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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 Revival of Motion Gaming For a wonderful moment in the noughties, video games became a truly universal pursuit. The Nintendo Wii flew off the shelves, inspiring a wave of competitors such as the Xbox Kinect camera that encouraged people to play games by moving their bodies. But the tide turned: outside of still-niche VR gaming and the odd controller-waggler on the Switch, motion-controlled gaming has barely been seen for more than a decade. Nex Playground Enters the Scene Now, 20 years later, a new console is aiming to get the whole family flailing in front of the TV once again: the Nex Playground. Launching in the UK later this month, the first thing that struck me about this family-friendly device is just how tiny it is. The size of two and a half Rubik’s Cubes taped together, this impressively unintrusive device swaps cumbersome controllers for camera-controlled minigames, putting you and your family directly in the game. The Technology Behind Nex Playground Using a wide-angle lens and AI-powered tracking tech, the Nex Playground offers over 50 games that track players’ bodies as they leap, flail and dance about the living room. It’s not hard to see the appeal. Physically leaping through puddles in Peppa Pig: Jump and Jiggle, dancing in time to Rick Astley on Starri and slicing up watermelons with my hands in the perennial hit Fruit Ninja, I’m impressed by how seamlessly – and accurately – the tech works. Market Performance and Pricing The Playground retails at £269 ($299) – significantly less than any other games console at the moment. But it comes with just five free games. The rest of its library is locked behind an eye-watering £90 annual subscription. In the US, where it launched in 2023, the Playground has sold over a million units, even outselling Microsoft’s Xbox consoles during 2025’s Black Friday week. Safety and Future Plans Nex appears to be taking great care to earn families’ trust. None of the camera data from Nex play sessions is saved – either offline or online – meaning that families can happily embarrass themselves without worrying that an omniscient tech firm is tracking their every movement. Online multiplayer is coming to Playground soon, via parent-controlled “playdates”, and Lee hopes that this will also help older relatives stay connected with their families. The Future of Family Gaming Game publishers who’ve previously made games for Kinect and VR are already coming to Nex, Kang says. Child-focused brands such as Hasbro, DreamWorks and Mattel have already licensed games for it, perhaps seeing it as a safer alternative to social media and smartphone platforms – a view that most parents are likely to share. The most family-friendly dedicated games console currently available, Nintendo’s Switch 2, recently raised its price to £395.99, with new games at £50+ each; a lot of families are looking for a more affordable option. Nex Playground launches in the UK on 22 June.

The Vision for a Just and Sustainable FutureImagine a future in which everyone enjoys high levels of wellbeing; where 90% of the world's population doubles their income but works half the hours we work today. A world in which the bottom half of humanity sees its share of global wealth rise from just 2% today to 30%; a world where we consume enough, but nobody over-consumes. And imagine achieving this on a planet that can comfortably sustain human life without its climate breaking down.Against the bleak techno-authoritarian futures now being sold to us, a radical new vision for global progress in the 21st century feels urgently needed. The most credible vision is one in which the habitability of the planet is a precondition for human development and equality.The Three Pillars of Global TransformationOur new report examines the conditions required for the world to progress towards this ambition on an economically and ecologically compatible path, by the end of the century. Its conclusion? A global transformation that reconciles planetary habitability and high standards of wellbeing for all is possible – as long as three conditions are simultaneously met.Fast decarbonisation of energy systems is necessary. But we also need a major shift away from overconsumption towards 'sufficiency'. This would involve a sharp reduction in labour hours and the use of raw materials, along with big changes in consumption patterns, food habits, land use and forest cover. Financing and politically sustaining decarbonisation and sufficiency will require a drastic reduction in inequality of income, wealth and power, between countries and within them.Quantifying the Path to Global JusticeThe Global Justice Report is the first attempt to propose a fully quantified plan for this transition. It combines four dimensions that today's debates often treat separately: redistribution at the world scale; a deep reform of the international financial and economic order; a radical transformation of energy systems; and substantial shifts in consumption patterns. Compared with most climate scenarios (including those of the Intergovernmental Panel on Climate Change), the main novelty is that we model all four