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The New Era of Veteran FootballersAfter playing at Qatar 2022 at age 35, US national team defender Tim Ream thought it was "pretty unlikely" he could play in another World Cup. But he decided he would at least try to stay in the game as long as possible. "Because for me, it's about pushing boundaries, pushing myself, pushing the limits of what I can physically and emotionally handle," he told Al Jazeera.Last week, Ream was named as the US's captain for the upcoming football tournament in North America and, at 38, is the oldest ever outfield player in a US World Cup squad. "To be given the honour and the opportunity to wear the captain's armband in a home World Cup is incredible," he said.Ream is one of several outfield players in their late 30s and beyond at the 2026 World Cup; including Portugal superstar Cristiano Ronaldo, 41, the 40-year-olds Luka Modric and Edin Dzeko, Yuto Nagatomo, 39, and Argentina legend Lionel Messi, who turns 39 later this month.The Science Behind Extended CareersEvolving sport science plays a significant role in extending career longevity – the days when "recovery" meant having a few beers after the game are long gone, and many players now extoll all kinds of developments from lymphatic draining to cryotherapy.Huge amounts of data measuring biomarkers from heart rate variability and muscle oxygenation to hormonal fluctuations and inflammation are now available, including from wearable technology. But experts argue that sport science is just part of a complex system of interlocking factors needed to extend longevity in football, including culture, relationships, a learning mindset, luck, resources, and the motivation to keep going into a fifth decade."This question is always about people," Vlatko Vucetic, a professor of kinesiology at the University of Zagreb who has worked as a personal trainer with Croatian and Real Madrid star midfielder Modric for more than 10 years, told Al Jazeera.The Statistical Shift in Football LongevityFootballers tend to peak before the age of 30, with research suggesting a general decline in the early 30s in terms of speed, power and explosiveness, although endurance fades more slowly. As players age, recovery takes longer, and they also become more susceptible to injuries. Football has also gotten much faster and more physical over the last few decades, and the number of matches at the elite level has increased dramatically.According to Transfermarkt.com, only 15 players aged 35 or above appeared in the Premier League this season out of more than 500 players. However, there is evidence that the median age of footballers may be increasing, while the number of outfield players playing into their late 30s and early 40s at the upcoming World Cup is striking. Before this tournament, Cameroon's Roger Milla – who scored at USA 1994 aged 42 – was the only outfield player in their 40s to play at a World Cup.How Aging Stars Are Transforming Football CultureBen Rosenblatt was the lead performance coach for the England men's team for seven years and is the founder and director of 292 Performance, a sport consultancy firm that trains and advises elite individuals and organisations. He told Al Jazeera that advances in sport science and data collection – and an increased focus on health and wellness culture inside and outside the game – have helped extend careers in football."Within the game, there is more attention to detail over the last two decades being placed on an understanding and knowledge around training science and in particular, how to schedule organised training sessions to optimise athletes' performance and reduce injury risk – which is obviously going to be a big survival factor for players," he said.While Rosenblatt says longevity relies on "the amalgamation of all the different tools, resources, culture and behavioural shifts that are taking place within the game", the fundamentals remain crucial; training, recovery, sleep, lifestyle, nutrition and hydration."It's about doing the stuff that's quite boring and basic 99 percent of the time," he said.The Future of Athletic Longevity in FootballLooking ahead, Rosenblatt says putting the huge amount of available data together to create a more holistic picture of a player could be "transformative" for longevity. "That's kind of the Holy Grail, because you can give clarity to a manager or an owner game by game or across the course of a season about what the player is capable of delivering, and then obviously what development they require," he said.And extending longevity means establishing routines, discipline, and what works early on. "I know so many players who, towards the end of their career, tried to find a routine and they couldn't stick with it because they hadn't done it early enough," Ream said. "Find these things and get into them early, because it'll help you in the long run."Veterans playing into middle age will often adapt their game to compensate for slowing legs with assets like enhanced vision. "I think my biggest improvement is being able to see things as they're developing, and as they're happening, but then also understanding and adapting to different coaches," Ream said. "I think that's where you have to understand the interpersonal side with this game, because it's all about connections, it's all about communication, it's all about relationships on and off the field."

