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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.

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.

Opening the Escher Metaverse at Somerset HouseThe new MC Escher exhibition, running from 5 June‑6 September 2026, transforms the historic London venue into a mind‑bending journey through the artist’s “metaverse” of impossible architecture and mathematical wonder.Immersive Installations Reveal the Mathematical Roots of Escher’s WorkVisitors encounter large‑scale video projections, giant metal spheres, chessboard floors and interactive sculptures that let them step inside iconic prints such as Belvedere (1958) and Waterfall (1961). The show also highlights Escher’s wartime diploma design of 1945 and his early fascination with tessellation after seeing the Alhambra.Video walls that animate the shifting staircases of RelativityMetal spheres echoing the convex‑mirror motifChessboard floor that reacts to foot trafficWhy the Exhibition Redefines the Intersection of Art and ScienceBy linking Escher’s visual paradoxes to the insights of physicist Roger Penrose and the broader pop‑culture legacy (e.g., Pink Floyd’s Ummagumma cover), the show demonstrates how mathematical concepts can inspire both fine art and popular media.What the Future Holds for Escher’s Legacy in Digital SpacesCurators suggest that the immersive format could evolve into virtual‑reality experiences, allowing global audiences to explore Escher’s impossible worlds online, keeping his “language of mathematics” alive for new generations.

The Miraculous Discovery A Nepali Sherpa guide who went missing on Mount Everest six days ago has been found crawling alone to base camp after fears that he had died. According to Pemba Sherpa of 8K Expeditions, which was coordinating the search for the missing guide, Dawa Sherpa was found by a clearing crew on Thursday morning as he was crawling down snowy slopes around the Khumbu Icefall. The Dramatic Rescue Operation Dawa, 52, was carried down to safety and given food and water. A rescue helicopter flew him to HAMS Hospital in the capital, Kathmandu, where his wife and daughter, who had already begun funeral rituals, were waiting. "We first heard that he was still alive on the local news and from a person we know who called with the news that … he is being brought down," his wife, Damu Sherpa, said. The Timeline of Events Dawa was last seen around May 29 descending the mountain He did not reach base camp, although his client, a Polish climber, did There was a delay in organizing a search team When rescue helicopters were finally sent, they could not locate him He was found by a clearing crew from the Sagarmatha Pollution Control Committee Family's Emotional Journey For Dawa's family, hope of seeing him again was all but gone. His teenage daughter, Mendo Lhamu Sherpa, said they were already on the second day of a funeral ritual, which lasts for several days. "When we first heard about it, we could not be sure if that person was indeed our father," Mendo Lhamu said. "So to be certain, we asked for photos to be sent, and then only we were sure and very happy." Everest's Busiest Season The team that spotted him was part of the Sagarmatha Pollution Control Committee, which lays ladders and ropes on the route at the start of each climbing season and then removes the equipment and cleans up the site after the climbers have left. Last month, more than 1,000 climbers and their guides scaled Everest during the busiest climbing season ever on the world's highest mountain. At least five people have died this season.

