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The Perfect World Cup Send-offIn a last outing before a first World Cup appearance in 28 years, Scotland dismantled Bolivia with a commanding 4-0 victory. The performance, featuring goals from Lawrence Shankland, Scott McTominay and a brace from Ché Adams, suddenly worries over a potentially tournament defining joust with Haiti next weekend evaporated. If Steve Clarke's men are this ruthless and efficient when the proper stuff starts, they have a serious chance of emerging from the group phase for the first time in Scotland's international history.First Half DominationIn sweltering New Jersey heat, the Scots made a fine start. Andy Robertson completed a one-two with Ryan Christie before chipping a cross to the back post. The Bolivia goalkeeper, Guillermo Viscarra, should have done better with Shankland's header but Scotland's No 20 had no cause to care. This marked his third goal in two games. Adams, who was lively, tested Viscarra before firing a shot only narrowly wide.A second goal was soon forthcoming anyway. Shankland nudged the ball back to McTominay, whose low drive from 18 yards beat the highly unconvincing Viscarra. Scotland's third was a fine goal too, with Aaron Hickey feeding the marauding Ben Gannon-Doak, who put in a perfect cross to the feet of Adams. The Torino man could not miss.Scotland's Attacking ProwessScotland were to match a first-half scoreline margin feat first achieved against England in 1878 and, until now, last versus the Faroe Islands 20 years ago. Gannon-Doak, staking a huge claim for a World Cup start, drove from midfield. The Bournemouth man smoothly found Adams, who beat Viscarra at the second attempt. The Scots were 4-0 to the good at the break. This also meant they had scored a quartet of goals in successive games.Unlike Ally MacLeod's infamous hubris of 1978, Steve Clarke has never been prone to bold or rash predictions. Excitement will be left to everyone else. Who can reasonably deny them that? This friendly, in theory an exercise in box ticking, instead gave reasons for huge Scottish confidence. Scotland will remember their first ever game against Bolivia with great fondness.Tactical ConsiderationsShankland can now be considered a guaranteed Scotland starter for the Haiti clash. He joins Robertson, Hickey, McTominay and John McGinn in that bracket. The likelihood is that Clarke would be keen to deploy Adams in attack alongside Shankland, but the impact made by Lyndon Dykes during last weekend's win over Curaçao inserted doubt to that scenario.Clarke has tough calls over who starts in goal and at centre half in Boston. Christie excelled against Bolivia, which should enhance his Haiti prospects. Scott McKenna, Dykes and Nathan Patterson were the only outfield Scots not to feature at all. This was now a game they only had to manage adequately, including without the injury distress that ended Billy Gilmour's World Cup dream seven days earlier.World Cup OutlookBolivia are ranked above Haiti, whom Scotland will surely have to defeat for the opportunity to reach the World Cup's last 32. The performance against Bolivia suggests Clarke's team has the quality to achieve this objective. While it is fair to point towards limited opposition, that is precisely what Scotland will face in game one of Group C.Foot was removed from gas in the second period but there was still something hugely admirable about Scotland's approach. Now for the key question; will it be alright on the night? This time, there was no sour note. Clarke will have no desire to summon his inner or outer MacLeod. Nonetheless, Scotland head to the World Cup with collective spring in step.

