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Lead: A Fresh Set of Chess‑Inspired Brain TeasersToday the Guardian presents four quirky chess puzzles, curated by We Solve Problems, a UK charity that runs free maths circles for secondary‑school students. The puzzles range from graph‑theoretic parity proofs to knight’s tours, inviting readers to engage with mathematics through the lens of chess.Odd‑Numbered Games: Proving an Even Count of PlayersThe first puzzle asks participants to demonstrate that in any tournament where some players have played an odd number of games, the number of such players must be even. This classic result stems from the handshaking lemma in graph theory, where each game contributes two to the total degree sum.Knight’s Tour Challenge: From Bottom‑Right to Top‑LeftThe second puzzle explores whether a knight can start on the bottom‑right corner of an 8×8 board, visit every square exactly once, and finish on the top‑left corner. While a closed knight’s tour exists, the specific start‑end constraint makes the problem a subtle variation that tests spatial reasoning.Pawn Promotion Loop: Minimal Moves to Return HomeThe third puzzle asks for the fewest moves required for a pawn to leave its starting square, promote to a queen, and then travel back to its original position, assuming both players cooperate. Solving it involves coordinating pawn advancement, promotion, and a reverse queen’s path.Four‑Knight Swap on an Irregular GridThe final puzzle presents a strangely‑shaped grid where two pairs of knights must exchange places. A single insightful observation about symmetry unlocks a solution, illustrating how abstract thinking can simplify seemingly complex board problems.Scale of the Maths‑Circle InitiativeMore than a dozen cities across the UK host weekly maths circles.Each circle runs from September to May, targeting pupils aged 7‑11.Volunteer mentors are typically post‑graduates or PhD students.Why Chess‑Based Puzzles Matter for Youth EducationIntegrating chess puzzles into community programmes leverages the game’s universal appeal to foster logical reasoning, combinatorial thinking, and collaborative problem‑solving. By linking puzzles to popular documentaries about Judit Polgár and Hans Niemann, the charity taps into current cultural interest, boosting participation.Looking Ahead: Expanding Collaborative Math OutreachGiven the positive response, We Solve Problems plans to broaden its reach, potentially adding new puzzle formats and digital platforms. Continued media coverage could attract more volunteers and funding, ensuring that quirky challenges like these remain a staple of UK maths education.

A Lost Literary Treasure EmergesA never-before-published short story by Edith Wharton, the first female Pulitzer prize winner who encapsulated the so-called gilded age of US society in bestselling novels including The Age of Innocence, has received its first public airing more than a century after it was written.The Discovery of "The Men Who Saved the World"The story, discovered in the author's archives at Yale University, appears in The Strand, a quarterly magazine that has previously turned up lost or previously unknown works by literary luminaries such as Raymond Chandler, Graham Greene and Tennessee Williams. Believed to have been written no earlier than July 1918, the story was found "incomplete and unpublished" in the Edith Wharton Collection at Yale's Beinecke Rare Book and Manuscript Library.A Tale of Contrasting RealitiesSet during a dinner party in a French chateau towards the end of the first world war, the story tells of the country's wealthiest residents attempting to move on from the conflict that recently scarred them, even as guns are heard still booming and soldiers dying only miles away. The tale is punctuated by the meal being served on a grand dining room table that was used as an operating table for amputations only months before when the chateau was used as a field hospital.Wharton's War Experience Reflected in FictionA main character is a young American nurse called Milly Arden, who observes the household's easy return to its privileged prewar days as she wrestles with the horrors of war and the injuries she has seen and treated. Arden's character appears to be at least in part autobiographical: Wharton, who died in 1937 aged 75, had extensive experience of field hospitals during the conflict also known as the Great War, and helped set up medical care and facilities for affected women and children.Modern Parallels in a Century-Old NarrativeAndrew Gulli, editor-in-chief of The Strand, said the story from more than a century ago has parallels in global events of today. "We live in a time where we're very far away from a lot of horrific events that are happening around the world, and this story sort of encapsulates that mood where there's this beautiful chateau, and people are trying to go back to the old prewar era with the chandeliers and this wonderful dancing, and a dinner party, and not far away the war's still happening," he said.Scholarly Significance and Future DiscoveriesProfessor Isabelle Parsons, a British Open University professor and Wharton scholar who first uncovered the manuscripts, noted that "in the past decade, news of fresh archival discoveries has frequently thrilled Wharton's casual and critical readers." She described the story as "casting a satirical eye over the volunteer efforts of privileged women" and "reads like an experimental attempt – ultimately abandoned by Wharton – at confronting the traumatic effects of warfare through its explicit references to amputation as medical care at the front."

