Latest news with #Dudeney
Hindustan Times
12 hours ago
- General
- Hindustan Times
Find the square
I learnt something new and interesting recently. Most puzzle solvers, including you readers of Problematics, probably know this already, but here it is anyway. To check if a number is a perfect square, one way to proceed is to keep adding its digits until you reach a single digit. If it's a square, the ultimate 'digital root' in a single digit must be any one of 1, 4, 7 and 9 — and nothing else. Welcome to Problematics!(Shutterstock) For example, the digital root of 16 is 1 + 6 = 7, that of 81 is 8 + 1 = 9, that of 49 is 4 + 9 = 13 followed by 1 + 3 = 4, and that of 676 is 6 + 7 + 6 = 19 followed by 1 + 9 = 10 and finally 1. There are, of course, numbers that can have digital roots of 1, 4, 7 or 9 without being perfect squares, for example 70 whose root is 7. So the method may not always tell you if a number is a perfect square, but it will definitely help you rule out many possibilities. #Puzzle 148.1 A century ago, the English puzzler Henry Ernest Dudeney presented six numbers to his readers: 4784887 2494651 8595087 1385287 9042451 9406087 Three of them can be added to form a perfect square, Dudeney wrote, inviting his readers to identify them. I managed to find the three numbers using hit and trial, paired with some observations that eliminated one or more possibilities. Then I looked at Dudeney's solution and learnt about digital roots and how the rule could be applied to solve this puzzle. Who knows, there may be other methods too. Use any method — hit and trial, digital roots, or any procedure you may innovate yourself. But do send me the three numbers that satisfy the condition. #Puzzle 148.2 The Village of Music is organising a concert and has invited a musician from the Village of Astronomy. The Village of Astronomy, on the other hand, is inaugurating a telescope and has invited an astronomer from the Village of Music. By sheer coincidence, both events begin at the same time on the same day. The musician from Astronomy, who wants to get some exercise, decides to walk the whole distance and sets off towards Music at 12 noon on the day of the event. The astronomer from Music chooses to cycle the distance and sets off towards Astronomy at 2pm. Both are good puzzlers and can manage their respective speeds precisely. Indeed, each one arrives at his destination at the exact moment that his event starts. This is after the two had met on the way, which happened at 4:05pm. They called out 'HI!' to each other but neither stopped. At what time do the two events start? MAILBOX: LAST WEEK'S SOLVERS #Puzzle 147.1 HT picture Hi Kabir, Based on the conditions that surnames and addresses do not begin with the same letter, and that of four statements only one is true, we can map different scenarios as shown in the table. Statement 1 is not possible. From the other three statements, whichever one is true, only one address can be established for sure, i.e the Poonawala family lives in Surat. — Sabornee Jana, Mumbai *** Hi, The only address that can be definitely established is that the Poonawala family is from Surat. Statement (1) must be false. Statements (2), (3) and (4) give different combinations that do not violate the given conditions. Therefore any two of them can be false. But no matter which one statement is true, one address is common to each combination — the Poonawala family must live in Surat. — Ajay Ashok, Delhi #Puzzle 147.2 Hi Kabir, Each of the ten statements contradicts every other statement. Therefore, at the most one can be true. That is, either exactly one statement is true (this is what statement 9 is) or none of them is true (this is what statement 10 is). However, statement 10 contradicts itself. Therefore, only statement 9 is true and the remaining nine are false. — Professor Anshul Kumar, Delhi Solved both puzzles: Sabornee Jana (Mumbai), Ajay Ashok (Delhi), Professor Anshul Kumar (Delhi), Dr Sunita Gupta (Delhi), Yadvendra Somra (Sonipat), Vinod Mahajan (Delhi), Abhinav Mital (Singapore), Shri Ram Aggarwal (Delhi) Solved Puzzle 147.2: Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Dr Vivek Jain (Baroda) Problematics will be back next week. Please send in your replies by Friday noon to problematics@
Hindustan Times
05-05-2025
- Entertainment
- Hindustan Times
Play the magician