dimensions together – and place inequality and sufficiency at the centre of the analysis.The Economic Convergence by 2100What would this transition deliver? At its heart is convergence between countries. Average per capita national income, today separated by a 16-fold gap between the poorest (€290 a month in sub-Saharan Africa) and richest (€4,590 in North America/Oceania) regions of the world, would rise towards a common level of about €5,000 a month in all countries by 2100.But this convergence is not just monetary. Annual working hours per employed person would fall from roughly 2,100 to about 1,000, continuing the long shift towards shorter working time; while the share of global working hours devoted to education and health would rise from 11% to 43%. Women and men would converge on equal pay and on an equal share of economic and domestic labour.Climate and Wealth TransformationAll of this would unfold within a habitable climate. Thanks to sustainable convergence and fast decarbonisation, global heating would reach 1.8C, against more than 4C on current trends.None of this will be possible without a deep contraction of inequality. The income scale between individuals would narrow to a ratio of one to five and the wealth scale to one to 10, prolonging what western and Nordic Europe achieved over the 20th century. The share of global wealth held by the poorest half of humanity would rise from 2% to 30%, while the share held by the billionaire class would fall from 6% to 0.05%.Financing the Global Justice TransitionThese shifts would be financed and governed through new institutions. A global justice fund would spend an average of 10% of world GDP a year from 2026 to 2060 on country dividends and investment, against the less than 0.4% that aid and the combined budgets of the UN, the International Monetary Fund (IMF) and the World Bank represent today.Its resources would come from a world sovereign fund holding 10% of the world capital stock, a global wealth tax rising to 20% a year on billionaires and a global income tax rising to 90% at the very top, each touching about 1% of the world's population.The Political Path ForwardThe result is not a transfer from many to few but a gain for almost everyone. Close to 90% of the world's population would double their income between 2026 and 2100, and once leisure and a habitable planet are counted, more than 99% come out ahead.Our report is part of a broader international agenda for planetary habitability, social justice and reform of the global financial architecture – including the Bridgetown agenda launched by Barbados in 2022, the Sevilla Commitment on development finance, the UN tax convention process, and G20 initiatives led by Brazil and South Africa on global inequality.A habitable, equal and prosperous 21st century is materially possible. The carbon budget allows it and history offers precedents at comparable scales: universal suffrage, the universalisation of healthcare and education, the halving of working hours and the sharp compression of inequality over the 20th century. Technical impossibility is not what is standing in the way, but rather the absence of a shared vision of social progress, at once concrete and radical. What it will take instead is political choice, and the hard work of coalition-building behind it.

The Rise of Middle-earth: Tolkien's Triumph Over Literary ClassicsIn a remarkable shift from established literary canon, JRR Tolkien's The Lord of the Rings has topped The Guardian's readers' poll of the 100 greatest novels published in English, displacing George Eliot's Middlemarch from its previous position. The trilogy, which didn't even feature when authors, critics and academics made their selection, has resonated deeply with readers across the globe, from Uruguay to the Isle of Skye, Albuquerque to Sydney.The Enduring Appeal of Epic FantasyThe Lord of the Rings' victory speaks to its unique ability to connect with readers on a fundamental level. As one Alabama voter noted, the novel contains "profound meaning about the importance of life, sacrifice, the natural world, corruption of power, the evils of war, generosity of spirit." Its influence extends across generations and cultures, with readers from various backgrounds citing its immersive world-building, complex themes, and emotional resonance as reasons for its enduring popularity.The novel's journey to the top is particularly noteworthy given its unconventional publication history. Originally conceived as a single work but published as a trilogy after negotiations between Tolkien and his publisher, the series has transcended its format to become a cultural touchstone. Readers have been drawn to its blend of ancient mythological elements with modern storytelling techniques, creating what one voter described as a world that "still persists in my memory."Notable Shifts in Literary RankingsReaders exercised their power to significantly reshape the literary landscape compared to the previous critics' list. Joseph Heller's Catch-22, which "just squeaked into the first list," has now jumped to the eighth position, ranked higher than established classics like Ulysses, Anna Karenina, and The Great Gatsby. Similarly, David Foster Wallace's Infinite