The Author's Journey with Loneliness Author Olivia Laing first considered writing about loneliness in 2012 after experiencing intense isolation in New York City. Her book, 'The Lonely City', published in 2016, explores the complexities of loneliness and its consequences. The Definition and Impact of Loneliness Loneliness is defined as a state of longing for more connection and intimacy than one has. It is not the same as solitude and can have severe physical consequences, including increased blood pressure, ageing, and cognitive decline. The Role of Social Forces in Loneliness Laing's research revealed that loneliness is often a consequence of larger social forces such as stigma and exclusion, which isolate vulnerable populations. Factors like poverty, immigration status, illness, and divergent sexuality can drive isolation. The Shift in Public Perception and Discussion Since the publication of her book, loneliness has become a widely discussed topic, akin to depression or anxiety, and is now regarded as a global public health concern. The 2024 Health Survey for England reported that 22% of the adult population felt lonely at least some of the time. The Exploitation of Loneliness by Far-Right Groups Laing warns that far-right groups exploit loneliness, using feelings of isolation and disconnection as a recruitment tool. These groups offer narratives that stoke grievances and displace vulnerability onto other bodies that can be hated and attacked. The Role of Technology in Weaponising Loneliness Social media has played a significant role in the weaponisation of loneliness, facilitating the rise of the far right and violent exclusion. Algorithms herd people into digital pens, creating information silos that distort civic society. The Solution to Loneliness Laing argues that the solution to loneliness lies not in romantic partners or AI chatbots but in community assets and a solidarity of difference. Practical solutions focus on community resources such as transport, green spaces, and social centres.

The AI Market Surge The race is very much on. Elon Musk's SpaceX, which makes AI models as well as space rockets, announced last week it is seeking a $1.77tn (£1.31tn) valuation on the US stock market while Anthropic, the startup behind the Claude chatbot, said it had filed for an initial public offering. OpenAI, the developer of ChatGPT, is expected to follow. AI Has Sent Stocks Soaring The S&P; 500, which tracks the 500 biggest US companies, has been on a tear over the past five years – rising by nearly 80%. That jump has been driven by big tech stocks with a stake in the AI boom, the “magnificent seven” of Alphabet, Amazon, Apple, Meta, Microsoft, Nvidia and Tesla. Expenditure Is Growing at a Staggering Rate Spending on AI – from datacentres to chips – is racing ahead, from $765bn this year to $1.6tn in 2031, according to Goldman Sachs. The investment bank acknowledges there could be problems with this scale of commitment. What if the datacentres are delayed? Firms and Consumers Are Adopting AI at Pace Despite mixed reports on the benefits, the vast majority of companies are starting to use AI – up from 33% in 2023 to nearly 80% now, according to the consultancy group McKinsey. Usage among the general public is also high, with OpenAI's ChatGPT now reaching 1bn monthly active users, according to data from Sensor Tower – a record for any app. Claude Is Snapping at ChatGPT's Heels Anthropic began to gain ground on OpenAI late last year, when its Claude Code tool went viral among mostly San Francisco-area software developers, before spreading more widely. Claude Code represented a shift in how large language models – the core technology behind chatbots – are used, ushering in a transition towards autonomous AI agents that carry out tasks without human intervention, enabling even the non-tech-savvy to create software and do a wide range of tasks. AI Is Getting More Expensive to Use Every time an AI chatbot or agent issues a response, it is measured in “tokens” – building blocks of language that can be words, punctuation marks or syllables. The costs of these vary per model; OpenAI prices it at $5 a million input tokens for GPT-5.5, and $30 a million output tokens (ie the response given to your prompt). Datacentre Building Might Not Keep Pace with Demand Datacentre construction represents the central nervous system of AI products so growing development and use of AI tools must be matched by more capacity – otherwise there will be a compute crunch, which means rising costs for AI companies and users.

