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What’s on the board: Four new chess‑inspired puzzlesToday’s article presents a quartet of quirky chess problems curated by We Solve Problems. The puzzles are designed for maths‑loving readers and aim to spark discussion rather than reveal solutions.Odd‑game parity proof – why the count of odd‑play participants is evenIn a tournament where not every player faces every other, some competitors play an odd number of games. The task is to prove that the number of such players must be even, a classic graph‑theoretic result.Knight’s tour from bottom‑right to top‑left – is a full tour possible?Starting from the bottom‑right corner of an 8×8 board, can a knight visit every square exactly once and finish in the top‑left corner? This asks for a Hamiltonian path in the knight‑move graph.Pawn promotion round‑trip – minimal moves to return homeWith both sides cooperating, determine the fewest moves for a pawn to leave its starting square, promote to a queen, and then travel back to its original position.Swapping knights on an irregular grid – the abstract solutionA strangely‑shaped grid holds two pairs of knights. The challenge is to exchange the positions of the black knights with the white knights using only legal knight moves.Why these puzzles matter – boosting maths circles and chess cultureThey promote logical thinking and problem‑solving among secondary‑school students.The article references recent documentaries on Judit Polgár and Hans Niemann, linking popular chess media to educational outreach.We Solve Problems runs free maths circles across the UK, using puzzles like these to engage young learners.Looking ahead – more weekly challenges from the charityThe author will return at 5 pm UK time with solutions and promises future puzzles every alternate Monday. Readers are encouraged to discuss the problems but avoid spoilers.

France defender Ibrahima Konaté opened up about a year marked by the death of former Liverpool teammate Diogo Jota and his father, describing how the grief triggered depression and affected his performance.Personal Tragedies That Upended Konaté’s SeasonKonaté recounted the shock of the crash that killed Jota and Jota’s brother André Silva on the eve of pre‑season, followed months later by his father Hamady succumbing to a long illness. He described “low points” and “depression” that “started in the heart, went up to the brain and took over the whole body.”Impact on On‑Field Performance and Club DecisionsThe emotional toll was evident in his form, but after a period of compassionate leave he returned to help Liverpool during a defensive injury crisis, scoring on an emotional comeback against Newcastle. While still under contract, Konaté is poised to leave Liverpool for Real Madrid after failing to agree a new deal.Wider Significance for Mental‑Health Dialogue in FootballKonaté’s candid remarks challenge the stereotype that wealthy players are immune to mental‑health struggles. He emphasized that “there’s no need to be ashamed” and urged players to speak up, highlighting the need for clubs and fans to provide supportive environments.Looking Ahead: Potential Shifts in Player Support StructuresHis story may accelerate the adoption of mental‑health resources within elite clubs, encouraging more open conversations and professional support for players dealing with personal crises. As Konaté prepares for a new chapter in Spain, his advocacy could influence how the sport addresses depression and grief moving forward.