Jest, absent from the original list, now sits in 31st position, sharing its ranking with The Master and Margarita, The Poisonwood Bible, and The Remains of the Day.The list also reveals interesting patterns in reader preferences compared to critics. While Victorian literature maintains a strong presence, with Middlemarch's "consistent showing" and other works by Eliot, Dickens, and Hardy, readers have elevated contemporary works that critics may have overlooked. The enduring popularity of Jane Austen, readers' most nominated writer overall, demonstrates the continued relevance of classic literature in modern reading culture.The Absence of Literary Giants and Changing TastesStaggeringly, the list shows no recognition for work by several male titans of recent American literature—no Bellow, no Roth, no Updike, no DeLillo. This absence highlights the "waxing and waning of reputation" and the "speed with which literary fashion forms and reforms." Similarly, some English novelists who were once central to cultural life—no Iris Murdoch, or CP Snow, or Angus Wilson—failed to make the cut.The list also reveals a notable absence of lighter, humorous works. While Terry Pratchett and Douglas Adams secured places with their respective series, other comedic authors like PG Wodehouse, Nancy Mitford, and Jerome K Jerome were overlooked. This raises questions about how "best" often equates to "serious" or "weighty" literature in critical assessments, despite the inherent value of humor in storytelling.The Future of Literary Canons and Reader InfluenceThis readers' poll demonstrates the power of audience participation in shaping cultural narratives. Unlike previous lists compiled by critics and academics, this one reflects the genuine preferences of a diverse readership, leading to a more eclectic and contemporary selection of works. The inclusion of newer entries like John Kennedy Toole's A Confederacy of Dunces—published posthumously and now sharing the 32nd position—suggests that readers are more willing to embrace overlooked or rediscovered literary gems.As literary tastes continue to evolve, we can expect similar shifts in how we value and rank literature. The enduring popularity of works like The Lord of the Rings, which combines epic storytelling with universal themes, suggests that readers continue to seek narratives that transcend time and place. While established classics will always have their place, the growing influence of reader preferences may lead to a more diverse and inclusive literary canon in the future.

The Lead: Democracy's Tipping Point in GhanaAccra, Ghana – Ghana has recorded 14 arrests linked to false news and offensive speech in less than 16 months, nearly double the number documented during the previous administration's entire eight-year tenure, according to the Media Foundation for West Africa (MFWA).The rise has triggered a sharp debate in one of West Africa's most stable democracies over whether authorities are simply enforcing long-standing laws in a new digital environment, or edging into a more restrictive approach to public speech.The Political Irony: Mahama's Past WarningsThe controversy carries added political weight because President John Mahama, while in opposition in 2022, warned that using state power to intimidate dissent was a "dangerous blueprint" for democracy.Government Position: Enforcement Not RepressionA senior ruling party official dismissed allegations that the arrests amount to a crackdown."The opposition intentionally sponsors people to insult the President," he told Al Jazeera. "When the law catches up with them, they cry persecution to score cheap political points."He pointed to the case of TikToker Prince Ofori, known as "Fante Comedy", who was arrested last August over alleged threats to President Mahama.Days after his arrest, Ofori appeared at a political rally alongside opposition figures, a development the official said showed how quickly such cases become politicized."They paraded him at an opposition rally," he said.Opposition Response: A Warning Sign for DemocracyOpposition leaders see something more troubling taking shape.Minority leader Alexander Afenyo-Markin has been among the most outspoken critics."The state-sponsored persecution must stop," he told Al Jazeera. "Arresting citizens for words that do not constitute genuine threats is not justice. It is intimidation."He said free speech has limits, but argued that the state is increasingly crossing a line."Excessive use of state power risks undoing Ghana's hard-won democratic gains," he said.Legal Framework: Where is the Line?At the centre of the debate are long-standing provisions in Ghana's Criminal Code and Electronic Communications Act, which authorities say are now being applied to a fast-moving digital landscape.Government supporters argue the increase in arrests reflects the explosion of anonymous and unregulated online content.Critics say the problem is not the laws themselves, but how they are being used.A legal consultant who reviewed recent cases said he counted at least 16 alleged misapplications of Section 208 in the past 18 months, compared with roughly a dozen in the previous eight years."The law has been abused beyond repair," he said. "Repeal is the