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 Budget iPhone Gets a Major UpgradeThe cheapest new iPhone has been upgraded for this year with a faster chip, double the storage, automatic portraits and MagSafe, providing even more of the core Apple smartphone experience for less. The iPhone 17e is an upgraded version of the mid-range "e" line launched last year with the first iPhone 16e and is the latest member of the iPhone 17 family. It starts at £599 (€699/$599/A$999), undercutting the iPhone 17 and iPhone 16 by £200 and £100 respectively to be the cheapest new iPhone sold by Apple.Design and Build QualityThe new 17e is the spitting image of the model it replaces, giving it the older iPhone 14-like design with a large notch at the top of the screen and a slower 6.1in OLED screen. The aluminium sides feel great and the screen glass has been upgraded to the latest Ceramic Shield 2, which is tougher and includes an extremely effective anti-glare treatment that makes it a lot easier to see outdoors. The 17e has MagSafe built into the back for magnetic accessories, such as Popsockets, wallets and chargers, which have been a key part of the iPhone experience since 2020.Key SpecificationsScreen: 6.1in Super Retina XDR (OLED) (460ppi)Processor: Apple A19 (4-core GPU)RAM: 8GBStorage: 256 or 512GBOperating system: iOS 26Camera: 48MP rear; 12MP front-facingConnectivity: 5G, wifi 6, NFC, Bluetooth 5.3, USB-C, Satellite and GNSSWater resistance: IP68 (6 metres for 30 mins)Dimensions: 146.7 x 71.5 x 7.8mmWeight: 170gPerformance and Battery LifeThe 17e has the A19 chip from the regular iPhone 17 but with one less GPU core, which reduces graphics performance slightly. Not that anyone will probably notice, as the phone is very fast and still capable of handling top-spec games. It also has a decent 256GB of storage as standard, which should be enough space for most with additional cloud backup. The battery life is great, too, lasting a good 52 hours between charges with general usage across 5G and wifi, meaning most will need to charge it every other night.The 17e lacks a few of the more advanced hardware features common to Apple's other phones, including wifi 7, Thread and Ultra Wideband (UWB), the latter of which is used for the precision finding tool and for some digital car keys, among other features.Sustainability and RepairabilityThe battery should last in excess of 1,000 full-charge cycles, with at least 80% of its original capacity, and can be replaced for £95. Out-of-warranty screen repairs cost £225. The 17e has repair guides available and was awarded seven out of 10 for repairability by the specialists iFixit.It contains more than 30% recycled material including aluminium, cobalt, copper, glass, gold, lithium, plastic, rare earth elements, steel, tin and tungsten. The company breaks down the phone's environmental impact in its report, and offers trade-in and free recycling schemes including for non-Apple products.Camera CapabilitiesThe single camera on the back may be a deal killer for some. The iPhone 17e features automatic portrait mode functionality, which was previously reserved for more expensive models in Apple's lineup. This allows users to create professional-looking portrait shots with depth effects even with the single rear camera setup.Market Position and Value PropositionWith the iPhone 17e, Apple is clearly targeting budget-conscious consumers who want to enter the iOS ecosystem without paying premium prices. The inclusion of features like MagSafe, the A19 chip, and 256GB of storage at this price point represents a significant value proposition compared to previous generations. This strategy helps Apple capture market share from Android manufacturers in the mid-range segment while maintaining brand loyalty.Future Outlook for Apple's Budget LineThe iPhone 17e sets a new standard for Apple's budget lineup, suggesting that future "e" models will continue to incorporate more premium features at lower price points. As Apple faces increasing competition in the smartphone market, particularly in the mid-range segment, we can expect continued innovation in this product category. The success of the iPhone 17e may influence Apple's entire product strategy, potentially leading to more aggressive pricing and feature inclusion across all iPhone tiers.

The Lead: Amazon's Grocery Delivery RevolutionAmazon is transforming the UK grocery landscape by expanding its ultra-fast delivery services to include fresh produce and same-day options across major cities. This strategic pivot comes after the company closed its standalone grocery stores, signaling a shift toward delivery-focused operations rather than physical retail locations.The Event Details: Expanding Ultra-Fast Delivery NetworksAmazon is significantly expanding its Amazon Now service, which delivers goods in less than 30 minutes, to now serve Manchester and Birmingham in 2026. The company is also extending same-day delivery services to Ipswich and Coventry, while enabling shoppers in London to add fresh groceries to same-day deliveries—a service previously trialled in the US.Shoppers can now add fruit and vegetables, meat, poultry, seafood, dairy, bread, eggs, and frozen foods to the same basket as other groceries and products ranging from fashion to DIY kits. The service will initially be available in parts of central and east London, with plans to expand to additional postcodes across the country in coming months.The Data Analysis: Investment and Market PositionAmazon's UK operations continue to grow, with the company reporting sales of about £32bn in the UK in 2025—a 10% increase from £29bn in 2024. The tech giant has committed to investing £40bn in the UK over three years starting from 2025, demonstrating its long-term commitment to the British market.The grocery delivery expansion represents a significant strategic shift after Amazon closed its 19 standalone Amazon Fresh stores, with five being converted to new Whole Foods outlets. This move comes as Amazon faces stiff competition from established players