inventing rumours of disaster in war‑time, or by imagining objects of terror, such as ghosts; sometimes it operates indirectly, by creating belief in something comforting, such as the elixir of life, or heaven for ourselves and hell for our enemies. Fear has many forms—fear of death, fear of the dark, fear of the unknown, fear of the herd, and that vague generalized fear that comes to those who conceal from themselves their more specific terrors. Until you have admitted your own fears to yourself, and have guarded yourself by a difficult effort of will against their myth‑making power, you cannot hope to think truly about many matters of great importance, especially those with which religious beliefs are concerned. Fear is the main source of superstition, and one of the main sources of cruelty. To conquer fear is the beginning of wisdom, in the pursuit of truth as in the endeavour after a worthy manner of life.

Nine Puzzles

_1.

A jeweler has 3 diamonds. They all look exactly alike, but one diamond is heavier than the others. How can she identify the heavier diamond by using a balance scale just once? Please outline your argument as carefully as you can.

2. Same as above, but now the jeweler doesn’t know whether the odd diamond is lighter or heavier than the other two. By using the scale twice, how can she tell (i) which is the odd one, and (ii) whether it is lighter or heavier?

3. What do you see in the following two sketches?

4. One morning, exactly at sunrise, a Buddhist monk began to climb a tall mountain. The narrow path, no more than a foot or two wide, spiraled around the mountain to a glittering temple at the summit. The monk ascended the path at varying rates of speed, stopping many times along the way to rest and to eat the dried fruit he carried with him. He reached the temple shortly before sunset. After several days of fasting and meditation he began his journey back along the same path, starting at sunrise and again walking at variable speeds with many pauses along the way. His average speed descending was, of course, greater than his average climbing speed. Prove that there is a spot along the path that the monk will occupy on both trips at precisely the same time of day.

5. Three glasses contain liquid, and three are empty. Rearrange the glasses so that they alternate—one with liquid, one without, one with liquid, one without, etc. You are allowed to touch or move only one glass.

6. In her drawer, Cathy has six pairs of black gloves and six pairs of brown gloves . In complete darkness, how many gloves must she take from the drawer in order to be sure to get a matching pair? Think carefully!!

7. Cigars cannot be smoked all the way to the end, so most cigar smokers generate and discard butts. A poor man can make one cigar from every 5 discarded cigar butts he collects. Today, he collected 25 butts. How many cigars will he be able to smoke?

8. To tackle this problem, imagine yourself a raven. You can still reason as well (or as badly?J) as you always do, but you have the body of a raven. You are starving, and ravens do love meat. There is a fine chunk of salami about 3 feet below you, tied to a string. The other side of the string is securely tied to your perch. By now, you have unsuccessfully tried the following:

q Bending down as far as you can, grabbing the string with your bill and lifting it up--but it was too long and it still dangled down below you.

q Grabbing the salami chunk while flying, jumping upwards from the ground, or falling down from the perch.

q Tearing or untying the string.

q Breaking the perch.

q Climbing down the string (ravens, you found out, can’t do that sort of thing).

q Swinging the string upwards towards you.

q Coiling the string repeatedly around your perch.

And yet, that salami down there smells so very good! What are you going to do??? (For an online hint, and to see how elephants solved this program, go to: http://youtube.com/watch?v=rplLLmx5xtY)

9. Tower of Hanoi Puzzle

9. Imagine that you are faced with a board that has 3 pegs, I, II, and III (see the figure above). Peg I has 3 disks of different sizes, with the largest disk, G(reen), at the bottom, the middle one, R(ed), in the middle, and the smallest one, B(lue), on top. You need to transfer all 3 disks to peg III, as shown in the figure below—this is you goal state. In doing so, you must follow five rules:

1. You can only move one disk at a time.

2. A disk must be moved from one peg to another.

3. You can only move the top disk of a peg (e.g., in the first figure above, you can only move Disk B of Peg I to either Peg II or Peg III).

4. A disk cannot be placed on a disk smaller than itself (e.g., Disk R can never be placed on top of Disk B).

5. Number of allowed steps: 7 or less.

Write a step-by-step solution to this problem, so that a dumb robot might be able to follow your instructions.

Step 1.

Step 2.

Step 3.

Step 4.

Step 5.

Step 6.

Step 7.

Photo: The real tower of Hanoi

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