only remedy."Media Freedom and Blurred BoundariesVeteran journalist Ben Ephson said Ghana needs clearer guidance on where free expression ends and harm begins."The government must properly explain the arrests so people can draw the line between press freedom and responsible journalism," he said.He added that both journalists and state institutions risk overstepping if the rules remain unclear."When you compare the freedom of the media and the rights of the individual, we need to be careful that the media, in trying to do their work, don't trample on people's rights," he said.Global Context: Shrinking Civic SpaceOthers say Ghana's debate mirrors tensions playing out in other democracies.Tegha King of the Universal Peace Federation Ghana said concerns about shrinking civic space are not unique to Ghana."The global civic space must cultivate more free speech, not less," he told Al Jazeera.He said stronger institutions, not more arrests, are needed to manage the pressures of the digital age."There must be independent courts, transparent enforcement, media self-regulation and digital literacy," he said.Civic Awareness and External ConcernSome analysts point to gaps in public understanding of constitutional rights."There is a lack of constitutional education among many Ghanaians," said David Adofo of the African Chamber of Content Producers. "People must know the consequences of their actions before they act, not after."Concerns are also being voiced outside the country."We have had many concerns from diasporans about perceived erosion of press and political freedoms, especially news of blogger arrests," said Nana Kofi Opoku-Agyemang of the NuGhana Expat Center. "Negative news sells fast. The government must be cautious so it does not project a negative image of Ghana in the diasporan community."Government Stance: Existing Laws, New ChallengesOfficials insist there is no coordinated effort to silence dissent.An NDC communicator said the legal framework in question predates the current administration and defended the approach."Ghana's laws, Section 208 of the Criminal Code and Section 76 of the Electronic Communications Act, have been on the books for decades," he said. "What has changed is the sheer volume of reckless, anonymous and sometimes dangerous content on social media. There is no systematic crackdown. There is simply enforcement of existing law."The Path Forward: Breaking the CycleGhana remains one of West Africa's more open democracies, with a competitive political system and active media landscape.But the rise in speech-related arrests has sharpened scrutiny of how far the state can go in policing online expression without undermining the democratic culture that helped define its reputation.The debate is also politically charged because of Mahama's own past warnings.As opposition leader, he described the use of state power against dissent as a "dangerous blueprint." Today, critics say his government faces accusations it once condemned.For Alexander Afenyo-Markin, the moment calls for restraint — and reflection."We should not continue to say that because it happened yesterday, it should happen today and tomorrow. That cycle must end," he said. "President Mahama has an opportunity to leave a legacy of tolerance and free speech. I hope he takes it."

Burnham's Vision for Social Care Andy Burnham has signalled he would begin transforming England's broken social care system this year if he became prime minister, accusing Westminster of 'flinching away' from tackling difficult policy problems. Plans for Social Care Reform The Greater Manchester mayor said politicians must be willing to take on 'the weight of the system' that stood in the way of radical change, as he began to set out his prospectus for government if he won the Makerfield byelection. Burnham first tried to change the social care system when he was Labour's health secretary in 2009, planning a levy on estates to pay for universal social care. He has talked about replacing inheritance tax with a progressive 'care levy' to fund a national care service. Leadership Ambitions and Labour Party Dynamics Burnham confirmed for the first time that he intends to run in a Labour leadership contest, suggesting there would be no snap election if he replaced Keir Starmer. He defended himself from criticism over a shadow leadership campaign. He argued Labour should be a broad church with more government ministers from the left of the party, but Jeremy Corbyn should not be allowed back in. Economic and Fiscal Policies Burnham denied he had left himself little room for manoeuvre by saying he would stick to the fiscal rules, arguing they had freed up significant resource for public investment. He suggested replacing 'iniquitous' council tax with a land value tax. He proposed reallocating £39bn earmarked for social and affordable housing solely to social homes. Brexit, Immigration, and Future Outlook Burnham argued it would be a mistake to rerun the Brexit referendum but that he wanted the UK to rejoin the EU in his lifetime. He praised Shabana Mahmood, the home secretary, for 'facing up' to the big issues on immigration. He suggested bringing forward the Casey review, tasked with drawing up proposals on funding, to 2026.