like Tesco, Sainsbury's, and the Ocado-Marks & Spencer joint venture in the UK grocery market.The Impact Analysis: Changing the Grocery Delivery LandscapeAmazon's expansion of ultra-fast grocery delivery is reshaping consumer expectations and competitive dynamics in the UK retail sector. By offering same-day delivery of fresh produce alongside other goods, Amazon is blurring the lines between traditional grocery shopping and general e-commerce.The company's approach leverages its vast logistics network and technological capabilities, including increased use of robotics in warehouses and AI-powered systems. The Darlington fulfillment center has begun trialling drone flights as the first UK location for its Prime Air delivery service, further demonstrating Amazon's commitment to innovation in last-mile delivery.For consumers, the service offers convenience with Prime members receiving free same-day delivery on orders worth more than £20, while non-Prime members pay a £5.99 delivery fee regardless of basket size. This pricing strategy aims to drive Prime membership while maintaining accessibility for all customers.The Prediction: Future of Grocery Retail and EmploymentAs Amazon continues to invest in its UK operations, we can expect further expansion of ultra-fast delivery services to more cities and regions. The company's focus on partnerships with retailers like Morrisons, Iceland, Co-op, and Gopuff suggests a hybrid approach combining Amazon's logistics infrastructure with specialized grocery offerings.Looking ahead, Amazon's increased use of AI and robotics will continue to transform the nature of work in logistics and fulfillment. While these technologies may reduce certain traditional roles, they will create new opportunities in engineering, maintenance, and oversight of automated systems. The company's commitment to taking on about 1,000 apprentices annually in the UK indicates a recognition of the need to develop future talent.However, challenges remain in aligning education with industry needs, as noted by John Boumphrey, who suggested that the current education system may not adequately prepare young people for the evolving job market. This could lead to increased collaboration between industry and educational institutions to develop relevant skills and potentially mandatory work experience programs.

The HBCU Radio Preservation Project After Shaw University's WSHA radio station went on air in 1968, several other historically Black colleges and universities (HBCUs) followed the North Carolina school's lead, launching a wave of their own. For decades, the students who worked on these channels used them to inform listeners about happenings on campus, while also playing musical selections and offering cultural programming. Preserving the Archives The HBCU Radio Preservation Project is working to ensure that the irreplaceable archives at these institutions are saved and accessible. As a result of the project's efforts, WSHA's archives are available through the American Archive of Public Broadcasting. Several other universities, including Fisk University in Nashville, Tennessee, have had their radio archive preserved for future generations. How the Project Works While working to preserve the archival collection of WYSO, a public radio station in Yellow Springs, Ohio, Jocelyn Robinson began wondering what collections at HBCU radio stations might include. She created a project that surveyed the radio stations to find out. Developed profiles of all the radio stations, including their founding, format, and broadcast footprint Wrote a report with recommendations for preserving radio stations in the campuses Remembering the History There is an oral history project component to the team's efforts, which is "where the storytelling becomes even more important and more apparent in the work". One of the very first oral history captures they did was with David Linton, a program director at WCOK at Clark Atlanta University, in Atlanta, Georgia, whose career started at WSHA at Shaw. Returning the History Celebrating the stations' histories helps different groups – from current students who might not be active listeners to family members of previous radio employees – understand the importance of the channels. Digitized over 1,125 hours of archival audio Visited nearly two dozen HBCU campuses Interviewed over 90 people, recording more than 140 hours of oral histories

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 Unlikely Motivation At 56, I am running my first marathon, an old, fat, bald dad surrounded by millennials in body-hugging Lycra and smiles that look AI-generated. But I am ahead of them. For they are only competing for positions and personal bests, and I am being chased by zombies. The Event Details I started off accompanied by audiobooks, but when Ben Elton’s autobiography got a bit whiny, I remembered Zombies, Run! – an interactive running game for smartphones that came out years ago. That became my running companion. The Data Analysis I am doing the Hal Higdon Novice Marathon Training Program, involving three “short” runs during the week and a “long” run at weekends. The distances slowly increase over 18 weeks. For the first few weeks, I am doing three- or four-mile runs during the week and six- to 10-mile runs at the weekend. The Impact Analysis Unfortunately, I spent the 90s playing football on hangovers and Red Bull without stretching once. My glutes and hamstrings give me constant pain after 10km, and the story is no longer enough to distract me. Luckily, the best bit about Zombies, Run! is that you can link the game to a playlist on your phone, so you get a minute of narrative, then the music fades up for a bit before returning to the story. The Prediction I ran the first half in two hours and 10 minutes and the second half in three-and-a-half hours. Now I have to train for another one so I can try to beat five hours – because that is what dafties like me do. Luckily, Zombies, Run! is now up to season 11, and I only got as far as the end of season 2.

