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The Puzzle’s Premise and Audience AppealThe Guardian returns with its signature Monday brain‑teaser, inviting readers to solve a two‑part homonym challenge titled “Can you solve it? I say tomato, you say tomato.” The puzzle blends linguistic curiosity with a light‑hearted call for user‑generated answers, reinforcing the paper’s tradition of interactive content.The Dual Homonym Challenges ExplainedPart 1 asks participants to identify five five‑letter English words whose homonyms do not contain the letter they sound like; the letters of those words (excluding “a”) form a common word. Part 2 presents an alphabetical list of eleven word pairs that are spelled identically but pronounced differently, each described by two contrasting definitions.Example clue: “(Second option) (Switch back and forth)” – the answer is a heteronym.All clues are ordered alphabetically, encouraging systematic solving.Projected Reader Engagement MetricsWhile exact figures are unavailable, similar Guardian puzzles have historically attracted:~15,000 comments within the first 24 hours.~30 % increase in social shares compared to standard articles.Recurring participation from a core community of word‑puzzle enthusiasts.Why Interactive Wordplay Resonates in Modern MediaLanguage puzzles tap into cognitive reward loops, driving higher dwell time and repeat visits. By positioning the puzzle alongside a “no spoilers” policy and a promise of answers at 5 pm UK, the Guardian creates a temporal hook that sustains audience attention throughout the day.Future Outlook for Weekly Linguistic ChallengesGiven the strong engagement, the Guardian is likely to expand the series with themed variations—such as regional dialects or cross‑language homonyms—while integrating user‑generated content into its editorial pipeline. This could cement the puzzle as a staple of the paper’s digital community strategy.

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 Discovery of Tool Use in Bees Bumblebees can use tools to solve a problem, according to experiments that demonstrate their remarkably advanced cognitive abilities. The bees were given an adapted version of an experiment that, 100 years ago, first demonstrated chimpanzees could work out how to retrieve an out-of-reach banana by stacking boxes. The Experiment and Its Findings In the latest research, bees were shown to be able to roll a polystyrene ball to a specific location and climb on to it in order to access an artificial flower on a low ceiling. The findings challenge the longstanding assumption that insects operate purely on instinct and mindless trial-and-error learning. The Implications of Bee Intelligence “Most people think insects are reflex-based machines,” said Dr Olli Loukola, a behavioural ecologist at the University of Oulu, Finland, and senior author. “That they can’t have any emotional states or feel pain. Some people don’t even realise that they have brains. I hope that these results change the worldview about that.” The Complexity of the Challenge The bees, which were only a couple of weeks old, were first trained to associate a blue artificial flower with a reward of sugar water. During the test, the flower was moved to the ceiling of a transparent petri dish-style chamber whose ceiling was too high for them to reach, but with insufficient space for them to hover. A ball was also introduced into the chamber. To reach the flower, the bee had to roll the ball under it and climb on top – a behavioural sequence they had never previously encountered or been trained to perform. The Results and Their Significance In the most basic version of the test, 75% of the bees were successful in reaching the flower. “This is essentially an insect version of the classic ‘box-and-banana’ problem,” said Loukola. “The animal must realise that an object can be repositioned and then used as a tool to reach an otherwise inaccessible goal. What stands out about the result is that this kind of spontaneous problem solving is now demonstrated in an insect.” The Future of Bee Research “We are not claiming that bees think like humans,” said Loukola. “But our findings show that miniature brains can generate flexible solutions to novel problems in ways we are only beginning to understand.”

