The puzzles presented in this book are by none other than the world-renowned mathematical prodigy, Shakuntala Devi. These are meant to. Puzzles To Puzzle You-shakuntala Devi in meteolille.info for more Puzzles To Puzzle You-shakuntala Devi to download in pdf This book is very very excellent. Shakuntala-Devi meteolille.info - Download as PDF File .pdf) or view presentation slides The Penguine Book of Curious and Interesting Puzzles.

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Can you tell the number of oranges she originally had? Oh, by the way, she never had to cut an orange.

I picked it up, noted the number and took it home. In the afternoon the plumber called on me to collect his bill. As I had no other money at home, I settled his account with the hundred rupee note I had found. Later I came to know that the plumber paid the note to his milkman to settle his monthly account, who paid it to his tailor for the garments he had had made. The tailor in turn used the money to buy an old sewing machine, from a woman who lives in my neigh- bourhood.

This woman incidentally, had borrowed a hundred rupees from me sometime back to buy a pressure cooker. She, remembering that she owed me a hundred rupees, came and paid the debt. I recognised the note as the one I had found on the footpath, and on careful examination I discovered that the bill was counterfeit.

How much was lost in the whole transaction and by whom? From this I took out peanuts for use in my own home and gave away the bag with the remainder of peanuts to three little brothers who live in my neighbourhood and told them to distribute the nuts between themselves in proportion to their ages—rwhich together amounted to 1 years. Tinku, Rinku and Jojo, the three brothers, divided the nuts in the following manner: As often as Tinku took four Rinku took three and as often as Tinku took six Jojo took seven.

With this data can you find out what were the respec- tive ages of the boys and how many nuts each got? We began to wonder how old the couple must have been each at the time of their marriage! Can you figure it out? A wholesale merchant came to me one day and posed this problem.

Every day in his business he has to weigh amounts from one pound to one hundred and twenty- one pounds, to the nearest pound. To do this, what is the minimum number of weights he needs and how heavy should each weight be7 I decided to send them through my boy servant Harish.

On settlement Harish received Rs 2. How many glasses did Harish break? This num- ber is three times the sum of its digits. Can you find the number. Ten-of the ways have twofiguresin the integ- ral part of the number, but the eleventh expression has only one figure there. Can you find all the eleven expressions? One day a man walked in and slamming seventy- five paise on the counter requested, 'Please give me some 2 paise stamps, six times as many one paisa stamps, and for the rest of the amount make up some 5 paise stamps.

How would you have handled the situation? One day both of them were obliged to return home when each had thirty marbles unsold. They put together the two lots of marbles and handing them over to a friend asked her to sell them atfivefor 2 paise. According to their calculation, after all, 3 for one paise and 2 for one paise was exactly the same as 5 for 2 paise.

But when the takings were handed over to them, they were both most surprised, because the entire lot together had fetched only 24 paisel If however, they had sold their marbles separately they would have fetched 25 paise. Now where did the one paise go? Can you explain the mystery? His wife drives him over to Howrah Station every morning and in the evening exactly at 6 P. One day he was let offat work an hour earlier, and so he arrived at the Howrah Station at 5 P. He started walking home. They drove home arriving 10 minutes earlier than usual.

How long did the man have to walk, before he was picked up by his wife? At each of the 25 stations the passengers can get tickets for any of the others 24 stations. How many different kinds of tickets do you think the booking clerk has to keep?

Every son should receive three times as much as a daughter, and that every daughter should get twice as much as their mother. What is my aunt's share? Ws also have some beautiful bone-china saucers that I recently brought from Japan.

Our table top is fifteen times the diameter of our saucers which are also circular. We would like to place the saucers on thetable so that they neither over lap each other nor the edge of the table. How many can we placein this manner? I did some quick cal- culations in my mind. I found that if I walk down twenty-six steps, I require thirty seconds to reach the bottom.

However, if I am able to step down thirty-four stairs I would only require eighteen seconds to get to the bottom. If the time is measured from the moment the top step beginsto descend to the time I step off the last step at the bottom, can you tell the height of the stairway in steps?