The LeadJamaica has emerged from a rare islandwide power outage that struck the Caribbean Island overnight, with Energy Minister Daryl Vaz announcing that all affected customers have had their power restored. Both Vaz and Prime Minister Andrew Holness described the situation as 'unacceptable,' highlighting concerns about the nation's electrical grid vulnerability as the Atlantic hurricane season begins.The Islandwide Power CrisisThe blackout began at approximately 9pm local time on Friday (2:00 GMT Saturday), affecting all of Jamaica's 2.8 million residents. The Jamaica Public Service Company (JPS), the sole electricity distributor on the island, reported the outage and began restoration efforts. By 2am Saturday (7:00 GMT), the company had restored power to 20 percent of customers, or approximately 140,000 people in areas including Kingston, St Andrew, and Clarendon. Three hours later, Minister Vaz announced that electricity had been returned to 500,000 of JPS's 700,000 customers overnight, with the remainder to be restored in the following hours.The Government ResponseMinister Vaz took immediate action, calling an emergency meeting with government and JPS officials to discuss the blackout. He committed to keeping the nation informed throughout the restoration process, stating on social media: 'I have been closely monitoring the situation all night and will continue to do so until full restoration is completed.' Vaz has formally demanded a full report from JPS within 24 hours, including a detailed explanation of what caused the power outage. The minister also encouraged residents experiencing any 'isolated issues' related to the blackout to contact him directly.The Grid Vulnerability ConcernsThe timing of the blackout has raised particular alarm, occurring at the start of the Atlantic hurricane season. This has intensified concerns about how Jamaica's electrical grid might withstand future weather events. The island's reliance on a single electricity provider, JPS—which was briefly nationalized before returning to private hands—has drawn scrutiny following this widespread failure. This incident is unusual for Jamaica, which typically only experiences islandwide outages during weather emergencies, such as last year's Hurricane Melissa, which caused billions of dollars in damage and dozens of deaths.The Aftermath and InvestigationAs of Saturday morning, JPS stated it was 'investigating the cause of the cause of this incident,' with no official explanation provided yet. The company had assured customers that its teams would be working throughout the night to restore power 'as safely and quickly as possible.' The government's strong reaction suggests potential regulatory consequences for JPS, as the nation seeks to prevent similar disruptions in the future. With hurricane season now underway, the resilience of Jamaica's energy infrastructure will likely face increased scrutiny and testing in the coming months.

The Bridge Between Art and ScienceWhy do we find things beautiful? More precisely, why do some paintings of coloured dots in rippling patterns inspire in me something like revelation? The idea that beauty is the feeling you get when encountering truth is unfashionable in the arts, but lingers in the sciences. The physicist Paul Dirac once proposed that it is more important that a formula is beautiful than that it can be proven: when a perfectly beautiful theory produces results that cannot be real, he argued, then we should not discard the theory but reconsider what is real.Since the 1970s, Terry Winters has been rebuilding that bridge between art and science. Taking inspiration from disciplines including botany – his early paintings, particularly, evoke sprouting pods and tangled roots – engineering, computer modelling and cybernetics, his paintings might be understood as diagrammatic approximations of the patterns that govern everything from the division of cells to the constellation of stars. If every era has to renew its standards of beauty to reflect new understandings of how the world is constructed, then Winters comes as close to providing that model as any living painter.Mathematical Patterns in Visual ArtThese eight new works take their titles from the language of geometry and mathematics: Area, Array, Field, Locus, Point, Scope, Sequence and Set. Each is composed of overlapping patterns that pull each other out of shape according to invisible laws of attraction and repulsion. Field is indicative: on a sooty pink ground, a dense grid of dusty blue cells bends inwards like a trampoline beneath a bowling ball, while an intersecting arrangement of larger circles swells outwards. The disorienting effect of this push-pull is exaggerated by an optical illusion, created by ragged phosphorescent orange haloes around the blue circles, that makes them appear to be craters sunk into the crust of paint. You have to walk up to the surface to be reassured that it is flat.Point shows a teeming landscape of cells bulging outwards at the centre, as if a scum of frogspawn had been skimmed off a pond and placed under a paperweight microscope. In Sequence, a storm of pink interference skims through a yellow circle split like a brain into hemispheres, while a nebulous weather system sweeps in from the right. In Scope, vaguely symbolic arrangements of freshwater blue and desert orange nodules move across the familiar circle-within-a-square geometry of Leonardo's Vitruvian Man. Where that famous demonstration of sacred geometries exudes stillness and calm, the systems that run through Winters' worlds are wild and strange. Here, as much importance is given to the subjective factors of perception and consciousness as the objective principles of logic and proportion.Optical Illusions and Sensory ExperienceAll of this should not distract from the pure sensory pleasure afforded by these pictures. In Locus, another optical illusion seems to lift the red edge of the painting off the canvas like a clumsy wooden frame, squeezing the pockmarked sphere at its centre so that it balloons outwards, threatening to burst. The same cadmium red, so sandy that the pigment seems barely to have been suspended in oil, turns carmine pockets into rock formations that climb off the surface of Set. These sleights of hand evoke the more secular movement of op art, in which patterns are manipulated to exploit the idiosyncrasies of human perception rather than to uncover deeper truths. Which begs the question: is this all just a conjuring trick?Rediscovering the Renaissance ApproachThere is something magical about these works. Even though Winters is generally credited with having extended the lineage of modernist American painting into the present, his practice is in this sense pre-modern. In its rejection of the idea that art should be separated from science, it resembles the Renaissance attitude according to which painting is no less a tool for understanding the world than mathematics, and magic is just the name for things we don't yet understand. His commitment to synthesising diverse spheres of knowledge, his alchemist's commitment to materials, and his sheer technical ability certainly mark him out in a scene recently overwhelmed by chancers and charlatans, bandwagoners and snake-oil salesmen. That his work is enjoying a revival might be taken as an encouraging sign.Beauty as a Path to TruthDirac, incidentally, was proved right. He formulated a theory that was so beautiful it couldn't possibly be wrong, even though it implied the existence of phenomena that everyone agreed must be impossible. He stood by it, and a few years later, someone else discovered anti-matter. Winters' paintings likewise offer a flash of those secret patterns that underpin the physical world, and which science has yet to illuminate. Which is to say, they're beautiful.Exhibition DetailsTerry Winters: Along the River is at Modern Art, London, until 11 July

