Mathematical Puzzle

While walking down the street, one morning, I found a hundred rupee note on the footpath. 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 neighbourhood. 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?View SolutionSubmit Solution 2569 views
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A little girl I know sells orange^ from door to door.
One day while on her rounds she sold 1/2 an orange more than half her oranges to the first customer. To the second customer she sold 1/2 an orange more than half of the remainder and to the third and the last customer she sold 1/2 an orange more than half she now had, leaving her none.
Can you tell the number of oranges she originally had? Oh, by the way, she never had to cut an orangeView SolutionSubmit Solution 2670 views
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We all know that the hour hand and the minute hand on a clock travel at different speeds. However there are certain occasions when the hands are exactly opposite each other. Can you give a simple formula for calculating the times of these occasions?
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While visiting a small town in the United States, I lost my overcoat in a bus. When I reported the matter to the bus company I was asked the number of the bus. Though I did not remember the exact number I did remember that the bus number bad a certain peculiarity about it. The number plate showed the bus number as a perfect square and also if the plate was turned upside down.? the number would still be a perfect square—of course it was not?
I came to know from the bus company they had only five hundred buses numbered from 1 to S00.
From this I was able to deduce the bus number. Can you tell what was the other numberView SolutionSubmit Solution 6387 views
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All the nine digits are arranged here so as to form four square numbers:
9, 81, 324, 576
How would you put them together so as to form a single smallest possible square number and a single largest possible square number?View SolutionSubmit Solution 2694 views
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A friend of mine runs a bicycle shop and he narrated to me this following story:
A man, who looked like a tourist, came to his shop one day and bought a bicycle from him for Rs. 350. The cost price of the bicycle was Rs. 300. So my friend was happy that he had made a profit of Rs. 50 on the sale. However, at the time of settling the bill, the tourist offered to pay in travellers cheques as he had no cash money with him. My friend hesitated. He had no arrangements with the banks to encash travellers cheques. But he remembered that the shopkeeper next door had such a provision, and so he took the cheques to his friend next door and got cash from him.
The travellers cheques were ^11 made out for Rs. 100 each and so he had taken four cheques from the tourist totalling to Rs. 400! On encashing them my friend paid back the tourist the balance of Rs. 50.
The tourist happily climbed the bicycle and pedalled away whistling a tune.
However, the next morning my friend’s neighbour, who had taken the travellers cheques to the bank, called on him and returning the cheques which had proved valueless demanded the refund of his money. My friend quietly refunded the money to his neighbour and tried to trace the tourist who had given him the bad cheques and taken away his bicycle. But the tourist could not be found.
How much did my friend lose altogether in this unfortunate transaction?View SolutionSubmit Solution 3372 views
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On Bagshot Island, there is an airport. The airport is the homebase of an unlimited number of identical airplanes. Each airplane has a fuel capacity to allow it to fly exactly 1/2 way around the world, along a great circle. The planes have the ability to refuel in flight without loss of speed or spillage of fuel. Though the fuel is unlimited, the island is the only source of fuel.
What is the fewest number of aircraft necessary to get one plane all the way around the world assuming that all of the aircraft must return safely to the airport? How did you get to your answer?Notes:
(a) Each airplane must depart and return to the same airport, and that is the only airport they can land and refuel on ground.
(b) Each airplane must have enough fuel to return to airport.
(c) The time and fuel consumption of refueling can be ignored. (so we can also assume that one airplane can refuel more than one airplanes in air at the same time.)
(d) The amount of fuel airplanes carrying can be zero as long as the other airplane is refueling these airplanes. What is the fewest number of airplanes and number of tanks of fuel needed to accomplish this work? (we only need airplane to go around the world)View SolutionSubmit Solution 27730 views
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4, 6, 12, 18, 30, 42, 60, 72, 102, 108, ?, ?, ?
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You can place weights on both side of weighing balance and you need to measure all weights between 1 and 1000. For example if you have weights 1 and 3,now you can measure 1,3 and 4 like earlier case, and also you can measure 2,by placing 3 on one side and 1 on the side which contain the substance to be weighed. So question again is how many minimum weights and of what denominations you need to measure all weights from 1kg to 1000kg.
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Two old friends, Jack and Bill, meet after a long time.
Jack: Hey, how are you man?
Bill: Not bad, got married and I have three kids now.
Jack: That’s awesome. How old are they?
Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jack: Cool… But I still don’t know.
Bill: My eldest kid just started taking piano lessons.
Jack: Oh now I get it.How old are Bill’s kids?
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