# 536 PUZZLES AND CURIOUS PROBLEMS PDF

Dudeney began his puzzle career by contributing short problems to to Puzzles and Curious Problems, "although he cared comparatively little. some read an uplifting story, and others may watch an inspiring inevosisan.ga I have quotes placed anywhere that I can see. Puzzles and Curious Problems Paperback – August 17, For two decades, self-taught mathematician Henry E. Dudeney wrote a puzzle page, "Perplexities," for The Strand Magazine. Martin Gardner, longtime editor of Scientific American's mathematical games column, hailed.

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Puzzles & Curious Problems - Ebook download as PDF File .pdf) or read book online. Curious Problems, Brain Teasers. By Henry Ernest Dudeney ( PUZZLES &CURIOUS PROBLEMS BY Henry Ernest Dudeney Download PDF Two posthumous collectionsappeared: Puzzles and Curious Problems () and A Puzzle-Mine (undated). Puzzles & Curious Problems book. Read 5 reviews from the world's largest community for readers.

Little Mike, who was forty months old when Pat built the sty,is now two years more than half as old as Pat's wife, Biddy, was when Patbuilt the sty, so that when little Mike is as old as Pat was when he built thesty, their three ages combined will amount to just one hundred years.

Howold is little Mike?

THEIR AGES Rackbrane said the other morning that a man on being asked the ages ofhis two sons stated that eighteen more than the sum of their ages is doublethe age of the elder, and six less than the difference of their ages is the age ofthe younger.

What are their ages? Age Puzzles 13four times as old; last year I was three times as old; and this year I am twoand one-half times as old. What was the age ofeach? Every age was an exact number of years. The readermay think, at first sight, that there is insufficient data for an answer, but hewill be wrong: A man's age at death was one twenty-ninth of the year of his birth. Howold was he in the year ? This tempted us to work out the day of his birth.

Perhapsthe reader may like to do the same. We will assume he was born at midday. Boadicea died one hundred and twenty-nine years after Cleopatra wasborn. Their united ages that is, the combined years of their complete lives were one hundred years. Cleopatra died 30 B.

When was Boadicea born? One little incident was fresh in my memory when I awakened. Isaw a clock and announced the time as it appeared to be indicated, butmy guide corrected me.

Except for this improvement, ourclocks are precisely the same as. At what time are the two hands of a clock so situated that, reckoningas minute points past XII, one is exactly the square of the distance of the other?

If it was set going at noon, what would be the first timethat it would be impossible, by reason of the similarity of the hands, to besure of the correct time?

Readers will remember that with these clock puzzles there is the conventionthat we may assume it possible to indicate fractions of seconds. On thisassumption an exact answer can be given. George fell into the trap that catches so manypeople, of writing the fourth hour as IV, instead of I1II. Clock Puzzles 15 Colonel Crackham then asked themto show how a dial may be broken intofour parts so that the numerals oneach part shall in every case sum to As an example he gave our illustra-tion, where it will be found that theseparated numerals on two parts sumto 20, but on the other parts they addup to 19 and 21 respectively, so it fails.

But it was found that they hadreally only changed places. As you know, the dancing commenced betweenten and eleven oclock. What was the exact time of the start?

What was the correct time? On his return between fourand five oclock he noticed that the hands were exactly reversed. What werethe exact times that he made the two crossings? How far was it to the topof the hill? Ackworth, who is leading, went up three steps at a time, asarranged; Barnden, the second man, went four steps at a time, and Croft, who. Undoubtedly Ackworth wins.

But the point is, howmany steps are there in the stairs, counting the top landing as a step? I have only shown the top of the stairs. There may be scores, or hundreds,of steps below the line. It was not necessary to draw them, as I only wantedto show the finish.

But it is possible to tell from the evidence the fewest pos-sible steps in that staircase. Can you do it? They met on the road at five minutes past four oclock, andeach man reached his destination at exactly the same time. Can you sayat what time they both arrived? How long would ittake him to ride a mile if there was no wind? Some will say that the average. That answer is entirely wrong.

How long would it take torow down with the stream? What isthe height of the stairway in steps? The time is measured from the momentthe top step begins to descend to the time I step off the last step at the bottomonto the level platform.

They hadonly a single bicycle, which they rode in turns, each rider leaving it in thehedge when he dismounted for the one walking behind to pick up, and walk-ing ahead himself, to be again overtaken. What was their best way of arrang-ing their distances?

As their walking and riding speeds were the same, itis extremely easy. Simply divide the route into any even number of equal stagesand drop the bicycle at every stage, using the cyclometer.