The LeadA supernatural play based on the Iranian horror movie 'Under the Shadow' explores the terror of life in Iran during the 1979 revolution and the Iran-Iraq war. The Event DetailsThe play, adapted by Carmen Nasr from Babak Anvari's 2016 film, is set in Tehran in 1988. It tells the story of Shideh, a woman who hides in her apartment with her terrified daughter as the Iraq-Iran war rages on. The play explores themes of fear, survival, and the supernatural. The Data AnalysisThe play's creative team, including director Nadia Latif and actress Leila Farzad, bring their own experiences of war and displacement to the production. Latif's family has experience in Sudan, while Farzad's family is from Iran. The play's themes of hope and survival are universal, resonating with audiences from different backgrounds. The Impact AnalysisThe play's use of horror as a genre allows it to tackle complex themes like politics and collective suffering. By making the horrors of war personal, the play aims to bring the audience closer to the experiences of those living through conflict. The PredictionThe play is expected to be a powerful and thought-provoking production, exploring the complexities of life in Iran during a time of war and revolution. With its talented creative team and timely themes, it is likely to resonate with audiences and leave a lasting impact.

The LeadAmazon's ambitious $200 million adaptation of the 80s toy franchise Masters of the Universe has been met with scathing reviews, with critics calling it a 'weak big-budget misfire' that fails to justify its massive budget or the revival of a property that modern audiences have little connection to.The Film's Production ChallengesThe film, directed by Travis Knight (Bumblebee), has been in development for years with various directors and studios attached. It follows Adam (Nicholas Galitzine), who transforms into He-Man to save the magical land of Eternia from the villain Skeletor (Jared Leto). Despite its hefty budget, the review criticizes the film for its confused tone, which attempts to be both a parody and an earnest adventure without succeeding at either.The Financial ImpactWith a reported $200 million budget, Masters of the Universe represents a significant financial risk for Amazon. Early tracking suggests the film may become one of the summer's biggest flops, joining other expensive franchise misfires like Universal's Dark Universe. The review notes that the film often looks surprisingly cheap for its price tag, with issues in lighting and action sequences that fail to justify the expenditure.Industry ImplicationsThe film's failure highlights Hollywood's ongoing struggle with reviving aging IP properties. While recent hits have relied on either beloved properties (Scream, Mario) or original ideas (Obsession, Backrooms), Masters of the Universe exemplifies the risks of investing in nostalgia for properties that modern audiences don't have strong connections to. The review contrasts this with Mattel's successful Barbie film, which was both auteur-driven and based on a still-popular brand.Future OutlookGiven the negative reception and early box office predictions, it's unlikely that Masters of the Universe will spawn a franchise. The review suggests the film will be filed alongside other big-budget misfires like the Chris Pine-led Dungeons & Dragons, serving as a cautionary tale about reviving properties without a clear vision or audience demand. The film's release on June 5, 2026, will test whether audiences share the critics' negative assessment.

The Inauguration of the Rwanda Genocide Memorial French President Emmanuel Macron has presented a memorial in Paris dedicated to the victims of the 1994 Rwandan genocide, as France pursues closer ties with the East African country and continues to grapple with its role in the historic atrocity. The Monument's Significance Speaking at the inauguration event alongside his Rwandan counterpart Paul Kagame on Tuesday, Macron said the monument marked “the culmination of a long and patient quest for truth.” The memorial, dubbed “L’Archive” (The Archive), consists of two black brass steles and bears an engraved tribute to the estimated 800,000 men, women, and children, mostly ethnic Tutsis, massacred between April and July 1994. France's Role and Reconciliation Macron has said Paris and its Western and African allies did not have the will to halt the genocide, though he has stopped short of issuing a formal apology. A commission set up by Macron and led by historian Vincent Duclert concluded in 2021 that France had been ⁠blinded by its colonial attitude to events leading up to the genocide ⁠and bore a “serious and overwhelming” responsibility ⁠for failing to foresee the slaughter. The Impact on Franco-Rwandan Relations “An unprecedented reconciliation has emerged between Rwanda and France,” said Macron. “This monument, while it is an achievement, is not an end. It is a milestone on a path we have opened.” Kagame hailed France’s efforts to assume its share of responsibility and praised Macron for his “courage and humanity.” The Future of Acknowledgment and Justice The French courts, acting on the principle of universal jurisdiction to try the most serious crimes committed worldwide, have convicted several Rwandans for their part in the massacre. The unveiling of the monument was a “powerful” step, with Duclert saying, “The genocide against the Tutsi is now fully part of France’s public history.”