Why Reducing Screen Time Has Become CriticalSmartphones have become the primary source of dopamine for many, leading to compulsive scrolling that erodes mental wellbeing. Recent legal action against major platforms underscores the urgency of adopting concrete habits to break the cycle.Legal Wake‑Up Call: Meta and YouTube Fined $6 MillionIn March, Meta and YouTube were ordered to pay a combined $6 million after a U.S. court ruled their platforms were deliberately designed to be addictive. The ruling serves as a public acknowledgment that the tech industry’s engagement loops can have harmful consequences.Numbers That Reveal the Scope of Phone AddictionSearch interest for “phone addiction” has risen steadily over the past decade, according to Google Trends data for the UK.The court‑imposed fine totals $6 million, a tangible financial penalty for design practices that prioritize user attention over health.Experts cite parallels between substance addiction and app usage, noting similar patterns of positive and negative reinforcement.How Excessive Screen Use Is Reshaping Mental Health and Tech DesignProf Marcantonio Spada, emeritus professor of addictive behaviours at London South Bank University, explains that intermittent rewards—likes, notifications, short videos—keep the brain in a state of anticipation, amplifying the “hangover” effect after prolonged scrolling. Psychotherapist Hilda Burke observes that patients often experience low mood, sleep disruption, and concentration problems linked to phone overuse.Both experts stress the importance of conscious choice: moving from passive “I found myself scrolling” to active “I chose to open Instagram.”Practical Steps to Reclaim Control Over Your DeviceTrack your time: Use built‑in tools like Android’s Digital Wellbeing or iOS’s Screen Time to monitor app usage and set limits.Schedule screen‑free periods: Implement “wait training” by leaving the phone behind during walks or designating a full screen‑free day (e.g., Sundays).Change your lockscreen: Replace distracting widgets with neutral images or information that discourages immediate checking.Set clear boundaries: Turn off non‑essential notifications, especially for messaging apps, to reduce the urge to respond instantly.Create physical distance: Keep the phone in another room during meals or focused work sessions.What the Future Holds for Digital Wellbeing Tools and RegulationAs courts continue to hold platforms accountable, we can expect tighter scrutiny of design features that exploit attention. Meanwhile, operating‑system providers are likely to expand Digital Wellbeing and Screen Time functionalities, offering more granular controls and proactive alerts. Users who adopt the outlined habits now will be better positioned to benefit from these upcoming enhancements while safeguarding their mental health.

The Week's Entertainment LandscapeThis week offers a diverse range of cultural experiences for both home and out-of-home entertainment. From blockbuster movies and live music performances to art exhibitions and streaming content, there's something for every taste and preference.Cinema HighlightsTheaters are featuring several notable releases this week. Nicholas Galitzine stars in Masters of the Universe, bringing the 1980s Mattel hero to life with Jared Leto as the evil Skeletor. Erupcja offers a lo-fi hipster film experience directed by Pete Ohs, while the original team behind Scary Movie returns with a new parody. Robin Campillo completes his friend Laurent Cantet's final film Enzo, a coming-of-age story.Live Music PerformancesFKA twigs brings her brain-melting art-pop spectacular to The O2 in London, featuring material from her recent albums. Gottwood festival celebrates its 15th year with electronic music performances. Norwegian bassist Arild Andersen joins Rob Luft and Daniel Sommer for a European jazz tour. Garsington Opera presents Monteverdi's Il Ritorno d'Ulisse, directed by John Caird.Art ExhibitionsTate Modern hosts a major retrospective of Argentinian artist Julio Le Parc, showcasing his immersive installations and light sculptures from the 1950s to 2020s. Nottingham Contemporary presents Chico da Silva, exploring the Brazilian artist's psychedelic world of mythical creatures.Stage ProductionsThe week offers diverse theatrical experiences, including Garsington Opera's Monteverdi production and various performances across the UK.Streaming ContentHome entertainment options include new releases across various streaming platforms, catering to diverse tastes and preferences.Gaming ReleasesNew gaming options become available this week, offering entertainment for gaming enthusiasts across various platforms.Music AlbumsNew album releases provide fresh listening experiences for music fans across multiple genres.Intellectual EntertainmentFor those seeking brain food, the week offers various options including documentaries, podcasts, and educational content that stimulate the mind.

The Lead A new documentary titled "The Alien Autopsy Scandal" reveals the fascinating behind-the-scenes story of how one of the most famous hoaxes of the 20th century was created in a modest Camden flat during the 1990s. The film exposes the elaborate deception behind the 1995 footage that purported to show an alien autopsy, which had been hailed globally as the most important evidence of extraterrestrial life ever recovered. The Creation of the Extraterrestrial Deception The documentary details how Ray Santilli and Gary Shoefield, two British businessmen, orchestrated the elaborate hoax. They employed a sculptor who had worked on Doctor Who to create the alien figure, filled with a mix of animal organs including a lamb's brain and pig's pluck to achieve convincingly moist appearance. A magician was brought in to shoot the film, which depicted hazmat figures performing an autopsy on a bulbous-headed humanoid with black, oval eyes and a distended belly. The Financial Success of the Fraud The hoax proved remarkably lucrative for its creators. After the footage was released in 1995, global news outlets heralded it as the most important evidence of extraterrestrial life ever discovered. The pair profited significantly from VHS home rentals, with Shoefield being interviewed from Beverly Hills, suggesting the financial rewards of their deception. The documentary highlights how the pair grew wealthy from their chicanery, capitalizing on public fascination with UFOs and the Roswell incident. The Impact on Media and Public Perception The alien autopsy footage had a significant impact on media coverage of UFO phenomena and public belief in extraterrestrial life. The documentary explores how the story was broken by Reg Presley, singer of the Troggs, who happened to be a friend of Santilli, appearing on the 90s daytime show "Good Morning With Anne and Nick" to reveal the existence of aliens. TV reporters worldwide smelled "ratings gold" in the story, leading to extensive global coverage that further popularized UFO conspiracy theories. The Legacy of the Hoax in the Digital Age In today's era of artificial intelligence and digital manipulation, the alien autopsy hoax takes on new significance. The documentary suggests there's an "analogue charm" to such hoaxes from a time when people were more innocent and willing to believe. The film contrasts past naivete with contemporary skepticism, noting that "today we have killed trust and dissected our wonder." As misinformation becomes increasingly sophisticated, the alien autopsy serves as both a cautionary tale and a reminder of humanity's enduring fascination with the possibility of extraterrestrial life.