The Rise of Anti-Tech Extremism in the AI AgeWhen a 20-year-old man from Texas was arrested earlier this year for allegedly trying to burn down OpenAI's headquarters and Sam Altman's house, authorities found an anti-AI manifesto alongside his lighter and a jug of kerosene. This incident is part of a spate of attacks that has caused alarm among researchers, the tech industry and law enforcement about the rise of anti-tech extremism.In April, an Italian "nature pilled" Instagram influencer was arrested in Rome and charged with plotting a series of anti-tech attacks that took inspiration from Ted "The Unabomber" Kaczynski. Two self-described "ecofascists" that carried out a deadly anti-Muslim attack on a mosque in San Diego last month also cited "AI slop" and JD Vance's ties to Palantir as motivations for their violence in their manifesto. An Indianapolis city councilor woke up earlier this year to gunshots being fired into his home before finding a note that read "NO DATA CENTERS".The growing public backlash to the tech industry's rapid rollout of artificial intelligence has taken many, mostly-non violent forms such as local communities organizing against datacenters and political candidates promising increased oversight. Yet at the fringes, researchers say grievances against the AI industry and its leaders are animating old violent extremist movements and fomenting new ones."AI is becoming this driver of political violence, and that's a very new phenomenon," said Jordyn Abrams, a researcher at the Program on Extremism at George Washington University.AI as a Unifying Factor for Extremist GroupsWhile much of the early public discussion around generative AI and extremism focused on how malign actors like terrorist groups could misuse products such as ChatGPT for propaganda purposes or plotting attacks, there is more recent attention given to how the AI industry as a whole can radicalize people. What motivates someone to extremist violence might not be a conversation with a chatbot, researchers say, but the society-wide disruption, narrative of existential threat and lack of accountability that has come with the AI boom.In the same way that AI has come to pervade many facets of modern life, the technology has also filtered into the way that extremists think about the world. Whether it is violent anti-government groups opposing mass surveillance, ecofascists with environmental grievances, neo-Nazi accelerationists bent on collapsing critical tech infrastructure or the man who allegedly targeted Altman's house worried about superpowerful artificial intelligence destroying humanity, AI has become a fixation across the extremist spectrum."It really transcends these left-right dichotomies," said Yannick Veilleux-Lepage, an associate professor at the Royal Military College of Canada. "We're seeing a lot of different groups, a lot of different ideologies being framed through a lens of anti-AI."The Unprecedented Speed of AI TransformationThe modern anti-tech movement has a long lineage. Periods of technological change are historically accompanied by backlash from the people most affected, with researchers often pointing to the early 19th-century luddite rebellion of British textile workers smashing automated knitting machines as they demanded more labor rights. The next 200 years brought waves of violent labor disputes and political violence that accompanied tech's market disruptions, uneven accumulation of wealth and disenfranchisement of workers.In the 1990s, there was cultural pushback against the rise of the personal computer and the fear of how it would disrupt society. Common complaints included fears of replacing human workers, environmental harm and crumbling healthy social structures."Haven't you heard? It wants your job. It peddles you smut. It corrupts your kids. It's cold, sterile, inhuman. Suddenly, it's okay to hate your computer," read a New York Magazine cover story from 1995 on the "New Luddites".The same year as New York Magazine ran its cover story, the Washington Post and the New York Times published the Unabomber's anti-tech manifesto, a 35,000-word screed against industrial society that has proliferated online in the years since and become the closest thing that anti-tech extremism has to a foundational text.What separates anti-AI extremism from these previous waves of tech backlash, researchers say, is partly the speed and scale of how AI is bringing about economic, social and political change."Not only are these whole-of-society changes and not only are they really disruptive, they're happening really quickly," Veilleux-Lepage said. "There isn't time for people to build resilience or to inoculate themselves from these changes".The AI industry's longstanding talking points – that the technology will revolutionize the world, if not end it – also lend themselves to a radicalizing narrative that AI poses an existential threat and must be stopped at all costs. When Veilleux-LePage gives talks to policymakers about anti-tech extremism, one of his slides simply features a series of quotes from CEOs."In order to radicalize people, you don't actually need to have theorists or ideologues that are calling people to