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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 download 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 download 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 download 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 download 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 download 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. Data Structures and Algorithms Alfred V.
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