The Lead After a decade leading the National Theatre, director Rufus Norris reflects on life after leaving the prestigious institution. The acclaimed theatre artist discusses his new production of Arthur Miller's "Death of a Salesman" in Istanbul and the personal freedom he's discovered in stepping away from the spotlight. A New Chapter: Post-National Theatre Life Norris's tenure at the National Theatre concluded in 2025, coinciding with several significant personal milestones: the loss of his mother, turning 60, and completing a decade at the helm of one of Britain's most prestigious cultural institutions. "It felt important to have a complete break," Norris explains, noting his transition involved DIY projects, kayaking, and a house move. "I'm a bit of a workaholic, but I'm also a bird of simple brain so I can as easily lose myself in how to build a shed or do up a place." Istanbul Venture: Death of a Salesman Norris's first major project after leaving the NT is directing a Turkish-language production of Arthur Miller's "Death of a Salesman" at Istanbul's Zorlu Performing Arts Centre. The opportunity arose serendipitously when Norris was teaching a workshop at the venue, and general manager Filiz Ova approached him to direct the play in the complex's largest space, which seats 2,300 people. "We had been thinking of doing this play for several years and it had never been done at Zorlu PAC," Ova explains, noting her admiration for how Norris connects with people. Creative Collaboration Across Cultures The production features a hybrid creative team blending international and Turkish talent. Set designer Es Devlin, Olivier award-winning choreographer Javier de Frutos, renowned Turkish composer Oğuz Kaplangı, and Turkish deputy director Balım Kar join forces for this ambitious project. The casting includes Turkish national mega-stars: Halit Ergenç (known for "Magnificent Century") as Willy Loman, Zerrin Tekindor as Linda Loman, with Fatih Artman and Kerem Arslanoğlu as their sons. The play features English surtitles to accommodate non-Turkish speakers. Personal Connection to Miller's Masterpiece Norris found a profound personal connection to Miller's exploration of a man abandoned in childhood, striving for acceptance, and experiencing early dementia symptoms. This resonated deeply with Norris, whose mother lived with vascular dementia for years before her death. "My mum went through a very long process of decline. She hadn't recognised me for three years before she died," he shares. For Norris, the play presents "the tragedy of that human condition alongside the toxic illusions of America's capitalist dream." Freedom from the Spotlight Norris embraces his new life with a sense of liberation, particularly enjoying the freedom from the intense scrutiny that came with his NT position. "I like not having that focus on me. It's a relief... I'm irrelevant," he admits. "There's no point in thinking: 'Why aren't I important any more?' The culture moves on and it has to move on. That's how it stays healthy and relevant." He now resides in Fife, Scotland, with his partner, playwright Tanya Ronder, finding contentment in a simpler existence. Artistic Reawakening Having primarily focused on plays for the past two decades, Norris is now broadening his reading habits, exploring novels and history books. "I've got time and space finally to think, 'Oh that looks interesting,'" he explains. "You have to train yourself to actually lose yourself in a novel or nonfiction work when every 45 minutes your brain goes 'Oh surely I should be having a meeting or doing something else'." This renewed intellectual freedom is feeding his creative spirit as he considers future projects. The Future of Theatre Without Institutions Norris rejects the notion of needing to reinvent himself or seek a new institutional position. "There's nowhere like the National so you can't go beyond that. I don't have any ambition to run another building," he states. Instead, he's finding fulfillment in the creative process itself, unburdened by administrative responsibilities. "It's really about what's going to make me feel alive and engaged and content," he concludes, suggesting a new model for artistic leadership that prioritizes creative freedom over institutional power.

The Tobacco Industry's Strategic Pivot to the Grocery AisleA comprehensive new investigation published in the American Journal of Public Health (AJPH) has exposed how titans of the tobacco industry seamlessly transitioned their controversial business practices into the food sector. After acquiring major food brands in the late 20th century, companies like RJ Reynolds and Philip Morris utilized the exact same playbook used to sell cigarettes to engineer and market ultra-processed foods (UPFs). This strategic crossover fundamentally altered the global food landscape, prioritizing consumer addiction over nutritional value.Engineering Addiction: From Nicotine to Hedonic FoodsAccording to Tera Fazzino, a psychology professor and addiction researcher at the University of Kansas, an analysis of over 100 previously secret industry documents proved that tobacco executives replicated their international tobacco strategies to build their food businesses. The primary focus was on optimizing product formulations to create a rapid, fleeting sense of reward.Maximizing Hedonic Impact: Formulations of carbohydrates and fats were optimized for rapid delivery to the brain's reward centers.Portion Manipulation: The introduction of king-sized food items directly mirrored the strategy behind king-sized cigarettes.Illusion of Health: The development of light and reduced-fat UPFs was borrowed directly from the tobacco industry's creation of light cigarettes, designed specifically to retain health-conscious customers who might otherwise quit.Targeting Children: Following Philip Morris's acquisition of Kraft in 1988, the company launched Lunchables. Laura Schmidt, a health policy professor at UC San Francisco, noted