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The Guardian
13 hours ago
- Entertainment
- The Guardian
Did you solve it? The deductive decade – ten years of Monday puzzzles
To celebrate ten years of this column, this morning I selected ten puzzles from the Monday Puzzle archives. Here they are again with solutions. Click on the solutions to be taken to the original columns, which have full explanations. 1. Bat and ball Three friends (A, B and C) are playing ping pong. They play the usual way: the winner stays on, and the loser waits their turn again. At the end of the day, they summarise the number of games that each of them played: A played 10 B played 15 C played 17. Who lost the second game? Solution A 2. Tricky trams Why are the tram's overhead cables positioned to make a zigzag, rather than straight line? Solution The metal structure on the roof of the tram, the pantograph, rubs against the cable as the tram moves forward. If the cable was in a straight line, it would rub the same point on the pantograph, which would begin to fray. But if the cable is in a zigzag, the rubbing happens evenly across the top of the pantograph, and the pantograph wears down less quickly. 3. Read the question 3. What is never odd or even? Solution 'never odd or even' is a palindrome, i.e. it reads the same back to front. 4. Catch the cat A straight corridor has 7 doors along one side. Behind one of the doors sits a cat. Your mission is to find the cat by opening the correct door. Each day you can open only one door. If the cat is there, you win. If the cat is not there, the door closes, and you must wait until the next day before you can open a door again. If the cat was always to sit behind the same door, you would be able to find it in at most seven days, by opening each door in turn. But this mischievous moggy is restless. Every night it moves randomly either one door to the left or one to the right. Although if it is behind the first or last door, it has only one option for where it can move. How many days do you now need to make sure you can catch the cat? Solution ten days 5. Mystery number I have a ten digit number, abcdefghij. Each of the digits is different, and a is divisible by 1 ab is divisible by 2 abc is divisible by 3 abcd is divisible by 4 abcde is divisible by 5 abcdef is divisible by 6 abcdefg is divisible by 7 abcdefgh is divisible by 8 abcdefghi is divisible by 9 abcdefghij is divisible by 10 What's my number? [To clarify: a, b, c, d, e, f, g, h, i, and j are all single digits. Each digit from 0 to 9 is represented by exactly one letter. The number abcdefghij is a ten-digit number whose first digit is a, second digit is b, and so on. It does not mean that you multiply a x b x c x…] Solution 3816547290 6. Disappearing cub This picture has not been doctored. Explain why the reflection has a yellow lion cub. Solution: The cub is camouflaged by a cleverly-coloured flap 7. Crazy triangle Show that there is a triangle, the sum of whose three heights is less than 1mm, that has an area greater than the surface of the Earth (510m km2). Solution Here's one: 8. Deck dilemma Your friend chooses at random a card from a standard deck of 52 cards, and keeps this card concealed. You have to guess which of the 52 cards it is. Before your guess, you can ask your friend one of the following three questions: is the card red? is the card a face card? (Jack, Queen or King) is the card the ace of spades? Your friend will answer truthfully. What question would you ask that gives you the best chance of guessing the correct card? Solution It doesn't matter. In all three cases, your chance of guessing the correct card is 1 in 26. 9. The question with no question (a) All of the following. (b) None of the following. (c) Some of the following. (d) All of the above. (e) None of the above. [Just to reassure you, nothing has been omitted here.] Solution (b) 10. Triangle fold Find a way to fold a square piece of paper into an equilateral triangle. The triangle can be of any size. Solution Here is one way, that uses the side length of the square as the side length of the triangle. I hope you enjoyed these puzzles. I'll be back in two weeks. Sources: 1. Adrian Paenza, 2. Kvantik magaizine, 3. Des MacHale, 4. New York Times. 5. John Conway, 6. Matt Pritchard, 7. Trần Phương, 8. Henk Tijms, 9. Parabola, 10. The Paper Puzzle Book. I set a puzzle here every two weeks on a Monday. I'm always on the look-out for great puzzles. If you would like to suggest one, email me.
Telegraph
29-05-2025
- Health
- Telegraph
Allowing 70-year-olds to have a baby is appalling. Why don't we ever say no anymore?
