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How do you explain, it? This is what is known as a magic star. The total in every row adds up to the same. The sum of the numbers at the points do not add upto Now can you replace the numbers in such a way that their sums in every row and every point add upto 26? There was an old woman in the candy shop. I noticed something very strange, while she was weighing out the sweets.
She had just six wieghts and a balance scale. That's all she had. With just this she was able to weigh any unit number of ounces of candyright from 1 to Can you say what the six weights were? Here is an epitaph of the celebrated Greek mathematician of A. C a n you calculate his age from this? C a n you tell me what time it will be hours later?
O n e da she conducted a test for three of her students and when they handed back the test papers, they had forgotten to write their names. Parveen returned the papers to the students at random.
W h a t is the probability that none of the three students will get the right paper?
W e have an angle of 1 y2 How big will it look through a glass that magnifies things three times? A day to exchange gifts. Two fathers gave their sons some money.
O n e father gave his son Rs. But when the two sons counted their money, they found that between them they had become richer by only Rs.
How do you explain this? Try to figure out the answers: a Is there a largest pair of twin primes? This problem is a sure test of your ingenuity and resourcefulness. W h e n he counted the legs he found that there were altogether How many beetles and how many spiders did he collect?
O n e condition. The coins must be of 50F, 20P and 5P denominations. N o other coins would do. O n e hundred rupee for five! N o one went forward. S o m e people began to look for bits of papers and pencil in their pockets evidently to calculate their chances.
But no one went forward. The magician renewed his offer once agaig. N o one wants to make easy money! O f course, in the same denominations as I mentioned already. Twenty coins. How about that n o w? The magician went on. Only two rupeesjust two rupees' he showed his two fingers 'for rupees one hundred'. Y o u can't let go of such an opportunity, 37 really. Ladies and gentlemen. Just two rupeesin the denomination I mentioned alreadytwenty coins for rupees one hundred! He renewed his offer several times and finally he gave up.
W h y do you think no one came forward to take advantage of the magician's most attractive proposal? I had to send off the typescript to my publisher by the evening's mail. Mr Das G u p t a , my stenographer is a very experienced person and he, 39 I knew could do the job neatly and quickly.
But even he would take 2 hours to finish the job. This couldn't have done! Sq I decided to engage another typist. She would do a neat job, I was told, but she was not a fast typist like Mr Das Gupta. She looked at the job and said that if she were to do the entire job by herself, it would take her three hours. I decided to let them do the job side by side. Within how much time, can you tell, the two of them finished the work? And on this day we decided that my whole family should meet.
The gathering consisted of one grand-father, one grand-mother, two fathers, two mothers, four children, three grand-children, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in-law. 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 two figures in 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 at five for 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 off at 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? 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 the table so that they neither over lap each other nor the edge of the table. How many can we place in 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 begins to 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 of the 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 the judges. 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 at five past 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 of each kind must he use to make a blend of 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 temple they 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 weight of 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: 'The ship is twice as old as its boiler was when the ship was as old as the boiler is now.
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 a matching 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 training and 82 had had some in literature.
How many applicant shad had training in both mathe- matics and literature? PROBLEM FROM LILAVATI Here is an ancient problem from Bhaskaracharya's Lilavati: 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, it sounds complicated, doesn't it?
No, not if you know how to go about it. The distance from the foot of the ladder to the wall is 9 feet.