The Decision to Shut Approximately 150 BHF Retail OutletsThe British Heart Foundation announced it will close about 150 charity shops and cut jobs after a review deemed a quarter of its high‑street locations commercially unsustainable.Financial Strain Evident in Plunging Net ProfitNet profit across the charity’s 640 UK stores dropped from £18.8 million in 2024 to £3.6 million in the year to 31 March 2025. Total income for 2025 was £181 million, but net income after direct costs fell by almost £9 million to £129.6 million. The wage and pension bill reached £136 million, and the proportion of income allocated to charitable work fell to 72% from 77% the previous year, still above the 70% benchmark.Operational Implications for Staff and VolunteersRetail arm employs nearly 3,700 staff (3,692 FTE).Head office workforce totals 795 employees, bringing total headcount to 4,545.180 staff earn £60,000 or more.Chief executive Charmaine Griffiths received a £35,000 pay rise to £268,239 for the financial year.Job cuts are planned in central functions supporting retail operations.Broader Implications for the UK Charity Retail LandscapeThe closures reflect a wider shift toward online shopping that is pressuring traditional high‑street charity retailers. With a significant portion of income funding cardiovascular research, the BHF’s move underscores the tension between maintaining a sustainable retail model and preserving charitable impact.Outlook: Timeline for Closures and Future Funding StrategyThe charity aims to shutter 90 stores by the end of March 2027 and the remaining locations by March 2028. Executives stress that the difficult short‑term decisions are intended to protect the long‑term mission of funding lifesaving research.

The U-Turn on Reusable Water Bottles Spectators will not be allowed to carry reusable water bottles into World Cup venues owing to safety concerns, Fifa has said, after a last-minute change to its stadium code of conduct. Details of the Ban The governing body had earlier permitted empty, transparent, reusable plastic bottles inside stadiums but said the updated code prohibited that. Other items such as bottles, cups, jars and cans are also banned to prevent the risk of injury if thrown. Ensuring Safety and Health “Fifa is committed to protecting the health and safety of all players, referees, fans, volunteers, and staff,” it said. “Fifa made the decision to prohibit bottles to prevent risk and injury to players and attendees. Concerns Over Heat and Hydration The move has raised concerns among supporters about coping with heat, with temperatures at a few venues expected to range between 26C and 28C, and access to drinking water inside stadiums. Measures to Mitigate Heat Fifa said measures would be in place to deal with the conditions. “Fifa works closely with each host city committee and local authorities on heat mitigation factors for fans travelling to the stadium, which can include resources such as misting stations, fans, hydration stations, cooling tents and more around the stadium footprint,” it said. Water Availability and Pricing “Inside the stadium footprint, pricing for water bottles for the Fifa World Cup 2026 will remain consistent with other events held at each stadium.”

A team of researchers from Princeton and Oxford has uncovered a decades‑old handwritten note by Richard Feynman that formulates a mathematical solution to the classic “restaurant‑stopping” problem faced by travelers.Decoding Feynman's Hidden Stopping ProblemThe study, published in the Proceedings of the National Academy of Sciences, reconstructs Feynman's original equation, which advises diners to keep trying new venues until a quality threshold is met. That threshold is not static; it declines more rapidly as the remaining nights in a city decrease, reflecting the diminishing value of future visits to a discovered gem.Feynman's notes were handwritten in the 1970s after a lunch with friend Ralph Leighton.The model assumes a fixed range of restaurant quality and equal probability of encountering any quality level.When the distribution of restaurant quality is uneven, the optimal threshold shifts—higher when few gems exist, lower when most venues are above average.Experimental Findings from 2,520 ParticipantsTo test human behaviour, the authors recruited 2,520 volunteers for an online simulation where participants imagined staying in a city for varying lengths of time and chose restaurants from a grid.Participants’ thresholds fell linearly with the proportion of nights remaining, rather than the rapid decline predicted by Feynman's formula.Despite its simplicity, the linear rule performed comparably to the original solution in the simulated environment.Implications for Decision‑Making and Tourism BehaviourThe findings bridge theoretical optimal‑stopping theory with everyday intuition, suggesting that people naturally adopt a decreasing‑threshold strategy when faced with limited opportunities. This insight could inform:Tourism recommendation engines that adapt suggestions as a trip progresses.Behavioral economics models of consumer search in other domains (e.g., housing, job hunting).Design of AI assistants that balance exploration and exploitation in real‑time.Future Directions for Adaptive Choice ModelsThe authors propose extending the model to dynamic environments where restaurant quality distributions change over time, and to incorporate personal preference heterogeneity. Real‑world field trials in travel apps could validate whether a linear decreasing threshold improves user satisfaction and discovery rates.