Here goes. I know little ears might be listening. More saliently, I know elderly ears might be listening, too. A British couple in their 70s have just been granted permission by the courts to become the legal parents of a 14-month-old baby boy. Not because of family breakdown, not through necessity. But because they paid a surrogate in California £151,000 to carry the embryo made from the husband's sperm and a donor egg. Now, I also know that whatever the unfortunate, regrettable or just plain awful circumstances of its conception, once a baby is born, the slate is wiped clean and jubilation is the only possible human, humane response. Because babies are a blessing. They represent hope, love and all that is squidgy and precious – they should never be burdened with the sins of their proverbial fathers and mothers. But sometimes – and it would seem, more often than just sometimes – we need to speak up and say 'enough'. Speak out and shout: 'NO! No, you can't. No, you mustn't. JUST STOP!' The court papers describe how the wealthy retired couple, referred to as Mr and Mrs K, decided to have a surrogate baby after their son 'A' died from cancer in 2020 shortly before he turned 27. By any measure that is an out-and-out tragedy. A life-long bereavement. But how could they possibly believe that having another baby in their twilight years was the best course of action? Did no-one advise them against it? Did they not have friends or wider family to forcefully impress upon them that effectively replacing their son with a new baby would be an act of grief-induced madness? It would seem not. In a written judgment handed down last month in the family division of the High Court, Mrs Justice Knowles said she had made her judgment public because it raised an 'important welfare issue and offers some advice for those who may, in future, engage in a foreign or other surrogacy arrangement'. She added that it was an 'undeniable fact' that when the child – referred to as 'B' – started primary school, Mr and Mrs K would be both aged 76. 'Put starkly, Mr and Mrs K will both be 89 years old when B reaches his majority,' Judge Knowles said. Despite those concerns, she granted a parental order to give 'permanence and security' to the child's care arrangements 'in circumstances where no one else other than Mr and Mrs K seek to provide lifelong care for him'. The couple, it was said, have made provisions in their will for friends of their deceased son – a couple in their early 30s – to become the child's legal guardians if they die or are unable to look after him. So that's all right then. Or is it? It is troubling to note this is the third such case to emerge in the last year where a 'parental order' has been given to British 'intended parents' in their 60s and 70s for children born to surrogate mothers abroad. And none of that is OK. These acts of blind selfishness are so egregiously wrong that it's hard to fathom where to start – and I speak as someone who suffered the torment of infertility for many years. Even as I struggled and invested my life's savings, I knew deep down there was a cut-off point; and it was a good two and a half decades before my 70th birthday. Not just because any reputable clinic would have stopped treating me – although many a less scrupulous outfit beyond these shores would have stepped in. But because it would have been weird and icky and unnatural (the irony of being pumped with drugs is not lost on me) to keep going and going. I felt – I still feel – that beyond 50 it would be wrong. For me, 45 was my limit. Just because my husband and I looked young and fit, didn't mean we were. Above all, however, it felt immoral to bring – let's be honest, engineer – a baby into the world at the point when menopause decreed my reproductive days were over. I was lucky. I had two daughters by the age of 42. I will urge them that if they want families they should start early in case my infertility is inherited. Or in case their partner has been hit by 'spermageddon'; over the past 40 years, sperm counts worldwide have halved and sperm quality has declined 'alarmingly', with one in 20 men currently facing reduced fertility. I would never have gone down the surrogacy route to become a mother although I know women who have and that's their business. It becomes society's business, however, when elderly couples start doing the same. There's no legal age limit for people in the position of Mr and Mrs K. There should be – if only because, as a nation, we seem to be increasingly in the thrall of the pernicious 'you do you' hands-off mentality fostered by social media. Blithely letting people do as they like without regard for the consequences might empower the individual, but it sure as hell disempowers the rest of us. Time and again we fail to condemn unpalatable behaviour because a spurious and deeply juvenile notion of 'kindness' takes precedence over common sense. Activists have taken advantage – why wouldn't they? For years our pusillanimous institutions have fallen foul of aggressive transgender ideologues demanding rights to which they were never entitled. I for one found it downright humiliating that it took the Supreme Court to assert the biological fact that trans women are not women (the clue being in the title). Then we have doctors lambasted for doing their jobs. GPs informing patients they are obese and their health is at risk has been reframed by campaigners as 'weight-shaming'. And as that might 'cause offence' it is, of course, to be avoided. What are medics supposed to do? Send a text? Mime it? All too often we find ourselves kowtowing to the few at the expense of the many and tolerating the intolerable. At dinner tables the length of the land, the tiresome cry from younger generations of 'you can't say that!' goes up daily. When the grown-ups acquiesce for an easier life, that doesn't burnish our liberal credentials, it makes fools of us all. We have a responsibility to safeguard our values. And when it comes to pensioners commissioning babies, age isn't just a number. Yes, Mr and Mrs K suffered a terrible loss, but what they desperately needed was a grief counsellor not a fertility clinic.