This can be completely covered by 32 cardboard rectangles, each cardboard covering just 2 squares. If it can be done how can we do it? And if it cannot be done, prove it impossible. Every cat killed an equal number of mice. How many cats do you think there were? Ob, by the way let me clarify just two points—it is not one cat killed the lot, because I have said 'Cats' and it is not cats each killed one mouse, because I have used the word 'mice'.

I can give you just one clue—each cat killed more mice than there were cats. It was found that the fore wheels ofthe carriage make four more revolutions than the hind wheel in going 96 feet. Can you find the circumference of each wheel? Can you find this temperature?

Two gentlemen by the name of Sr. Guittierez and Sr. Ibanez decided to have a Llama race over the mile course on the beach sands. They requested me and some of my other friends whom I had met at the resort to act as thejudges.

We stationed ourselves at different points on the course, which was marked off in quarter miles. But, the two Llamas, being good friends decided not to part company, and ran together the whole way. How- ever, we the judges, noted with interest the following results: The Llamas ran the first three quarters in six and three quarters minutes. They took the same time to run the first half mile as the second half. And they ran the third quarter in exactly the same time as the last quarter.

From these results I became very much interested in finding out just how long it took those two Llamas to run the whole mile. Can you find out the answer? The numerals in each part in every case summed to a total of Can you show how the four parts of the clock face was broken? I decided to get only half the area of the window painted. Even after the painting I found that the clear part of the window still remained a square and still measured 4 feet from top to bottom and 4 feet from side to side.

How is it possible? One day he decided to sell them all and sold them to eight dealers. Each of the eight dealers bought the same number of animals and paid at the rate of Rs. My friend recieved from the dealers in total Rs.

How many animals in all did he have and how many of each kind? Recently while shopping in New Market in Calcutta, I came across two very nice frocks selling at a discount.

I decided to buy one of them for my little girl Mammu. The shopkeeper offered me one of the frocks for Rs. Of the two frocks which one do you think is a better bargain and by how much per cent? I started exactly at noon. We met on the Bangalore-Tumkur Road atfivepast four, and we both reached our destination at exactly the same time.

At what time did we both arrive? A cyclist rides along to work along the road every day at a constant speed of 12 miles per hour. He normally meets a train that travels in the same direction at the crossing. One day he was late by 25 minutes and met the train 6 miles ahead of the level crossing. Can you figure out the speed of the train? However, she felt bad after selling it and decided to buy it back from her friend' by offering her Rs.

After having bought it ooce again she felt that she did not really need the cooker. So she sold it at the auction for Rs. How much profit did she make?

Did she at all make any profit? Can you find the number? I am told that there are three other ways of arranging the numbers so as to produce the same result. Can you find the other three ways? The manufacturer knows the correct weight for a flywheel. However, one day one of the machines begins to pro- duce faulty parts—either overweight or underweight.

How can the manufacturer find the faulty machine in only two weighings? He bought one type of coffee powder at Rs. That gave him a profit of 25 per cent on the cost. How many kilos ofeach kind must he use to make a blendof a hundred kilos weight? I gave them a rupee more than half the money I had in my purse.

I must have walked a few more yards when a group of women approaphed me for donations for an orpbange. I gave them two rupees more than half the money I had in my purse. Then, after a few yards I was approached by a religious group for a donation to the templethey were building. At last when returned to my hotel room, I found that I had only one rupee remaining in my purse.

How much money did I have in my purse when I started? What are the numbers? The sari cost Rs. I saw an intelligent looking little boy playing all by himself on the grass. I decided to talk to him and just as an excuse to start the conversation I asked him his age. A mischivious glint flickered in his eyes and he replied, 'Two days back I was ten years old, and next year I shall be thirteen.

If you know what's today you'll be able to figure out my birthday and that'll give you my age. How old was the boy? What is the weightof the whole block.

They pooled in their savings, which came to Rs 2, They were both lucky, their business pros- pered and they were able to increase heir capital by 50 per cent every three years.

How much did they have in all at the end of eighteen years. I was curious to look around the ship one day and in the boiler room I asked a man how old the ship was.

He smiled and replied me in this way: And the combined age of the ship and the boiler is thirty years. The 19 ounce container is empty but the 13 and 7 ounce containers are full. How can we measure out 10 ounces by using only the three above mentioned containers? Taking all things into consideration how many were going to market? But if you add 8 to the denominator, the value of the fraction would then become 1. Can you find this fraction?