Each man wouldthen walk half way and ride half way. But here is a case that will require a little more thought. Anderson and Brownhave to go twenty miles and arrive at exactly the same time. They have onlyone bicycle. Anderson can only walk four miles an hour, while Brown canwalk five miles an hour, but Anderson can ride ten miles an hour to Brown'seight miles an hour.

How are they to arrange the journey? Each man always either walks orrides at the speeds mentioned, without any rests.

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As a matter of fact, I understand that Andersonand Brown have taken a man named Carter into partnership, and the positiontoday is this: Anderson, Brown, and Carter walk respectively four, five, andthree miles per hour, and ride respectively ten, eight, and twelve miles perhour.

How are they to use that single bicycle so that all shall completethe twenty miles' journey at the same time? Atkins had a motorcycle with a sidecar for one passenger.

How was he to take one of his companions a certain distance, drop him on theroad to walk the remainder of the way, and return to pick up the second friend,who, starting at the same time, was already walking on the road, so that theyshould all arrive at their destination at exactly the same time? The motorcycle could do twenty miles an hour, Baldwin could walk fivemiles an hour, and Clarke could walk four miles an hour. Of course, each wentat his proper speed throughout and there was no waiting.

I might have complicated the problem by giving more passengers, butI have purposely made it easy, and all the distances are an exact number ofmiles-without fractions. It was found that when they went in oppositedirections they passed each other in five seconds, but when they ran in the samedirection the faster train would pass the other in fifteen seconds.

A curious. Can the reader discover the correct answer? Of course, each train ran witha uniform velocity. A passes C milesfrom Pickleminster and D miles from Pickleminster. Now,what is the distance from Pickleminster to Quickville? Every train runs uni-formly at an ordinary rate. We had to continue the journey at three-fifths of the former speed.

It madeus two hours late at Clinkerton, and the driver said that if only the accidenthad happened fifty miles farther on the train would have arrived forty minutessooner. Can you tell from that statement just how far it is from Anglechesterto Clinkerton? Brown was the best runner and gave Tompkins a start of one-eighth of thedistance. But Brown, with a contempt for his opponent, took things too easilyat the beginning, and when he had run one-sixth of his distance he metTompkins, and saw that his chance of winning the race was very small.

How much faster than he went before must Brown now run in order to tiewith his competitor? The puzzle is quite easy when once you have grasped itssimple conditions. Two ships sail from one portto another-two hundred nautical miles-and return. The Mary Jane travels. The ElizabethAnn travels both ways at ten miles an hour, taking forty hours on the doublejourney. Seeing that both ships travel at the average speed often miles per hour, whydoes the Mary Jane take longer than the Elizabeth Ann?

Perhaps the readercould explain this little paradox. Jones executed his commissionat B and, without delay, set out on his return journey, while Kenwardas promptly returned from A to B. They met twelve milesfrom B. Of course, each walked at a uniform rate throughout. Howfar is A from B? I will show the reader a simple rule by which the distance may be foundby anyone in a few seconds without the use of a pencil.

In fact, it is quiteabsurdly easy-when you know how to do it. One day, forexample, he waited, as I left the door, to see which way I should go, and whenI started he raced along to the end of the road, immediately returning to me;again racing to the end of the road and again returning.

He did this four timesin all, at a uniform speed, and then ran at my side the remaining distance,which according to my paces measured 27 yards. I afterwards measured thedistance from my door to the end of the road and found it to be feet. Now,ifl walk 4 miles per hour, what is the speed ofmy dog when racing to and fro? Andersonset off from an hotel at San Remo at nine oc1ock and had been walking an. Baxter's dog startedat the same time as his master and ran uniformly forwards and backwardsbetween him and Anderson until the two men were together.

Anderson'sspeed is two, Baxter's four, and the dog's ten miles an hour. How far had thedog run when Baxter overtook Anderson? He drinkss quarts of beer for every mile that he runs. Prove that he will only need onequart!

## 536 Puzzles and Curious Problems

They wish to explore the interior, always going due west. Each car can travelforty miles on the contents of the engine tank, which holds a gallon of fuel,and each can carry nine extra gallon cans of fuel and no more.

Unopenedcans can alone be transferred from car to car. What is the greatest distanceat which they can enter the desert without making any depots of fuel for thereturn journey? The circuit was exactly a hundred miles in length and he had to do itall alone on foot. He could walk twenty miles a day, but he could only carryrations for two days at a time, the rations for each day being packed in sealedboxes for convenience in dumping.

He walked his full twenty miles every dayand consumed one day's ration as he walked. What is the shortest timein which he could complete the circuit? This simple question will be found to form one of the most fascinating. It made a considerable demandon Professor Walkingholme's well-known ingenuity. The idea was suggestedto me by Mr. He is an invalid, and at12 noon started in his Bath chair from B towards C.