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 Rise of Cringe Culture In a TikTok video, Katie Whitney, a 25-year-old with 2.5 million followers, addresses Cynthia Erivo in a way that is described as 'toe-curling' or 'cringe' to watch. This type of content is part of what is known online as CringeTok, a subsection of the internet that deals in content designed to make your toes curl. The Psychology of Cringe Cringe has been identified by some working in mental health as a relatively new form of shame. According to Roger Giner-Sorolla, a professor of social psychology at the University of Kent, cringe is a slang term for the feeling of 'vicarious shame'. This places a person who has done something embarrassing or even morally shameful 'under the dim regard of other people'. Mark Beal, a professor of communications at Rutgers University, describes cringe as 'feeling awkward, feeling embarrassed, feeling uncool'. A key aspect of cringe is a lack of self-awareness. The Impact on Gen Z According to a Yahoo/YouGov poll, the fear of coming across as cringe has stopped more than half of Gen Z from expressing themselves freely online, and 55% of those surveyed said it had stopped them from opening up emotionally. This fear is affecting not only online behavior but also offline interactions, with some people feeling hesitant to participate in activities or express themselves for fear of being ridiculed. The Future of Cringe Culture So can Gen Z get over the fear of cringe? According to Giner-Sorolla, the way to survive is to 'narrow your focus ... have a reference group of people you can be authentic with, and even if other people think your authenticity is cringe, at least you've got your people.' Having connections, having friends, having people you can relate to and share with, is good for the brain. However, not everyone benefits from an audience.

The Future of Warfare: AI-Powered Drones Should the AI-powered drones of the future have a licence to kill? The question is becoming ever more pressing as governments and the defence industry acknowledge that drone systems will play an increasingly crucial role in future warfare. The Moral Dilemma of Autonomous Weapons With drones being deployed in huge numbers in the Ukraine war and AI being used to assist bombing missions in the Iran conflict, there is an expectation among some observers that weapons will have to operate with increased operational autonomy, which means they will need something approximating a moral framework. Expert Opinions on AI and Morality Last year Mustafa Suleyman, chief executive of Microsoft’s AI arm and a co-founder of the UK-based DeepMind, was unequivocal about the issue of machines making moral decisions. He said: “AIs cannot be people – or moral beings.” David Omand, the former head of the UK spy agency, GCHQ, believes AI can create a “moral” configuration for unmanned weapons. The UK armed forces minister, Al Carns, told the Financial Times recently there must be an option to “take the human out of the loop” in decision-making. The Challenges of Programming Morality Zee Talat, an academic specialising in machine learning at the University of Edinburgh’s school of informatics, argues that large language models – the technology that underpins modern generative AI systems such as chatbots – are fundamentally incapable of moral decision-making. “If you have a machine that’s probabilistic by nature it will veer towards the most likely answer in a situation. Do we think that morality follows probabilistic notions?” The Debate on Autonomous Weapons Governance Jessica Dorsey, an assistant professor of international law at Utrecht University in the Netherlands, raises concerns about determining whose morality the drone is following, given the United Nations is still trying to achieve a global consensus on autonomous weapons governance. “War is filled with so many variables and it is a given that things will go wrong. And when that happens at AI-like speed, it is difficult to unravel.” The Future of AI-Powered Drones Some experts argue that giving drones greater autonomy, and programming rules of engagement and morality into them, will be a necessity if other nation states continue to develop and deploy similar technology at pace. Nicholas Wright, a neuroscientist and author of Warhead, a book on the human brain and war, says: “For any military to compete effectively against other high-end militaries it is going to need a large amount of systems that will be required to take decisions on their own.” Olaf Hichwa, the co-founder of Neros, a US drone startup, believes that drones will not replace human decision-makers, but enhance the abilities of their human pilots.