They both start out on the left foot. How many steps do they have to take before they are both stepping out on the right foot together? She keeps them all in the same drawer in a state of complete disorder. She has altogether 20 white socks and 20 brown socks in the drawer. Supposing she has to take out the socks in the dark, how many must she take out of the drawer to be sure that she has amatching pair?

Now how should the executor divide the land between Rashmi and Mala in a fair manner? He took out a coin from his pocket and said to me, 'Heads I win, tails I loose. I'll bet half the money in my pocket. He repeated the bet again and again each time offering half the money in his pocket. The game went on for quite some time. I can't re- collect exactly how long the game went on or how many times the coin was tossed, but I do remember that the times he lost was exactly equal to the number of times that he won.

What do you think, did he, on the whole, gain or loose? The response was good. One hundred people applied for the position. The company, however, wanted to make their selection from the applicants who had some training in both mathematics and literature. Of the one hundred applicants the company found that 10 of them had had no training in mathematics and no training in literature. Seventy of them had had some mathematical trainingand 82 had had some in literature.

How many applicantshad had training in both mathe- matics and literature? Beautiful maiden, with beaming eyes, tell me which is the number that, multiplied by 3, then increased by three- fourths of the product, divided by 7, diminished by one- third of the quotient, multiplied by itself, diminished by 52, the square root found, addition of 8, division by 10 gives the number 2?

Well, itsounds complicated, doesn't it? No, not ifyou know how to go about it. The distance from the foot of the ladder to the wall is 9 feet. How long should the ladder be? I was cu- rious to know how many of each he had. I stopped the car and inquired. Leaning on the stilejovially, he replied,'I have alto- gether 60 eyes and 86 feet between them.

What do you think is the answer? So when he came the next morning I demanded an explanation from him. He told me the following story: The previous morning when he just came out of the house carrying a basketful of eggs oh his head to start his daily rounds and stepped on to the street, a car going full speed brushed against him and knocked down his basket destroying all the eggs.

The driver, however, a thorough gentleman admitted his responsibility and offered to compensate him for'damages. But Rasool could not remember the exact number of eggs he had, but he estimated the number at between 50 and He was also able to tell the gentleman that if the eggs werecounted by 2's and 3's at a time, none would be left, butif counted by S's at a time, 3 would remain, and that he sold the eggs at SO paise a piece.

How much did the gentleman pay Rasool? A society of farmers who own farms in the vicinity of my home town Bangalore, planned on holding a raffle and persuaded me to buy a ticket. The value of the ticket was Rs. As I did not want to pay the entire amount myself, I asked my friend Radha to chip in with me, and offered to share with her in proportion the prize bounty— if there was going to be any. She paid Rs. As luck would have it—Bingo! Niether of us knew what to do with the sheep Where would we take them in the first place?

Neither of us had had any train- ing as shepherds! So we decided to sell the sheep back to the farmers. As per our original understanding 20 of the sheep belonged to Radha and 30 were mine. However, I decided that we had won the prize because of our combined luck, and so we should divide its value equally. The sheep—30 of mine and 20 of Radha's—were sold, each at the same-price, and I paid her Rs. What was the value per sheep? I decided to have it seen to.

Was my watch gaining or losing time, and how much per hour? Just when the trains' start out, a falcon leaves the first train and flies directly to the other train, and as soon as it reaches the second train, the bird starts backtowards the first train. It continues doing so, flying backwards and forwards from one train to the other until the trains meet.

Both the trains travel at a speed of 25 miles per hour, and the bird flies at miles per hour. How many mileswill the falcon have flown before the trains met? A businessman advertised twojob openings for peons in his firm. Two men applied and the businessman decided to engage both or them. He offered them a salary of Rs. They could have a raise of Rs.

The two men thought for a few moments and then one of them expressed his wish to take the raise at Rs per year, while the other man said he would accept the half yearly increase of Rs. Between the two men, who was the gainer, and by how much? What do you think? Sareen had three daughters Sudha, Seema and Reema—and their combined ages were half of hers.

During the next five years Sonny was born and Mrs. Sareen's age equalled the total of all her children's ages. After some years Kishu was born and then Sudha was as old as Reema and Sonny together.