His friend, who hadarranged to join him and help push back, left A at He joined him, and with his help they went backat four miles per hour, and arrived at A at exactly 1 P.

How far did ourcorrespondent go towards C? A passenger at theback of the train wishes to walk to the front along the corridor and in doingso walks at the rate of three miles per hour. At what rate is the man travellingover the permanent way? We will not involve ourselves here in quibbles anddifficulties similar to Zeno's paradox of the arrow and Einstein's theory ofrelativity, but deal with the matter in the simple sense of motion in referenceto the permanent way.

Right away!

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What is the correct number of trains? His gardener and a boy both insisted on carrying the luggage; butthe gardener is an old man and the boy not sufficiently strong, while thegentleman believes in a fair division oflabor and wished to take his own share.

They started off with the gardener carrying one bag and the boy the other,while the gentleman worked out the best way of arranging that the three shouldshare the burden equally among them.

How would you have managed it? It isassumed that each man travelled at a uniform rate, and the speed of thestaircase was also constant.

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The four cyclists started at noon. Each person rode round a different circle, one at the rate of six miles an hour,another at the rate of nine miles an hour, another at the rate of twelve milesan hour, and the fourth at the rate of fifteen miles an hour.

They agreed to ride. The distance round each circle was exactly one-third of a mile. When did theyfinish their ride? Atkins could walk one mile an hour, Brown could walktwo miles an hour, and Cranby could go in his donkey cart at eight miles anhour. Cranby drove Atkins a certain distance, and, dropping him to walk theremainder, drove back to meet Brown on the way and carried him to theirdestination, where they all arrived at the same time.

Of course each went at a uniform ratethroughout. Andrews is acertain distance behind Brooks, and Carter is twice that distance in front ofBrooks. Each car travels at its own uniform rate of speed, with the result thatAndrews passes Brooks in seven minutes, and passes Carter five minutes later. In how many minutes after Andrews would Brooks pass Carter?

A car, A, starts at noon from one end and goesthroughout at 50 miles an hour, and at the same time another car, B, goinguniformly at miles an hour, starts from the other end together with a flytravelling miles an hour. When the fly meets car A, it immediately turnsand flies towards B. The fly then turns towards A and continues flying backwards and forwardsbetween A and B.

A bit of exercise, you know.

## 536 puzzles and curious problems

But this is the long-est stairway on the line-nearly a thousand steps. I will tell you a queer thingabout it that only applies to one other smaller stairway on the line. If I go uptwo steps at a time, there is one step left for the last bound; if I go up threeat a time, there are two steps left; ifl go up four at a time, there are three stepsleft; five at a time, four are left; six at a time, five are left; and if I went upseven at a time there would be six steps left over for the last bound.

Now,why is that? The bottom floor does not count as a step, and thetop landing does. He constructs by means of folding an equilateral triangle, a right-angled triangle, a regular hexagon, a regular octagon, and a divides a segment into two pieces so that the ratio between the pieces is the golden ratio. He uses the last construction in order to indicate that the pentagon can also be constructed using the former construction. To emphasize: paper folding was already thought of as a recreational mathematical activity starting from the 17th century [Friedman, Rougetet ].

He gives, for example, the equations of the curves which can be constructed with folding — a tradition that only began with Row. Even if Ahrens brought paper folding to the awareness of the broader public in general and mathematicians in particular in the 20th century, he himself claims that precisely the games and activities that he presents in his book, trying to consider them mathematically, are or were usually considered uninteresting or non- scientific either by the mathematicians or by the layman, as they could not prompt any scientific interest [ibid.

To give two examples: the mathematician Adolf Hurwitz refers to it, writing on 24 December in his diary an entire section on how to construct regular polygons using only paper folding, adding that Ahrens has written about these kind of constructions [Oswald ]. A second example appears six years later. This section, however, only describes how one may construct several regular polygons [Ghersi, , p.

In his book Mathematische Spiele [], Ahrens does not mention paper folding. This reproduction results, according to Ahrens, in a non-harmonic work. He also published several books, such as Amusements in Mathematics [], Modern Puzzles [], and Puzzles and Curious Problems [] — the latter appearing posthumously. His book already contained a few folding exercises, which cannot be regarded, however, as strictly mathematical.

It is important to note that all the solutions Dudeney provided in no way explain the mathematical principles involved in their resolution. This situation changes in Sundara Row Madras, A second type of problem is completely new, which involves a more complicated mathematical argument for its solution. That is about as simple a question as we could put, but it will puzzle a good many readers to discover just where to make that fold.

The solution Dudeney provides, however, is unclear. Now the line DEF gives the direction of the shortest possible crease under the conditions. In addition, drawing the semicircle is not an operation that can be done only with folding. The book Puzzles and Curious Problems also contained a few other folding problems.