that product designers used psychological research to target children's underlying drives for independence, autonomy, and play.The Cognitive and Cardiovascular Toll of UPFsThe health ramifications of applying addiction-driven frameworks to everyday foods are now becoming undeniably clear. During the AJPH press briefing, Cindy Leung, a public health nutrition professor at Harvard, highlighted the severe cognitive risks associated with high UPF consumption. Because clinical trials on long-term nutrition are often impractical, experts rely on robust observational studies that are considered biologically plausible.The data reveals that individuals with diets high in UPFs face:A 58% higher risk of developing dementia.A 46% higher risk of developing mild cognitive impairment.An overall 47% higher risk of experiencing either of these cognitive decline outcomes.Furthermore, UPFs are heavily linked to a rise in cardiovascular diseases and certain cancers, drawing a grim parallel to the historical public health battles fought against the tobacco industry.Political Movements and Flawed Agricultural SubsidiesThe growing outrage over UPFs has fueled political movements like Make America Healthy Again (Maha). While experts like nutritionist Marion Nestle applaud the movement for shifting the blame away from a lack of personal willpower and onto the food industry, they warn that current policy directions are actively exacerbating the crisis.Instead of redirecting government corn subsidies toward whole fruits and vegetables, current policies continue to prop up the production of high fructose corn syrup, a cornerstone ingredient in UPFs. Additionally, efforts by the Trump administration to reduce enrollments in the Supplemental Nutrition Assistance Program (Snap) threaten to limit public access to affordable whole foods, pushing lower-income populations further toward cheap, ultra-processed alternatives.The Looming Regulatory Reckoning for Food ManufacturersAs the scientific evidence linking UPFs to severe health crises mounts, the food industry is facing a landscape increasingly reminiscent of the 1990s tobacco lawsuits. With Philip Morris having rebranded as Altria, and Kraft merging with Heinz to form Kraft-Heinz, these corporate giants may soon face intense regulatory scrutiny. As public awareness shifts from personal diet choices to systemic industry manipulation, we can expect a surge in legislative demands for transparent formulation practices, stricter marketing limits on child-targeted foods, and a fundamental overhaul of agricultural subsidies.

The Lead: New Hope for Brain Injury RecoveryDr. Orlando Swayne, a consultant neurologist at the National Hospital for Neurology and Neurosurgery in London, is challenging the long-held medical belief that broken brains cannot mend. Through his pioneering work in neurorehabilitation, Swayne demonstrates that the brain's remarkable capacity for neuroplasticity can lead to meaningful recovery even years after severe brain injuries, offering new hope to patients who were once considered beyond help.The Case of Claire: A Journey from Severe Impairment to RecoveryClaire, a mother of three in her late 30s, experienced life-changing trauma when an artery at the base of her brain ruptured, causing severe damage to her frontal lobe. Initially brought to the ward on a stretcher, she was unable to speak, with flat eyes and an expressionless face. While she could move her right arm slightly, her left arm and both legs were immobile. When asked if she had any questions, she wrote with a clenched pencil: "Questions, questions, questions," revealing characteristic signs of brain damage through pathological repetition.The Science of Neuroplasticity: How the Brain Heals ItselfThe key to recovery lies in the brain's capacity for neuroplasticity—its ability to make new connections and reorganize in the face of changed circumstances. After a stroke or brain injury, chemical changes in the brain trigger neuronal growth processes that were last active during development. Surviving neurons are spurred into making new connections to work around dead tissue. While this process occurs naturally, targeted therapy can significantly enhance and guide it, leading to more substantial functional improvements.The Critical Window for Recovery: Timing MattersWhile the brain's capacity for plasticity is greatest in the first few months after injury, research shows that neuroplasticity doesn't simply switch off. In one study, intensive therapy improved upper limb movement in patients 18 months after their strokes. This finding is crucial as it extends the potential for recovery beyond the traditional "golden window" of the first few weeks or months, offering hope to those who may have missed early intervention opportunities.The Moral and Economic Imperative of NeurorehabilitationStroke is a leading cause of adult disability in the UK, with approximately 12 million people globally suffering a stroke each year, and one in five dying within 30 days. The economic and human costs of untreated brain injuries are enormous. Swayne argues that providing early, targeted, and intense therapy is not just a moral obligation but also an economic imperative, as proper rehabilitation can significantly reduce long-term care costs while dramatically improving patients' quality of life and independence.The Future of Brain Injury Treatment: Balancing Hope with RealismWhile Swayne emphasizes that recovery is possible, he is careful to balance hope with realism. "There is hope, but clearly you have to balance that. Some people just don't recover," he acknowledges. His approach represents a middle ground between the false promises of miracle cures and the previous hopelessness surrounding brain injuries. By focusing on evidence-based interventions and realistic expectations, Swayne and his colleagues are transforming the landscape of neurorehabilitation, offering meaningful improvements even for those with the most severe impairments.