And now, the combined age of all the children is double Mrs. Sareen's age, which is, as a matter of fact, only equal to that of Sudha and Seema together. Sudha's age is also equal to that of the two sons. What is the age of each one of them? The manager of the building told me that the building consisted of different kinds of apartments large and small. Altogether the building contained apart- ments.

Can you figure out how many apartments are there in eacb type, using round figures? The plate I got had a peculiar number on it.

It consisted of 5 different numbers and by mistake when I fixed it upside down the number could be still read, but the value had increased by What was my actual license number? He bought two lathes to use in his workshop.

However, he found out afterwards that they did not serve the purpose for which he had bought them, and so he decided to sell them. He sold them each for Rs. Did he lose or gain in the transaction, and how much did each machine cost him? I curiously noted that she just balanced against sixteen bricks, when these werefixedto the short end of the plank and I also noticed that if she were to fix them to the long end of the plank, she only needed eleven as balance.

I wondered what was the girl's weight. The brick, I could guess weighed equal to a three quarter brick and three quarters of a pound. If you were to close your eyes and pick them at ran- dom, how many marbles must you take out to be sure that there are at least two of one colour among the marbles picked out Can you find this number? How long will it taketo saw it into twelve equal pieces?

He was fond of both the women and had no special preference for either. One lived near Churchgate and the other in Bandra. He worked near a station midway between Churchgate and Bandra. After work he generally went to the station, and took whichever train got into the station first—Churchgate or Bandra. He arrived at whichever his destination it wast at random times, but found that be was visiting his Churchgate wife much more often than the other, despite the fact that both the Churchgate and Bandra trains were on schedules which brought him to hiS station equally often.

Since the same thing had been happening for a very long time, chance has been ruled out as the reason. Can you find the reason for the frequency of his Churchgate trips? Our party consisted of 4 different professional groups, namely 25 writers, 20 doctors, 18 dentists and 12 bank employees.

We spent altogether Rs. Later it was found that five writers spent as much as four doctors, that twelvedoctors spent as much as nine dentists, and that six dentists spent as much as eight bank employees.

How much did each of the four professional groups spend? When I came put I found that I had just as many paise as I had rupees and half as many rupees as I had paise when I went in.

How much money did I have on me when I entered? I spent a few days in a small town, where I stayed as a paying guest with a British landlady. The heaters in the rooming house were all coin operated. One day my landlady requested my help in sorting out a problem.

There were one hundred and twenty coins in her gas- meter and one of them, she knew, was counterfeit. The counterfeit coin was either heavier or lighter than the others.

Now the problem was to isolate this counterfeit coin and find out whether it was lighter or heavier, in five weighings. How can one do it? A certain container contains just one bacteria on the first day and there are twice as many on the next day. In this manner the number of bacteria in the container doubles itself everyday. Assuming that the container would be full of bacteria on the 10th day, on which day would the container be half full.

A man passing through the meadow one day saw Gopal grazing a number of sheep and in the course of a short cpnversation asked him how many of the grazing sheep were his own. Gopal's reply absolutely baffled him, which was as follows: Npw figure it out for yourself the number of sheep I own. They had agreed that whenever a player won a game he should double the money of each of the other players, in other words he was to give the players just as much money as they had already in their pockets.

In all they played seven games and, strangely, each won a game in turn in the order in which their names are given. But what was even more strange was that when they had finished the game each of the seven young men had exactly the same amount, Rs.

Can you find out how much money each person had with him before they began the game? So when he went around looking for a job as a farm-hand everyone refused to engage him, except farmer Gulab Singh, who was a very smart person. Gulab Singh engaged the services of Ram Rakhan at a salary of Rs. How- ever, he set a condition that he would forefeit Rs.

Ram Rakhan accepted the job. At the end of the month it was found that neither owed the other anything. This tought a lesson to Ram Rakhan. Can you tell jusf how many days Ram Rakhan worked and how many days he idled? A group of match sticks is placed on the table and then it is reduced in turn by eachplayer by removing from the group at least 1 but not more than 4 match sticks. The player who takes the last match stick is the winner. If there is a group of 17 match sticks on the table how would you make your first move, if it was your turn and how would you continue to play to win?