## Post Pagination

One of these problems is the folding of the pentagon by using only a rectangular piece of paper [Dudeney , p. The solution that Dudeney presents see figure 2 c , however, does not mention this related problem.

Moreover, the solution uses implicitly unstated geometrical principles related to folding such as that folding exactly one section on another implies that the two have equal lengths [Dudeney , p. Even if Dudeney certainly contributed to how folding was mathematically conceptualized within recreational puzzles, this manner of dissemination also came with some disadvantages.

A break from other folding traditions — also within recreational mathematics8 — is to be noticed, as well as a few vague geometrical considerations; the solution of the shortest-crease problem might indicate the way to solve the problem, but does not explain why it is the solution.

This enabled Beloch to prove that one can, using paper folding, construct segments whose length is the real solution of equations of the third and the fourth degree. Lotka [] and C. Rupp []. Although the influence of Row on the pedagogical methods within schools is beyond the scope of this article, I would like to make a detour and examine the works of two mathematicians: Robert C.

Yates and Donovon A. Dudeney does not, however, provide any references to Lucas in his book.

The methods he gives, however, are quite involved in a structural sense. Hence, it is not surprising that two years before, in his book Tools.

A Mathematical Sketch and Model Book, where he deals [, pp. He also provides instructions how to knot from a rectangular paper regular polygons [ibid. Johnson thanks Yates at the beginning of his book. An intriguing way of adding realism and interest to mathematics teaching is to fold paper.

Such an omission may be seen as a disservice, since mathematical research on knot theory was flourishing at that time. Similar figures of the right side appeared in Yates [, p.

## 536 Puzzles and Curious Problems

Other exercises, which are regarded as recreational, are the construction of a cube, of a sphere or of a Christmas-star. Qu This is quite a delightful book, many of the puzzles here especially the ones on combinatorics, number theory, and topology are quite interesting and have a lot of mathematical thought hidden within them.

I find these rather irritating. Perhaps it would have been better to have or so good puzzles and leave it at that. All of the currency and distance questions are in imperial instead of decimal. Don't let this discourage you however, it can just easily be considered part of the puzzle. While puzzles with a mathematical theme have been around for thousands of years, two people that lived in the nineteenth century codified the field and developed most of the forms of puzzles that people still enjoy today.

This book was edited by the late great recreational mathematician Martin Gardner and he has selected many of the best puzzles produced by Dudeney. The breadth of the material is so thorough that you could take nearly any puzzle book published in the last decade and recognize the ancestry of all the puzzles from those in this book. The main categories of the puzzles are: This is a great book for all to enjoy, it will exercise your mental muscles and like all great puzzles, the solutions are in almost all cases obvious in retrospect.

This review appears on site. A differenza del suo collega e rivale Sam Loyd - e si nota subito la differenza tra un inglese e un americano! Questo libro, edito dall'onnipresente Martin Gardner, raccoglie due sue opere: Modern Puzzles e Puzzles and Curious Problems.

Le note di Martin Gardner sono poche ma preziose, raccontando degli ulteriori miglioramenti di alcuni risultati o dei pochi errori del libro. Lena Nechet rated it it was amazing Feb 24, Com rated it really liked it Jul 05, Jeffrey rated it liked it Jun 07, Rajesh rated it really liked it Apr 06, Ken Brooker rated it it was ok Dec 04, Yashika Sharma rated it it was ok Aug 13, A good collection of puzzles, but showing its age.

Who now remembers "The Turkish stampede in Thrace"? Some of the explanations are a bit perfunctory. Still , Dudeney was undoubtedly the foremost puzzlist of his age, and many of these puzzles remain classics today. Obstreperouspear rated it it was amazing Dec 01, Llewellyn Sterling rated it it was amazing Oct 03, Arnost Stedry rated it liked it Feb 03, Adam Tervort rated it liked it Mar 03, Arun Kadam rated it did not like it Apr 17, Troy Chertok rated it liked it Jun 22, Sage rated it really liked it Jul 30, Srinusree rated it did not like it Dec 10, A curious.

The point is to express all possible whole numbers with fourfours no more and no fewer , using the various arithmetical signs. Original Title. Spectrum, , The motorcycle could do twenty miles an hour, Baldwin could walk fivemiles an hour, and Clarke could walk four miles an hour. He picked it up, noted the number, and went tohis home for luncheon. Someof these additions correct errors or point out how an answer has been improvedor a problem extended by later puzzle enthusiasts.

But Brown, with a contempt for his opponent, took things too easilyat the beginning, and when he had run one-sixth of his distance he metTompkins, and saw that his chance of winning the race was very small. How far apart are theyexactly an hour before they meet? Similar figures of the right side appeared in Yates [, p.

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