National Geographic
21-02-2025
- Science
- National Geographic
This is what a surgical clinic looked like in ancient Rome
Doctor in the house What caught the attention of archaeologists most was the first of these houses, which had been rebuilt several times over the years. The last reconstruction took place during the second half of the second century A,D., when the main rooms were remodeled to include rich mosaics and paintings and new rooms were added. Archaeologists were able to identify the areas of a typical Roman mansion: the vestibule; the triclinium (where banquets, receptions, and social gatherings were held); several cubicula (rooms usually identified as bedrooms that also served as reading or meeting rooms); and a latrine. They also found remains of a richly decorated upper floor comprising several rooms, including a kitchen. Heat therapy Archaeologists believe that this life-size, foot-shaped terra-cotta vessel found in the Surgeon's House was either used as a flask for storing ointments or medicines or for performing therapeutic heat treatments. It is one of only two such objects found in the Roman world. Ministero Della Cultura. Soprintendenza Archeologia, Belle Arti e Paesaggio per le Province di Ravenna But what made this particular Roman house so special were the belongings of the person who lived there in the early third century. A spectacular array of some 150 surgical instruments, made of bronze and iron and manufactured between the first and third centuries A.D., were found among the remains. This was clearly the home of a Roman surgeon. The tools, which would once have been stored in cases and boxes, form the most complete set of surgical instruments ever found from the ancient Roman world. The archaeologists also found mortars that must have been used in the preparation and storing of drugs. The evidence suggests that the house functioned as a private clinic, or taberna medica, of the early third century, containing both study space and a medical consulting room. They dubbed it the Domus del Chirurgo—the Surgeon's House. (How ancient remedies are changing modern medicine.) Tools of the trade These hooks and scalpels were among some 150 instruments found at the Surgeon's House. Ministero Della Cultura. Soprintendenza Archeologia, Belle Arti e Paesaggio per le Province di Ravenna One-third of the instruments found in the Surgeon's House were intended for bone surgery. Others were used for operating on hernias, eyes, and tonsils. They range from hooks and scalpels to instruments for specialized interventions, such as cranial trepanations where part of the skull was removed. The latter instrument is of special interest to historians of medicine, as its design conforms with the written description of an object left by the medical writer Galen, who died in the early third century. None of the Rimini instruments were for gynecological use, strengthening the theory that the surgeon learned his trade on the battlefield. A good man At the heart of this taberna medica was a room paved with a mosaic depicting the mythical Greek hero Orpheus. In this room archaeologists discovered most of the surgical instruments. They also found medical paraphernalia in the cubiculum next to the Orpheus room and in the entranceway. And it was there, on a wall, that archaeologists found an intriguing graffito. The inscription in Latin read: Eutyches homo bonus hic habitat. Hic sunt miseri. This translates as: 'Eutyches, a good man, lives here. Here are the miserable ones.' It seems reasonable to hypothesize that the text was scratched onto the wall by a sick person being treated by a doctor called Eutyches. Researchers believe that the doctor trained in Greece and Asia Minor where, in addition to gaining medical knowledge, he acquired cultural artifacts that he took with him to his residence in Ariminum. This would explain the presence of objects outside the city's typical trading circles. These include a panel of fish in glass paste thought to be from what is now Turkey, a bronze votive hand associated with the cult of Jupiter Dolichenus, and a statue of Hermarchus, a Greek Epicurean philosopher. Objects from places outside Rimini's trading circles suggest the surgeon had traveled widely, like this glass-paste panel with three fish. It likely came from what is now Turkey. Ministero Della Cultura. Soprintendenza Archeologia, Belle Arti e Paesaggio per le Province di Ravenna The sophisticated surgical instruments found in the house suggest that Eutyches, if that was indeed his name, had specialized in treating trauma wounds and performing surgery. It is therefore likely that he acquired at least part of his training as a military doctor in the camps, and on the battlefields, of the Roman Empire.