The War Economy: A Billionaire’s Perspective from the FrontlineUkraine is reeling from its heaviest aerial raid in months, with at least 25 people killed in the night sky. In the aftermath, Rinat Akhmetov, the country's wealthiest oligarch and owner of Shakhtar Donetsk, gives a rare interview from a location outside Kyiv. This conversation marks the 90th anniversary of the club and the 30th year of Akhmetov's leadership, offering a unique insight into how the war has reshaped his personal and professional life.From Coal Traders to Champions: The Akhmetov StrategyAkhmetov’s rise from a child in 1970s Donbas to the owner of one of eastern Europe’s most influential football clubs is a story of calculated risk and strategic foresight. His journey began not in football, but in the volatile economy of the 1990s.The Proximity of Danger: Akhmetov was five seconds away from death when his business partner and predecessor, Akhat Bragin, was killed in a stadium explosion in 1995. This tragedy left the club abandoned, with players earning as little as $200 or $300 a month.Industrial Expansion: Leveraging the collapse of the Soviet Union, Akhmetov moved from trading coke and coal to acquiring cheap stakes in metallurgy plants. He revitalized the Yenakiieve plant, where workers previously earned $45 a month, transforming it into a globally competitive enterprise.Breaking the Mold: To break Dynamo Kyiv's dominance, Akhmetov hired foreign managers like Nevio Scala and Mircea Lucescu. He argued that a patriot is someone who works for Ukraine's benefit, regardless of origin, a philosophy that yielded 22 trophies over 12 years.The Financial Toll of Occupation and the Iron and Steelworks of AzovstalThe conflict in Donbas has been devastating for Akhmetov’s industrial empire. Since the occupation began in 2014, his businesses have suffered severe losses. The Azovstal iron and steelworks became a global symbol of Ukraine's resilience during the 2022 siege, though it came at a massive cost to the local economy.Shakhtar was forced to flee their home, losing the Donbas Arena—a stadium that once held 40,000 to 50,000 fans—to the occupying forces. The club's relocation to Lviv and Poland turned them into a powerful ambassador for the Ukrainian state, using the Conference League semi-finals to keep the world's attention on the war.Shakhtar as a Symbol of Ukrainian ResilienceAkhmetov reveals that Shakhtar has always been pro-Ukrainian, evidenced by their 2007 decision to use the Ukrainian spelling of their name over the Russian one. However, the full-scale invasion has crystallized this identity. The club is now viewed globally as a symbol of the fight for independence, sovereignty, and freedom.The Road to Donbas: A Promise Kept and BrokenFor years, Akhmetov maintained a moral imperative: he vowed not to attend another game until Shakhtar returned to their beloved Donbas Arena. This promise was broken last month when he returned for the Conference League quarter-final following the death of his long-time manager, Mircea Lucescu. The spontaneous decision was driven by emotion, as the players' applause during the warm-up moved him to tears. It marks a significant moment in the club's history, signaling a potential return to the region that birthed them, even as the war continues.