violence against AI, because the tech CEOs are doing a pretty good case," Veilleux-LePage said.Corporate Response and Security ConcernsAltman has often framed the changes AI will bring as something that may be difficult, but is ultimately both positive – above all, he describes the change as inevitable."I expect some really bad stuff to happen because of the technology which also has happened with previous technologies," Altman said on venture capital firm Andreessen Horowitz's podcast last year.While tech CEOs are publicly optimistic about the resilience of society and the change that AI will bring about, it is also clear that they are privately concerned with the threat of political violence. Spending on personal security for executives has ballooned over the past five years amid incidents such as the killing of UnitedHealthcare CEO Brian Thompson, while tech leaders such as Elon Musk now pour millions into their own protection. SpaceX revealed in its IPO filing earlier this year that it paid $4m last year to Musk's private security firm, double what it had spent only two years before.There are signs over the past year that the AI industry is shifting its rhetoric as it grapples with widespread public distrust. Altman claimed last month that AI would probably not lead to the "jobs apocalypse" that he once discussed, even as companies like Meta lay off tens of thousands of workers. OpenAI and Anthropic have meanwhile both announced funds and thinktanks this year aimed at helping civil institutions adapt to AI, with OpenAI's non-profit organization committing $250m to grants for programs that help workers navigate AI upheaval.Major AI firms are hiring national security, intelligence, and weapons experts to monitor threats and misuse of their technology, including some with a background in extremism and counter-terrorism research. OpenAI's head of intelligence previously worked as one of the foremost academic experts on the Islamic State and wrote a book on the group's belief that it was bringing about the apocalypse. OpenAI and Anthropic did not respond to requests for interviews with their intelligence or security experts.The Accountability Gap and Future RisksThe closing off of legitimate avenues to address public opposition to AI, as well as the feeling that the technology is being forced upon society, is creating what researchers describe as a gap in accountability that can further incentivize terrorism and political violence.Donald Trump, in alignment with tech leaders, issued an executive order last year attempting to block any state-level legislation that would rein in AI development and has said that nothing will slow down the US in the global AI race. Tech billionaires are also pouring millions of dollars into lobbying and political spending in an attempt to prevent regulation of AI."When authorities are too busy, or just don't care enough, to regulate and take action, then people affected are going to take action," said Mauro Lubrano, a lecturer at the University of Bath and author of Stop the Machines: The Rise of Anti-Technology Extremism.Federal law enforcement documents acquired by Wired and the Intercept show that US authorities are increasingly monitoring anti-tech movements, while authorities have declared they will aggressively prosecute violent attacks. Following the attempted arson at Altman's house earlier this year, authorities vowed that "the FBI will not tolerate threats against our nation's innovation leaders".Yet researchers warn that authorities risk conflating the nationwide protests and calls for increased regulation of AI with more fringe, anti-tech extremist views, which is both inaccurate and counterproductive. Programs aimed at mass surveillance and attempts to silence nonviolent anti-AI movements will inevitably backfire, Lubrano says, further pushing people to the violent fringes if they feel their legitimate grievances aren't being addressed."We have this opportunity to be proactive in this while avoiding mistakes that we've made in the past when responding to other forms of extremism," Lubrano said. "Something tells me that we're not off to a great start".

The Final Curtain: A Pivotal Moment in Music HistoryThe Beatles' last official concert on August 29, 1966, at Candlestick Park in San Francisco marked more than just the end of a touring era—it symbolized a fundamental shift in how music would be created and experienced. As Jim Marshall's photographs capture, the band was already feeling nostalgic for what they were leaving behind, even as they stood on the precipice of their most innovative period.The Creative Divide: Studio Innovation vs. Live PerformanceTwo months before their final show, the Beatles had completed recording "Revolver," an album that would push the boundaries of popular music. Yet during their final tour, they performed none of these groundbreaking tracks. The complexity of songs like "Eleanor Rigby" and "Tomorrow Never Knows" simply couldn't be replicated in a live setting with their four-piece band configuration.This creative divide reveals a crucial moment in music history. Until the Beatles, recordings were essentially documentation of live performances. Their