The Struggle to Find Employment in Grimsby In the Lincolnshire seaside town of Cleethorpes, a 19-year-old man named Cohen is sitting in the back seat of a car, putting on an Easter bunny outfit. He is hoping to use new photographs to advertise his mascot business for the upcoming holidays. Cohen, who has a learning disability, lives with his parents in neighbouring Grimsby and set up Co Co Mascots last year as one of his many attempts to find work. The Challenges of Job Hunting with a Disability Cohen has been applying for roles in holiday parks, retail, charity shops, and even the local football club Grimsby Town FC, which was recruiting for a new mascot. Despite his efforts, he has yet to find paid work. "The hardest thing is not hearing back [from a job application] and not getting feedback," says Cohen. "I start overthinking because I want it [a job] too much. A lot of the time, I think they [employers] will see you have a disability and will pick the person without one because they think the person with a disability is more work." The Economic Reality of Grimsby Grimsby was recently dubbed Britain's "worklessness capital" by the Telegraph due to the large proportion of its working-age people claiming benefits. The town has a higher number of working-age adults out of employment than the national average, and 41% of under-16s in the town live in relative low-income families. Once one of the world's largest fishing ports, Grimsby is still the UK's biggest fish-processing hub, reportedly making every other fish finger eaten across the country. The Impact on Young People For many young people in coastal places such as Grimsby, finding paid employment is hard – and having a disability compounds the issue. Cohen has been volunteering in charity shops and at food banks for more than a year now, and doesn't see his disability as a barrier to working. "My mind can wander a bit when I work so I need a nudge every so often. I just need a bit of support until I get used to the job and what is expected of me." The Future Outlook The Guardian's Against the Tide project aims to report on the lives of young people in coastal communities across England and Wales. The project will examine what kind of changes young people need to build the futures they want for themselves. For Cohen, he will continue to throw everything at his job search, hoping to find a permanent role that suits his needs and abilities.

Ali’s Mantra Reimagined: Service as Humanity’s RentMuhammad Ali once said, “Service to others is the rent we pay for our room here on Earth.” Ten years after his passing on June 3, 2016, his widow Lonnie Ali is foregrounding that credo as the centerpiece of a worldwide call to action.The Muhammad Ali Center’s ‘Day of Compassion’ BlueprintThe Ali Center in Louisville is designating the anniversary week as a global “Day of Compassion,” urging individuals to mark the date with concrete acts of service. The Center, where Lonnie Ali serves as lifetime director, hopes the observance will evolve into an annual tradition that spotlights volunteerism and community uplift.Milestones that Quantify a Decade‑Long Tribute10 years since Ali’s death (June 3 2016‑2026)Three‑time heavyweight champion and 1960 Olympic gold medalistAli’s portrait featured on a U.S. postage stamp in 2024Why the Message Resonates in Today’s Divided LandscapeLonnie Ali warns that the United States is “losing touch with our humanity,” citing growing political and cultural polarization. By linking Ali’s legacy to a universal ethic of service, the Day of Compassion aims to bridge divides, encouraging people to reach beyond echo chambers and support those in need.What the Next ‘Day of Compassion’ Could Look LikeOrganizers envision a decentralized model: schools, faith groups, and corporations worldwide will host service projects, from food drives to voter‑registration assistance. If the inaugural observance gains traction, it could become a fixture on the global calendar, reinforcing Ali’s belief that lasting impact stems from everyday kindness.