The Deadly Hotel Fire At least 21 people have been killed, including 18 foreign nationals, as a fire ripped through a hotel in New Delhi, police said, in one of the deadliest blazes in the Indian capital in years. Foreign Nationals Among Victims The dead included people from Bangladesh, Nigeria, Mozambique, and Liberia, CNN-News18 said. Many of them had come to the city for medical treatment, the Indian Express and other local media reported. Fire Details and Rescue Efforts The fire took place on Wednesday in a building in the Malviya Nagar neighborhood in the southern part of the city, which has a restaurant on the ground floor and a hotel above. The blaze was extinguished with the help of eight fire engines, and more than 40 people were rescued and taken to nearby hospitals, Delhi police said in a statement. Cause of the Blaze and Aftermath The cause of the blaze was not immediately known, but building fires are relatively common in India due to a lack of firefighting equipment and frequent disregard for safety regulations. Prime Minister Narendra Modi said the loss of lives was tragic and extended his heartfelt condolences to those who have lost their loved ones and wished a speedy recovery to the injured.

The Summer Art RenaissanceLondon's cultural landscape is experiencing a vibrant transformation this summer with a diverse array of exhibitions spanning optical illusions, light installations, and Pan-African perspectives. From the mind-bending works of MC Escher to the provocative presence of Julio Le Parc, the city's galleries are offering immersive experiences that challenge conventional artistic boundaries.The Escher Paradox ExperienceThe spotlight shines on MC Escher at Somerset House, where the Dutch master's renowned optical illusions and impossible constructions take center stage. This retrospective goes beyond mere visual trickery, incorporating video installations and musical elements to create a multi-sensory exploration of Escher's mathematical precision and artistic vision. The exhibition, running until September 6, represents a rare opportunity to experience the full breadth of Escher's printmaking genius in an environment designed to enhance the paradoxical nature of his work.Light, Colour, and Action in Modern ArtSimultaneously, Tate Modern presents Julio Le Parc: Light. Colour. Action, a comprehensive survey of the Argentinian artist who became a provocative force in the French art scene. Le Parc's innovative use of light and movement challenges traditional notions of static art, creating dynamic environments that respond to viewer interaction. The exhibition, running through May 2027, positions Le Parc as a pivotal figure in bridging the gap between artistic expression and scientific inquiry.Pan-African Artistic ExpressionThe Barbican Gallery hosts Project a Black Planet, a monumental exhibition showcasing the depth and diversity of Pan-African artistic expression. Featuring prominent artists such as Chris Ofili, David Hammons, and William Kentridge, the exhibition presents a comprehensive narrative of African diasporic art from multiple perspectives. Running from June to September, this ambitious survey underscores the growing recognition of African artistic contributions on the global stage.The Marilyn Phenomenon RevisitedAt the National Portrait Gallery, Marilyn Monroe: A Portrait offers a fresh perspective on the cultural icon's enduring fascination. While acknowledging Andy Warhol's iconic representations, the exhibition explores how numerous artists have been drawn to Monroe's image, each interpreting her legacy through different artistic lenses. The exhibition runs until September 6, providing a timely reconsideration of Monroe's cultural impact.Glasgow's Artistic CapitalGlasgow International reinforces the city's status as Scotland's artistic capital, featuring biennial exhibitions from notable artists including Victoria Morton, Cathy Wilkes, and Luke Fowler. The event, running through June with some exhibitions continuing into the summer, highlights Glasgow's unique contribution to contemporary art and its role as a cultural hub outside London's dominant art scene.Architectural Statements and ControversiesAcross the Atlantic, Chicago's Obama Presidential Center has sparked intense debate, with critics likening the $850m structure to 'a Klingon prison.' Designed by Tod Williams Billie Tsien Architects, the complex features a central tower intended to resemble four hands coming together to protect a flame—a beacon of hope. The architectural controversy surrounding the center reflects broader discussions about the role of public buildings in contemporary society and the challenges of creating meaningful civic architecture.Artistic Legacy and Historical ContextThe week's artistic offerings also include a fascinating connection between past and present. The National Gallery's 17th century masterpiece 'A Peepshow With Views of the Interior of a Dutch House' by Samuel van Hoogstraten demonstrates how artists have long played with perspective and illusion—techniques that would later influence modern masters like Escher. This historical context enriches our understanding of artistic innovation across centuries.