first album, "Please Please Me," captured songs honed on stages in Hamburg and Liverpool. By 1966, however, the Beatles had come to see the studio as a creative platform in its own right—a place where experimentation with sounds and techniques could create something entirely new.The Changing Landscape of Live MusicWhile the Beatles were pioneering studio techniques, other artists were revolutionizing the live concert experience. Bob Dylan and the Rolling Stones were developing what we now recognize as the modern rock gig—longer performances, more artistic expression, and a direct connection with audiences that extended beyond simple entertainment.The Beatles' live shows, by contrast, remained stuck in the past. Their 1966 concert format resembled a package-tour variety show, with five or six acts and the Beatles appearing last for a breathless half-hour set before saying goodnight. This disconnect between their recorded work and live performances became increasingly unsustainable as their studio work grew more ambitious.The Legacy of the Final TourThe Beatles' decision to stop touring wasn't merely a practical response to the challenges of performing complex music live—it reflected a deeper artistic evolution. By focusing on studio innovation, they paved the way for future artists who would similarly embrace recording technology as an integral part of the creative process.Ironically, this decision that seemed to separate them from their audience would ultimately transform how musicians connected with fans. The studio innovations pioneered by the Beatles during this period would influence generations of artists, creating new possibilities for musical expression that continue to resonate today.The End of an Era and the Birth of a New Musical LanguageThe Beatles' final tour marked not just the end of an era for the band, but a turning point for popular music as a whole. As they transitioned from live performers to studio innovators, they helped create a new musical language that would define the decades to come.The photographs from this period, capturing the band at this transitional moment, serve as a visual document of one of music history's most significant transformations. They show a group on the cusp of their most creative period, already looking back with nostalgia at the live performances that had made them global superstars, while simultaneously embracing the future possibilities that studio recording would unlock.

The Significance of Xi Jinping's Visit Chinese President Xi Jinping's meeting with North Korea's Kim Jong Un in Pyongyang on Sunday is significant for one reason: it's a rare trip abroad for Xi. The two men met in Beijing just a year ago, but Xi's travel has been limited in recent years. China's Changing Relationship with North Korea Traditionally, Beijing played the role of senior partner in the China-North Korea relationship, with North Korea heavily dependent on China for as much as 95 percent of its trade. However, that dynamic has been changing since Russia's 2022 invasion of Ukraine, with North Korea providing Russia with critical weapons, artillery, and manpower. The Data Behind the Relationship North Korea may have received between $580m and $1.5bn of the $14.4bn paid by Moscow in the form of 'goods' China shares a mutual defence treaty with North Korea, but is wary of North Korea acquiring new military technology The Impact on Regional Security Xi's visit comes amid concerns about North Korea's growing military ties with Russia and its impact on regional security. North Korea has carried out eight missile launches since the start of the year, and has unveiled a new AI-guided tactical cruise missile. The Future of North Korea-China Relations Xi's trip may also be aimed at smoothing over relations with South Korea, which has been critical of North Korea's military actions. The visit could play a constructive role in addressing issues related to the Korean Peninsula, including a possible meeting between Kim and Trump later in the year.

The Rise of Tech-Savvy Farmers in KenyaKericho County, Kenya – A typical Saturday morning starts before sunrise for Chepkorir Rotich, a farmer in Kiboito village in western Kenya's Kericho County. By then, Rotich has already milked her cows and sold the milk, fed her chickens, and headed back to pluck vegetables for orders already placed. Her work starts this way every day, and she does it with passion.When the 33-year-old mother of two left college more than a decade ago, she was excited and ready to join the formal employment sector and secure a full-time job."I thought I would be employed as a business administrator, but after looking for a job for too long, I accepted contract offers in three different companies," she says. "The highest paid me about $200 in a month. While living in Nairobi, that wasn't enough."From Job Seekers to Agricultural EntrepreneursA lack of white-collar jobs has kept young Kenyans like Rotich out of employment, leaving them to innovate ways to survive and earn a living. In doing so, many youths have resorted to agriculture and other fields, with many using digital as well as vocational skills to stay ahead of the game.Digital