And in 30 years the son will be half as old as his father. Bat they were so small that I made the vendor throw in two extra guavas for the samfe price. As I began to walk away thevendor mumbled that this transaction had made him lose 10 paise a dozen less the price we had settled. How many guavas did I get for my Rs. I bad Rs. Which 6 coins did I have? Can you find the year of the twentieth century which gives the greatest number of occasions of this kind?

She pushed a large circular table we have at home, into the corner of the room, so that it touched both walls and spilled a spot of ink on the extreme edge, and she said, 'Mummy here is a little puzzle for you. Look at that spot. It is exactly eight inches from one wall and nine inches from the other, Now tell me the diameter of the table without measuring it.. Can you? Can you cut the spade into three pieces that will fit to- gether and form a heart?

Remember, no part of the material should be wasted. Can you find the numbers? There are at least two solutions. Finally he decided to propose marriage to his beloved and invited her to travel towards his place and offered to meet her on route and bring her home.

The man is able to cover 4 miles per hour to the woman's 3 milesper hour. How far will each have travelled upon meeting? However, in some States the law permits a custo- mer to consume, after the deadline, what has been sold before the curfew. In a certain bar 2 men ordered sufficient beer to cover their probable requirements in anticipation of the curfew. One man ordered and paid for 5 bottles and the other man ordered and paid for 3 bottles. But as the curfew sounded, an old friend of both the men approached and requested them to share with him the drinks.

The two man agreed and shared the total eight bottles of beer bet- ween them. The friend thanked the two men and put down Rs. How should this money be equitably divided between the two men? If you reverse my own age, the figures repre- sent my husband's age.

He is of course senior to me and thedifference betweenour ages is one-eleventh of their sum. Can you find out the woman's age as well as her hus- band's age? The passenger train takes three times as long to pass the goods—even when they are going in the opposite directions. If the trains run at uniform speeds, how many times faster than the freight train is the passenger train moving?

He had altogether kilos of rice and he wanted to distribute the grain to people in such a manner that each old person received three kilos, each youiig person two and each child half a kilo. How many old persons, young persons and children were there? The square root of half the number of bees in a swarm has flown out upon a jasmine bush; eightninths of the whole swarm has remained behind; one female bee flies about a male that is buzzing within the lotus flower into which he was allured in the night by its sweet odour, but is now inprisoned in it.

Tell me the number of bees? Last time there was load shedding in Calcutta, I was readinga very interesting book and I could not stop. My neighbour Parveen gave me two candles and assured me that I could manage with them. Though the candles were of the same length, Parveen told me that one candle would burn for four hours and the other for five hours.

After I had been reading for some time 1 put the candles out as the lights came on again. And I noticed that what remained of one candle was exactly four times the length of what was left of the other. Can you find out just how long those two candles were burning?

Can you connect 12 of these dots with straight fees to form a perfect cross which has five dots iaaido it and 8 dots outside? Can you find out how many goats did the last man have, if 6 cows eat as much as 4 mules, and 10 goats as much as 3 cows? And how much did the first and second man each pay? But if there were no stream they could row it in seven minutes less than it takes them to drift down the stream. Can you say how long it would take them to row down with the stream? Can you find the height of a steeple whose shadow at the same hour, is ft.

I had two bottles containing 10 ounces of each. I poured just a quarter of an ounce of spirits into the water and shook them up. You can see clearly that the mixture was forty to one. Now I thought that I should have the same quantity of fluid in both the bottles, and so I poured back a quarter of an ounce of the mixture into the bottle containing water.

It travels at the rate of one mile a minute through a tunnel which is also one mile long. Can you say how long it will take for the train to pus completely through the tunnel? He also owns a pasture to graze them all. During a visit I asked two of the men to tell me their ages. One replied, 'One of our ages subtracted from tke other's equals What were their ages?

Can you divide it into four pieces all of precisely the same size and shape? These are the smallest possible numbers. Can you find the tfumbers? I have two 10 paise coins. A man and a woman always played against a man and a woman. However, no person ever played with or against any other person more than once. They all played together in two courts on three successive days. Can you show how they could have done it? To quote an example three years ago a friend offered me a used typewriter for Rs.

A year later he offered me the same for Rs.