The Destruction of a Swift Habitat A noted nesting site for swifts in Surrey, UK, has been demolished during the nesting season, highlighting significant weaknesses in the protection of wildlife from development. The building, known as Regent House, was located near Dorking station and was home to one of the largest populations of swifts in the Mole Valley area. The Event Details Contractors for the housebuilder Hill Group carried out the demolition over the last few weeks, despite the nesting season running from 1 March to 31 August. Footage captured last week shows swifts attempting to return to nests in the building, only to find that their nests are no longer there. The Data Analysis The building was known to host about 40 swifts using around 20 sites in the eaves. Volunteers for Swift Protection Association Reigate had recorded intense low-level flying involving these birds in early spring and summer for several years. Demolition and construction work are heavily restricted during the nesting season under the Wildlife and Countryside Act. The Impact Analysis Annie Griffin of Banstead Swifts, a volunteer group that monitors and tries to stabilise swift populations, described the incident as a significant wildlife crime. Conservationists are now raising broader concerns about the enforcement of environmental protections during development across England. Several people have filed criminal complaints with Surrey police alleging a breach of the Wildlife and Countryside Act. The Prediction The destruction of this swift habitat has sparked fears about the declining population of these birds. Swift populations are massively in decline, and it would have been a simple thing to have carried out the demolition outside the nesting season. The incident highlights the need for stricter enforcement of wildlife protection laws during development projects.

The Lead Pointing to a photograph of dry brown long grass hugging the shoreline, Gerardo Bolaños stands in front of a green oasis of seedlings and trees potted in black plastic bags. "This is what Playa Guiones looked like when we started in 2011," says the executive director of Costas Verdes, a Costa Rican nonprofit. The Coastal Transformation As howler monkeys growl in the background, Bolaños points to the picture next to it – an image of the same patch of land but with scores of flourishing, lush green trees. Today, he says, this is how the beach looks. The reason for the stark difference, says Bolaños, a straight-talking man with a coloured tattoo of the turquoise-browed motmot bird on his left arm, is a sustained tree-planting programme that Costas Verdes started in 2011. The Roots of Reforestation Costas Verdes was founded by then Costa Rican university student Max Tattenbach in 2009. A keen surfer, he wanted to restore the shoreline at his favourite surf spot, Playa Hermosa. "Playa Hermosa is about 6km [3.5 miles] of beach, and it only had one [area of] shade along the entire beach," says Tattenbach. "I used to go surfing there and take my then girlfriend and now wife. She didn't surf and liked to read and chill on the beach, but Playa Hermosa had no shade, so she didn't like going, and it started to become an issue. I promised her I would reforest Playa Hermosa so we could enjoy the beach." The Environmental Impact The project has transformed deforested Pacific coastlines into thriving ecosystems through a community-driven environmental project that has planted more than 100,000 native trees across 34 beaches, reviving wildlife habitats and combating decades of deforestation from cattle farming. Walk along the seafront in Nosara, over 100km further down the coast from Hermosa, and the plan appears to have paid off, with thousands of trees such as tropical almond trees, madero negro (Gliricidia sepium) and frangipani lining the trails and offering shade to beachgoers, creating a thriving ecosystem for wildlife. The Historical Context of Deforestation Bolaños, who joined the organisation as a volunteer in 2011, became project director three years later and executive director in 2024, says deforestation has changed the area's landscape. "Last century, we had great coastal forests all along the Pacific coast of Costa Rica," he says. Bolaños estimates that between the 1940s and 1970s, Costa Rica lost 70% of its forest cover, including along the Pacific coast. He puts this down to a boom in livestock farming. "Farmers burned the ecosystems and grew grass to feed the cattle. It was extremely aggressive, poorly planned," he says. "The beachfronts were devastated by cattle farming." The Future of Coastal Restoration What began as a personal quest for shade has evolved into a community-driven environmental movement with significant implications for coastal conservation. The success of Costas Verdes demonstrates how small-scale, community-led initiatives can have a substantial impact on environmental restoration, offering a model for other regions facing similar deforestation challenges. As climate change continues to threaten coastal ecosystems worldwide, the reforestation efforts in Costa Rica provide a hopeful example of how human intervention can help restore natural habitats and build resilience against environmental degradation.