Exactly 20 episodes ago, readers solved a card puzzle that I had found, as I mentioned at the time, among the works of the English puzzler Henry Dudeney. I felt it necessary to mention that just in case this week's card puzzle sounds familiar. Indeed, there are similarities. In this puzzle, as in the last one, you are asked to count to 10 while you place a series of new cards on an exposed card. On both occasions, you count the court cards as 10. Rest assured, though, that the puzzle is quite different. Although you may (or may not) use the same kind of mathematical reasoning to solve it, that one came from Dudeney while the following one comes from the writings of Martin Gardner: #Puzzle 141.1 A magician invites you to take part in a card trick he wants to play on you. He hands you a deck of 52 cards and asks you to shuffle thoroughly. You do so and hand the deck back to him. The magician deals 12 cards from the top, one at a time, face down. From this pile, he asks you to select any four cards at random and place them side by side on the table. 'Place each card face up,' he says. You randomly turn up the 4 of clubs, 7 of diamonds, jack of hearts and ace of spades, and place them in a row. These are just illustrative examples; the trick will work with any four cards. The magician picks up the remaining eight cards and restores them to the deck. Your observant eye notes that he has placed these cards at the bottom of the deck, not the top. This must be significant, you guess. The magician hands the deck to me. 'Deal more cards face down on the top of each face-up card. Count to 10 while you deal, starting with the number immediately higher than the pip value of the face-up card. For example, on top of the 4 of clubs, you count 5, 6, 7, 8, 9, 10, and stop when you reach 10,' he instructs you. But what about the jack of hearts, you want to know. 'Count all court cards (jacks, queens and kings) as 10, so nothing needs to be added to this jack,' he replies. So you deal cards on the 4 of clubs (counting '5, 6, 7, 8, 9, 10'), then on the 7 of diamonds ('8, 9, 10') and finally on the ace of spades ('2, 3, 4, 5, 6, 7, 8, 9, 10'). You deal nothing atop the jack of hearts, which is already assumed to have a pip value of 10. 'Add the numbers on the face-up cards. Court cards are 10, as previously stated,' the magician says, and you add: '4 + 7 + 10 + 1 = 22.' 'What is the 22nd card in the deck you hold?' the magician teases you, then answers his own question: 'It's the six of diamonds. Check and see.' You check by dealing the cards from the deck and counting: '1, 2, 3, 4… 21.' You then turn the 22nd card face upwards. Indeed, it is the six of diamonds. You make an informed guess: 'This appears to be a mathematical trick. After I had shuffled the deck in the very beginning and handed it back, you quickly looked at one card in a certain position, knowing that the subsequent operations would bring this card to the exact position derived from the sum of the pip values.' The magician agrees. 'You are right, but can you identify which card I silently observed?' #Puzzle 141.2 'My turn now,' you say, offering to play a trick on the magician. After he agrees, you give him your instructions: (1) Write down the year of your birth. (2) Write down your age in years on your birthday in 2024. (3) Write down the year of your wedding. (4) Write down the number of years you had been married when you celebrated your anniversary in 2024. (5) Write down the number of people in this room. 'Don't show me any of these five numbers,' you continue. 'Add them all up, but don't tell me the sum either. Just tell me when you're done.' 'Done,' says the magician. 'Your total is 4061,' you announce. MAILBOX: LAST WEEK'S SOLVERS #Puzzle 140.1 Hi Kabir. The solution to the wages puzzle is shown in the table. Let us take s, w₁, w₂ and w₃ as the years of experience of the supervisor and workers #1, #2 and #3 at t = 0 (15 years ago). At t = 5 (10 years ago), let the experience of the new worker #4 be w₄. And at t = 15 (today), let the experience of the new worker #5 be w₅. From the equations that are given and/or formed (see table), we can equate (4) and (5) to get: w₃ = 2w₅ – 15 Now 0 < w₅ <10, and w₃ > 0., for which we need w₅ = 8 or 9. But from equation (1), we know s is an even number. So, from (3), w₅ must be odd. In other words, we need w₅ to be 9 and not 8. From the value w₅ = 9, we can derive s = 24, w₃ = 3, w₄ = 2 , w₁ = 6 and w₂ = 3. The completed years of experience will be (s + 15 = 39), (w₁ + 15 = 21), (w₂ + 15 = 18), (w₃ + 15 = 18), (w₄ + 10 = 12), and (w₅ = 9). — Sabornee Jana, Mumbai *** Worker 2's cryptic remark at the end (in response to worker 3's remark that worker #1 and worker #2 together earn as much as the sum of the other three workers' salaries) means that he could say the same about worker #1 and worker #3 together earning the same as the other three. Workers #2 and #3 earn the same amount. — Kanwarjit Singh, Chief Commissioner of Income-tax, retired #Puzzle 140.2 Hi Kabir, It could be that the two sisters, although born to the same parents on the same day of the same month in the same year, are not twins because they are two among triplets or two among quadruplets etc. — Dr Sunita Gupta, Delhi *** Here's how it works. They are not 'twins' because this word means exactly two babies born from the same pregnancy. If there were three (or more) babies born to the same mother on the same day, the term would be triplets, quadruplets etc. So if two of the triplets are celebrating their fifth birthday, they are sisters, same age, born on the same day — but not twins, because they are part of a larger multiple birth. — Vinod Mahajan, Delhi Solved both puzzles: Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Dr Sunita Gupta (Delhi), Sampath Kumar V (Coimbatore) Solved #Puzzle 140.1: Sabornee Jana (Mumbai), Professor Anshul Kumar (Delhi), Yadvendra Somra (Sonipat) Solved #Puzzle 140.2: Vinod Mahajan (Delhi), Aishwarya Rajarathinam (Coimbatore), Sanjay Gupta (Delhi), Ajay Ashok (Delhi)