The Legacy of Claude Lemieux Claude Lemieux, a legendary NHL player, has made a significant contribution to the understanding of Chronic Traumatic Encephalopathy (CTE) by donating his brain to the Boston University CTE Center. Lemieux, who won four Stanley Cups and played nearly 1,500 NHL games, died by suicide at the age of 60. The Brain Donation and CTE Research Lemieux's family gave permission for the CTE Center to publicly share any findings with his name, emphasizing that no conclusions should be drawn regarding any diagnosis. This donation aligns with Lemieux's post-playing career dedication to helping the next generation, particularly in his role as an agent. Understanding CTE CTE is a degenerative brain condition caused by repeated trauma to the head, diagnosable only after death. Symptoms include memory loss, brain fog, aggression, mood swings, and depression. The research aims to provide greater understanding, facilitate honest conversations, and improve protection for athletes and families. The Impact on Athletes and Families Lemieux's family hopes that his donation will have a lasting impact on the lives of athletes and families. By allowing his name to be connected to this research, they aim to promote better protection and support for those affected by CTE. Support for Those Affected In the US, the suicide prevention lifeline is 1-800-273-8255 and the domestic violence hotline is 1-800-799-SAFE (7233). Other international helplines can be found at www.befrienders.org. In the UK and Ireland, Samaritans can be contacted on 116 123 and the domestic violence helpline is 0808 2000 247. In Australia, the crisis support service Lifeline is 13 11 14 and the national family violence counselling service is 1800 737 732.

The Lead: A Modern Struggle with Classic LiteratureIn an era dominated by rapid-fire digital consumption, engaging with dense, classic literature has become an uphill battle. A recent reflection by a lifelong reader highlights a growing cultural phenomenon: despite a deep personal history with the classics, the modern brain—conditioned by screens and constant notifications—is struggling to process long-form, complex narratives.The Battle Against the Victorian BlockbusterSparked by The Guardian's list of the 100 best novels, the author attempted to rekindle his youth by diving into chunky Victorian classics. However, the attempt was met with frustration rather than nostalgia. The books that once captivated him now felt impenetrable.The Life and Opinions of Tristram Shandy, Gentleman by Laurence Sterne: Found to be verbose and infuriatingly digressive.Dracula by Bram Stoker: Entertaining initially, but ultimately derailed by the absurdity of its epistolary format and moralizing characters like Van Helsing.Our Mutual Friend by Charles Dickens: Despite a previous love for Dickens' pacing and humor, the 900-page narrative felt too heavy, leading to a loss of concentration and the urge to check football scores instead.The 15-Second Attention EconomyThis personal struggle is backed by alarming data regarding how we consume information today. The transition from the linear, monologic page to dynamic, ad-cluttered screens has fundamentally altered human cognition.Research by psychologist Gloria Mark indicates that screens compel us to constantly switch our attention toward new, shiny stimuli rather than focusing on content.Data from Chartbeat reveals a stark reality: one in three online readers spend less than 15 seconds on any given article.The Rise of Text Fatigue in the WorkplaceThe shift in reading habits is not merely a failure of willpower; it is a symptom of occupational and technological exhaustion. As more professionals occupy managerial roles, their days are spent drowning in emails, instant messages, and digital work tasks. According to University of Oxford professor Kate McLoughlin, while people are reading more than ever—consuming social media posts, blogs, and AI utterances—they are reading fewer books. This constant, shallow skimming has led to widespread text fatigue.Reclaiming the Page in a Screen-Dominated FutureIf three classic novels in a row end up abandoned, the issue is systemic rather than a flaw in the literature. The modern environment actively discourages the deep, sustained focus required by authors like George Eliot or Herman Melville. Moving forward, readers will need to be far more intentional about their media diets. Relearning how to read may require deliberate digital detoxes to rebuild the atrophied muscles of deep concentration, ensuring that the rich, complex works of the past do not become inaccessible artifacts of a bygone era.