But I have decided to buy it when he reduces next time. If he does a consistent reduction, at what price will he offer the typewriter to me next? If I could have bought 4 more pineapples for Rs. What would be the price of each? I took the sections to a goldsmith and asked him to give me an estimate to join the 5 sections into a one piece necklace. The goldsmith wanted Re.

What is the cheapest method and how much should it cost me to get the five pieces joined together into one full necklace? Can you find the exact measurements for the sides of the boards? Demochares has lived one-fourth of his life as a boy, one-fifth 9s a youth, one-third as a man, and has spent thirteen years in his dotage.

How old is Demochares? How old is Reena? If thecube is cut into 27 cubes of 1"x 1" x 1", how many 1" cubes do have any painted surfaces?

How many cigarettes can be made and smoked from 36 butts? One taxi driver I had the occasion to travel with was particularly lacking in courtesy, and so I asked for bis number. The driver gave me a sardonical smile and said, 'Well, if you divide my number by 2, 3, 4, 5 or 6 you will find there is always 1 remaining. But if you divide it by 11 there is no remainder. Do you want to know something more? There aren't no other cabby in this town with a lower number than—who can say the same,' and he drove off, while 1 stood there completely baffled.

What was the man's number? When they finally arrived, I had them cleared through the Customs and engaged three labourers to carry theip to my home 3 miles distant. As I was going to pay each of them equal amounts, they decided to carry a crate each equal distance. How did they manage to do it? Portchester" in London he was facing a serious problem pouring his wine from one vessel to the other.

Portchester had two ten quart containers full of wine. He also had a five quart and a four quart measure. All he wanted to do was put exactly three quarts into each of the two measures. He was standing there wondering how he is to do itl Now I offered to help and gave him some suggestions. Can you find out what was my suggestion, and how many manipulations of pouring from one vessel to the other did he require, without waste of any wine, tilting or other tricks.

Can you draw four straight lines, the second beginning where the first ends, the third beginning where the second ends, and the fourth beginning where the third ends so that each dot is or at least one line? If one-fifth of a hive of bees flew to the badamba flower, one-third flew to the slandbara, three times the difference of these two numbers flew to an arbour, and one bee continued to fly about, attracted on each side by the fragrant Ketaki and Malati, what was the number of bees?

If a player is eliminated as soon as he loses a match, how many matches are required to determine the winner? On the last day I did 51 miles, increasing my journey 4 miles each day. How many days did I travel and how far? How can these three, have each his own true Sabbath on the same day? He wanted the picture itself to occupy 72 square inches. What should be the smallest dimensions, the canvas he is going to obtain, should possess? The four sides of the garden are known to be 20, 16, 12 and 10 rods.

And it is also known that it has the greatest possible area for those sides. Can you find the area? The average price of the animals per head worked to Rs. How many animals of each kind did he buy? Before retiring they did some quick counting and found that the fruits were less than a hundred in number.

During the night one thief awoke, counted the mangoes and found that he could divide the mangoes into three equal parts if he first took one for himself. Shortly thereafter another thief awoke, counted the mangoes and he again found that if he took one Cor himself the loot could be divided into three equal parts. He ate up one mango, bagged J of. The third thief also awoke after some time, did the same and went back to sleep.

In the morning when they all woke up; and counted their mangoes, they found that the remaining mangoes again totalled 1 more than could be divided into three equal parts. Anonymous September 17, at 2: Amar Bharat Bhopi September 20, at Anonymous October 2, at Rajesh kumar Nayak October 26, at 1: Rocky The Star November 7, at Rohit Khairnar November 22, at 8: Unknown January 23, at 6: Rohan Kshirsagar February 3, at 8: Pragyesh Katyan February 5, at 8: Pritish Singhal March 4, at 4: Geeta Chawla March 15, at 3: Nived Sreenadhan March 20, at 6: Anonymous June 6, at 2: Anupam Patra October 2, at Anonymous October 20, at Biranchi Narayan Nayak October 21, at 8: Goondla Suresh October 24, at 3: Deepak Yadav November 7, at Beben Habibi May 16, at Unknown August 20, at Stacey Jones September 28, at Purva Khare October 17, at 2: Anonymous October 22, at Stiff Roy November 29, at 4: Joseph March 6, at 3: Unknown April 2, at