Transformation of Kenyan AgricultureRotich, for example, uses social media to market her produce and to learn how to practice agriculture using modern methods. Social media helps her share knowledge with young people who comprise a large portion of her nearly 50,000 followers. She also runs a YouTube channel where she shares her knowledge of farming.The Food and Agriculture Organization of the United Nations (FAO) reports that the average African farmer is 60 years old, something Rotich refutes, saying the presumed age of farmers has made many young people shun agriculture instead of embracing it as a way to earn a living going into the future."I think the reason they say that is because of access to land on which to do agriculture, which is mostly owned by older people," Rotich tells Al Jazeera. "In my case, I started farming in the compound of my rented house, and by the end of each month, my landlord owed me money after settling the rent because I sold him milk and vegetables. So, it's all about passion and consistency among the youth."Kiringai Kamau, a lecturer at the University of Nairobi with expertise in agricultural economics, agribusiness, and food systems, says young people should take up agriculture as full-time employment since they are the ones who can effectively understand and deploy technology."To do this, we have established the devolution agroecology and AI learning centre in Murang'a University, where we will be pushing to have the centre train the youth who will be going into agriculture to be able to link with the agricultural data ecosystem, deriving from the infrastructure that will be provided, and also giving information to the county and country, and any other professionals that may be interested in data coming there," he tells Al Jazeera.Derrick Ngigi, the technical head at Global Open Data for Agriculture and Nutrition (GODAN), says that while youth are embracing agriculture, technology also plays a role in providing them with opportunities."For example, content creation in agriculture brings a lot of opportunities, such as creating content around modern farming methods, which has been generating revenue for the youth," Ngigi says.AI Tools Revolutionizing Farming PracticesAbout five kilometres outside Kiboito, at Kaptoroi village, Geoffrey Kiprop is busy cleaning his cowshed after feeding his cattle for the early morning. The 32-year-old earned a bachelor's degree in information technology in 2017 but has never secured formal employment.Like Rotich, Kiprop has been surviving on contract work, such as jobs doing systems development and maintenance for schools. He says that the highest-paid contract was for 15,000 Kenyan shillings ($116). But now, he makes about 7,000 Kenyan shillings ($54) a day through farming.Kiprop also practices mixed farming, rearing cows for milk and chickens for eggs and meat, while also planting crops such as tea, coffee, capsicum, cabbage, and beans.He uses modern technologies to raise his crops and livestock and takes advantage of his IT training, which he utilises to ensure maximum profits.Examples of the tools he uses include the Plantix app, which he says helps detect crop disease and malnutrition using AI after he simply takes a photo of the crop and uploads it. The app also gives the farmer the weather forecast and the best crop practices to perform in line with current weather conditions."My favourite is the Virtual Agronomist. This is an AI-enabled platform where I use Google Maps to capture the coordinates of my crop field and then specify the types of crops I am growing," Kiprop explains. "In return, the Virtual Agronomist will enable me to know the size of the plots under farming. It also generates a nutrient plan by sampling the soil in the farm, guiding me in what the soil is missing in terms of nutrients and the exact amount to add," he tells Al Jazeera.For his cows, Kiprop also uses an AI tool to manage their health and production."Also, I use the Digicow app, which assists the farmer in managing dairy farm practices by tracking all the day-to-day activities in the dairy farm, which includes recording the amount of milk sold and used by the farmer, dairy inputs like feed and health practices, thus allowing the farmer to know if he's making a profit or not," Kiprop says.Financial Benefits of Tech-Enhanced FarmingBoth Rotich and Kiprop demonstrate that farming with AI tools can be more financially rewarding than traditional employment paths for educated young Kenyans. While contract work offered Rotich a maximum of $200 per month and Kiprop's highest contract paid 15,000 Kenyan shillings ($116), Kiprop now earns approximately 7,000 Kenyan shillings ($54) daily through his tech-enhanced farming operations.The Future of Agriculture in KenyaBoth Rotich and Kiprop agree on one thing: agriculture also comes with its own challenges, and one has to be deeply passionate and consistent to make something out of it."Consistency is key," says Rotich. "It's something that many young people lack, and they quit very early before they can break even and realise profits. One has to do things many times to be able to finally get it and learn from the mistakes made before."