Lead: A Columnist’s Warning About AI’s Empty VoiceNesrine Malik contends that AI‑generated text is fundamentally meaningless, a fact that makes it dangerously suited to today’s political climate of repetitive, low‑emotion rhetoric. She describes a personal “nightmare scenario” where AI research tools introduce misquotes and dilute the writer’s own intellectual labor.The Column’s Core Claim: AI Lacks Humanity and Fuels Empty Political RhetoricMalik frames AI as a “tinny chant” that pervades everything from customer‑service bots to social‑media posts, stripping language of its personal alchemy. She argues that while AI can mimic styles, it cannot generate truly original voices, leaving writers dependent on a chorus of existing tones.Lack of Quantitative Data – Qualitative Observations OnlyNo financial or usage statistics are cited in the piece.The argument relies on anecdotal evidence: misattributed quotes, a Commonwealth short‑story controversy, and personal writing habits.References to external research (e.g., a Time study) suggest AI may reduce brain engagement, but no specific figures are provided.Implications for Journalism, Politics, and Public DiscourseThe column warns that AI’s bland, repeatable tone amplifies disinformation and enables political actors to hide behind “empty slogans.”Keir Starmer‑like voices are cited as examples of how AI‑styled language can mute genuine ideological expression, allowing extremist narratives to surface unchecked.Future Trajectory of Human Authorship in an AI‑Saturated LandscapeMalik predicts a growing cultural atrophy if writers continue to outsource research and prose to LLMs. She urges a conscious resistance to preserve the “social contract” of trust and authenticity, suggesting that the battle for credible, human‑crafted content will define the next era of public communication.

The Clubs with the Fewest Sponsor Logos Various football clubs have had remarkably few sponsor logos on their shirts throughout their history. Let's take a look at some examples. PSV Eindhoven's Sponsorship History PSV Eindhoven have had only three sponsors: Philips (from 1982 to 2016), EnergieDirect (2016-2019), and Brainport Eindhoven (2019-present). Japanese Clubs with Long-Term Sponsors Sanfrecce Hiroshima: Mazda has been on the front of shirts since the club's inception in 1992, making it one sponsor in 34 years. Kawasaki Frontale: Fujitsu has been the principal sponsor of the team since its days as the Fujitsu Soccer Club in 1991, marking one sponsor in 35 years. Gamba Osaka: Panasonic has been on the front of the shirts since 1992. Yokohama F Marinos: Nissan has been the sponsor since 1992. Kashiwa Reysol: Hitachi has been the sponsor since 1993. Other Notable Examples FC United of Manchester: They have never had a front of shirt sponsor in accordance with their anti-commercial philosophy. Rangers de Talca from Chile: They have had only one sponsor, Productos Fernández, since 1977, with the current deal set to expire in 2031. Celta Vigo: They have had just two sponsors: Citroën between 1985 and 2016 and Estrella Galicia since 2016. The Impact of Sponsorship on Football Clubs The number of sponsor logos on a football club's shirt can be an interesting aspect of their history and identity. While some clubs have had multiple sponsors over the years, others have maintained long-term partnerships with a single sponsor.