The Independent
18-03-2025
- Science
- The Independent
Thousands of miles from home and -75C cold: Life is tough in Antarctica even before death threats from scientists
Around 2,500 miles from home and facing increasingly colder and darker conditions, life in an Antarctic research station is tough at the best of times. But at South Africa's Sanae IV in Vesleskarvet scientists have faced an extra challenge - alleged death threats from a colleague. 'It is imperative that immediate action is taken to ensure my safety and the safety of all employees,' said an email sent home by one of the station's staff. The alleged aggressor has now apologised to their victim, according to the South African Department of Forestry, Fisheries and the Environment (DFFE) who said they had'shown remorse'. The department has now begun the hard task of restoring relationships in the nine-person team who must continue working together through the rest of Antarctica's harsh winter. Such tensions between colleagues add what are already extreme conditions. Around 10,000 scientists and support staff work for 18 countries on stations around the continent, and tourists arrive in droves, but temperatures still rarely climb far above zero. In winter, which is fast approaching, temperatures will plummet to between -10C and -30C, and can reach as low as -75C. Antarctic expert and retired scientist Dr John Dudeney spent two consecutive winters in Antarctica early in his career, and told The Independent it takes resilience to live and work on the isolated continent. 'It's a very, very extreme experience, there's no doubt about that,' he said. Over winter the number of staff working in Antarctica will dwindle to about 1,000 scientists and support workers, who, outnumbered by penguins 5,000 to one, must endure long stretches without any sunlight at all depending on where they are stationed. At the South Pole, there is complete darkness for several months over winter. Dr Dudeney, whose career in Antarctic matters spanned nearly six decades, said the weather wasn't the biggest problem - even though there would be times when it would be difficult to go outside. 'There is this problem of sensory deprivation,' he said. 'Quite often, if you look out of a window all you'll see is snow driving past, and if the sun is shining or the moon is bright, then you'll just see a flat featureless snow plane.' Preparing to start a posting - and to rejoin normal life - takes serious preparation, to ensure people are physically and mentally prepared for the particular hardships of life in Antarctica. Teams undergo psychometric testing beforehand, and the South African DFFE said the alleged perpetrator has undergone a further psychological exam. Dr Dudeney, who was a base commander at Farady base in 1968, said normal relations could be challenging in Antarctic teams, and he was always conscious of watching his own behaviour and having the good of the team in mind. 'The team forms or it doesn't, and it forms as a sometimes what we call a storming team, a really good team that works really well together. Sometimes it fragments and becomes more than one team that works against each other. The key is to try and make a team that works together,' he said. Handling a difficult individual was also tricky, Dr Dudeney said. 'You don't have any sanctions at all really -if you have a difficult individual, you can sack them, but then what do you do? They've still got to be there, and they still need to pull their weight,' he said. Antarctica is one of the most remote places to work, besides the International Space Station: the British stations are more than 8,700 miles from the UK. The difficulties accessing Antarctica at particular times of year plus the sheer distance from most major cities mean workers stay for months at a time, and Dr Dudeney said sending in backup support in winter was still a difficult undertaking. 'You've got to know what the balance of risks is,' he said. 'If you're trying to extract somebody, for instance, in the middle of winter, then there has to be a careful assessment of the risk you're taking compared with the risk of taking no action.'
