New Delhi: 22 December is National Mathematics Day in India. It is celebrated to commemorate the birth anniversary of the Indian mathematical genius Srinivasa Ramanujan. On this occasion, here are 5 mathematical puzzles you can try to solve. These are not difficult at all, so most readers should be able to solve them.
Our first puzzle will be indirectly related to what we know as the Hardy–Ramanujan number. The story of the conversation between Ramanujan and the British mathematician GK Hardy is well known. An unwell Ramanujan was in the hospital, and Ramanujan’s mentor Hardy was visiting him. There, Hardy told Ramanujan that he had come to meet the latter in a taxi with a registration number, ‘1729’, and described it as “rather monotonous”. In response, Ramanujan has said: “No Hardy, that is a very interesting number! It is the smallest number that can be expressed as the sum of two cubes in two different ways.”
The anecdote led to the discovery of a special number – 1729 – which went on to be called the Hardy-Ramanujan number. This is Ramanujan’s most popular discovery till date.
National Maths Day Puzzle #1
1729 = 10³ + 9³ = 12³ + 1³.
1729 is the sum of 1000 and 729. 1000 is the cube of 10 and 72 is the cube of 99. Therefore, 1729 cube is the sum of 10 and 9.
Also, 1729 can be represented as the sum of 1728 and 1. 1728 is the cube of 12, and 1 is the cube of 1. Therefore, 1729 is also the sum of the cubes of 12 and 1.
Question: Can you find at least three other numbers that can be expressed as the sum of two cubes in two different ways?
National Mathematics Day Puzzle #2
Three persons are passing through a desert. X is carrying 15 liters of water, and Y is carrying 9 liters of water, but Z has broken his bottle and there is no water left. So X and Y pool their water, and all three share 24 liters equally.
When they finally cross the desert and reach a city, Z pays his companions Rs 800 to share water with them. But after he leaves, X and Y start fighting. X says that he should get more as he has contributed more water to the pool. “Let’s split it into a 15:9 ratio, or 5:3,” he says. But Y says that they should distribute the money equally as everyone has drank the same amount of water.
Question: Calculate the amount X and Y should get based on the amount of water deposited by them.
National Mathematics Day Puzzle #3
This is a puzzle inspired by another Indian mathematician Shakuntala Devi’s book. Here’s how it goes.
The length of the Delhi-Agra Expressway is 165 km. If we use other highway routes, the distance between the two cities is different, but always more than 200 km. Suppose there is a road of exactly 200 km between the two cities. One morning, you set out on a drive from Delhi to Agra. After checking the 4 tires of your car, you should also keep a spare. You decide that even if you don’t have a puncture, you will still use the spare.
In fact, being a mathematician, you decide that you will rotate and change the tires in such a way that at the end of the journey, each tire will have traveled the exact same distance.
Question: If you follow this plan, what will be the total distance covered by each tire?
National Mathematics Day Puzzle #4
In the book ‘The Moscow Puzzles’, the author of Entertaining Mathematics Boris A. Kordemsky describes a conversation between a lazy man and a devil, and ends it with a riddle.
In short, the devil makes a deal with the lazy person. If the lazy person crosses the bridge, Satan will double the lazy person’s money. If the lazy person crosses the bridge again, the devil will double his money again. This will continue as long as the idler fulfills one condition: after each crossing, he must pay 24 rubles to the devil.
The lazy man crosses the bridge, finds double his money, and gives 24 rubles to the devil. After crossing it a second time, his money is doubled again, of which he gives 24 rubles to the devil. After the third crossing, although his money has doubled for the third time, the idler learns that he has exactly 24 rubles. He gives it to the devil, who laughs and leaves.
Q: How much money did the idler have to start with?
Read also | Ramanujan Jayanti: 5 interesting facts about the great mathematical genius
National Mathematics Day Puzzle #5
In the wide ocean, two sharks are about to clash after seeing each other from a distance of 12 km. For the sake of this puzzle, we can ignore the fact whether it is possible for a shark to see and identify another shark so far away. On top of one shark is a seabird, which can see other sharks as well. As the shark under the bird rushes towards the other shark at 35 km/h, the bird also flies to the other shark in fun.
The bird’s flight speed is 80 km/h, which means it reaches the second shark long before the first shark arrives. In addition, the second shark is also running towards the first shark at a speed of 25 km/h. In fact, both the sharks started running towards each other right at that very moment and the bird also started its flight at that very moment.
When the bird approaches the second shark, it, without wasting time, turns back at that very moment, and begins flying towards the first shark, maintaining a flight speed of 80 km/h. When she gets to the first shark, she turns around once more and moves on to the second shark. It keeps on repeating this back and forth flight, never wasting a second, until the two sharks finally meet and begin their fight.
Question: What is the total distance covered by the bird?
Did you find the quiz interesting? Just take out your pen, notebook and calculator, or do the math in your head, and write to us if you think you have the right answers. use hashtags #ABPNationalMathematicsDayQuiz and post your answer Twitter, Facebook And Ku Latest by December 22 midnight. Don’t forget to tag us.
Solutions will be posted on ABP Live on Thursday 23 December.
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