The Return of a Hip-Hop LegendAfter nearly two decades away from the UK stage, Mike D—founding member of the legendary Beastie Boys—made a triumphant return to British shores with an unexpected yet fitting performance in a Tyneside bingo hall. The 60-year-old hip-hop icon brought his unique energy and style to North Shields, where he became what is likely the first legendary rapper to ever yell "Wassup, North Shields?!" to an adoring crowd.An Unconventional Venue for a Legendary PerformerThe setting itself was part of the charm—a bingo hall in the northeast of England, far from the traditional concert venues that typically host artists of Mike D's stature. The stage featured turntables, a six-piece band in matching outfits, and even bingo tables at the back, creating an atmosphere that was simultaneously low-key and monumental. Backed by 5D—a band that includes his own sons and members who are more than half his age—Mike D delivered a performance that blended nostalgia with fresh energy.New Material Takes Center StageRefreshingly and bravely, Mike D's setlist focused almost entirely on new material, including tracks from his forthcoming album. The performance featured storming recent singles like "What We Got" and showcased his distinctive reedy wordplay over hypnotic grooves in tracks like "I Don't Care." The set included "Make It Stop," which paid homage to Kraftwerk, and "True Colours," a massive electronic-rock-rap mashup that demonstrated his continued musical evolution. The only nod to his past came with an uproarious performance of "So What'cha Want," a Beastie Boys classic that had the crowd chanting for more.Bridging Generations and Musical ErasThis performance marks a significant moment in Mike D's career, representing both a continuation of his musical journey and a bridge between generations. Performing with his sons as part of 5D, the show highlighted the passing of the musical torch while maintaining the inimitable joie de vivre that defined the Beastie Boys' legacy. The reference to Newcastle's "Venom sample"—a nod to the time the Beasties sampled the Geordie metal band on "Check Your Head"—demonstrated his connection to the local music scene and his appreciation for the region's contribution to his own musical heritage.A New Chapter for a Hip-Hop IconMike D's return to the UK stage suggests a renewed period of activity for the artist following years of relative quiet following the death of bandmate Adam "MCA" Yauch in 2012. The enthusiastic reception and the focus on new material indicate that fans can anticipate more music and performances from the hip-hop legend in the coming years. As the only disappointment noted by reviewers was that there wasn't more of the engaging, fun hour-long show, it appears that Mike D's comeback is not just a nostalgic trip down memory lane but the beginning of an exciting new chapter in his already illustrious career.

The Revival of a Spoof Classic The Scary Movie series has made a comeback with its sixth installment, bringing back original cast members Anna Faris and Regina Hall, as well as creators Marlon and Shawn Wayans. The film aims to revive the spoof comedy genre, which was popular in the 2000s. The Challenges of Timing The release of Scary Movie comes at a time when horror movies are thriving, with recent hits like Backrooms and Obsession dominating the box office. However, Scary Movie's reliance on outdated references and gags makes it feel less relevant. The Data Analysis The film's attempt to parody recent horror movies, including the Scream series, falls flat due to its lack of originality and sharpness. The Wayans brothers' approach to comedy seems to prioritize broad, shallow jokes over clever satire or insightful commentary. The Impact Analysis The Scary Movie series has always depended on timing, and this installment's release feels poorly timed. The film's failure to effectively parody modern horror movies may indicate that the spoof comedy genre is no longer viable. The Prediction While Scary Movie may still appeal to fans of the series, its lack of originality and impact may signal the end of the franchise. The film's reliance on nostalgia and familiar gags may not be enough to sustain its popularity in the long term.