The Lead: Introduction to Chess PuzzlesEarlier today I set these four chess puzzles. Here they are again with solutions.The Event Details: Analysis of Puzzle Solutions1. OdditiesA chess tournament is taking place with several participants. Not every player played against every other player, and some players may have played many more games than others.Some of the players played an odd number of games. Prove that the number of such players must be even.Solution:The total number of games played by everyone must be even, since every game has two players. When you add up odd and even numbers to make an even number, there must be an even number of odd ones, because if you have an odd number of odd numbers the total will be odd.2. L of a tripA knight in chess moves in an "L" pattern - two squares in one direction and one square in a perpendicular direction. Starting in the bottom right corner of a regular 8×8 chessboard, is it possible for a knight to visit every square on the chessboard exactly once and end up in the top left corner?Solution: No.A knight move goes from a white to a black square, or vice versa. To visit every square on the board exactly once requires 63 moves. If you start on white, you will end on black, or vice versa. You cannot start on one corner and end on the opposite corner, since opposite corners of a chess board are the same colour.3. Pawn returnTake a chessboard with the standard initial setup of pieces. What's the fewest number of moves needed for a pawn to leave its initial place, get promoted/queened, and then return to its original position?(Assuming the two players are collaborating to achieve this, not that the one is scuppering the other).Solution: 6Here's one way. The pawn begins on B2. (second column, second row.)White: B2-4. Pawn moves two in knight column.Black: A7-5. Pawn moves two in adjacent rook column.White: B4-A5. Pawn takes pawn.Black: B7-6. Pawn moves one in knight columnWhite: A5-B6. Pawn takes pawnBlack: B8 – A6. Knight moves out of way.For the next three moves, white's pawn advances one by one in the B column, queens and then returns to B2 in the sixth move.4. Four knightsShow how to swap the two pairs of knights on the following strangely-shaped grid.The knights make one move at a time. You're trying to get the black nights to where the white knights are, and the white knights to where the black knights are.If you try to solve this problem using knights on a physical grid, you will get very confused. Try to think abstractly. With one simple(ish) insight, the problem is quickly solvable.Solution:The positions that the knights can move to are very constrained. Here are all possible moves and positions;This looks like a mess! However, if we untangle it, we can see the pattern. If we number boxes from the top row, and from left to right, so the white knights are on positions 1 and 5, and the black knights on 7 and 9, the board now looks like this:To exchange the positions of the knights is now a train shunting problem.Move the black knights to 8 and 6Move the white knight at 5 into the '"side track"' at 9Move the black knights back to 5 and 7.Move the white knight at 9 to 3Move the black knights back to 6 and 8Tuck away the white knight at 1 to square 9Move the black knights to 1 and 5, which is where we want them.Finally, move the white knight at 3 to 7, and we're done.The Mathematical Principles: Logic and Problem SolvingThese chess puzzles demonstrate fundamental mathematical principles including parity (odd and even numbers), graph theory (knight's tours), and optimization (minimum moves). The solutions require abstract thinking and pattern recognition, skills that are essential in both mathematics and chess strategy.The Impact on Problem-Solving: Developing Critical ThinkingChess puzzles like these help develop critical thinking skills that extend beyond the chessboard. They teach players to think several moves ahead, recognize patterns, and approach problems from multiple angles. These cognitive skills are valuable in academic pursuits, professional challenges, and everyday decision-making.Future of Chess Puzzles: Digital and Educational ApplicationsAs technology advances, chess puzzles continue to evolve with digital platforms offering interactive experiences and adaptive difficulty levels. Educational institutions increasingly recognize the value of chess in developing mathematical and logical reasoning skills. Organizations like We Solve Problems are expanding their reach, offering free math circles and chess programs to students across multiple cities, fostering the next generation of problem solvers.

Podcast Overview and Core PremiseThe Guardian’s latest audio feature dives into the scientific side of the 2026 World Cup, exploring how extreme temperatures, political narratives, and video‑assistant‑referee (VAR) technology intersect on the global stage.Heatstroke Risks for Players and FansExperts discuss how high‑temperature venues increase the likelihood of heat‑related illnesses, outlining preventive measures for athletes and spectators alike.Sports Washing: Politics Meets the PitchThe episode analyses how host nations use the tournament to improve international image, a practice known as sports washing, and its implications for global perception.VAR Psychology: Decision‑Making Under ScrutinyPsychologists explain how referees and players cope with the pressure of VAR interventions, shedding light on the mental dynamics that shape match outcomes.Where to Listen and Support Further CoverageListeners can subscribe to Football Weekly for ongoing World Cup analysis and support the Guardian’s science podcast at theguardian.com/sciencepod.