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The US political landscape is increasingly dominated by money, with billionaires and corporations spending vast amounts to influence elections and policy. In California, signature collectors are being paid $15 apiece to gather signatures in support of countermeasures against a proposed billionaire tax.The crisis has escalated since the 2010 Citizens United decision, which shredded limits on independent corporate election spending, fueling the growth of cash-flush Super Pacs and anonymous dark money non-profits. In 2024, $1.5bn in Super Pac donations came from organizations that aren’t required to name their donors.The ruling has, on balance, boosted conservatives, with Republicans receiving a four-point electoral bump in states where Citizens United struck down existing bans on corporate donations. Meanwhile, rampant income inequality has fueled a parallel democratic deficit, with the richest 10% of Americans now owning 93% of the stock market.To rebalance the scales, alternatives such as public election financing are being explored, which helped Zohran Mamdani secure his mayoral victory in New York City last year. Currently implemented in 15 states and Washington DC, these programs issue grants, vouchers and matching funds that augment the power of small donations.Citizens United might also be circumvented by novel legal maneuvering, with states holding considerable authority to define the powers they grant to incorporated entities. In Montana, organizers are collecting signatures for a Transparent Election Initiative that would strip corporations of the power to engage in election spending.

Leeds United delivered a seismic upset at Old Trafford, beating Manchester United 2‑0 and moving six points clear of Tottenham in the Premier League table. The victory marked United’s first league loss at the stadium since February 1981, ending a 45‑year unbeaten home run.Michael Carrick recorded his first home defeat as United’s interim manager. The team never found rhythm, a situation worsened when defender Lisandro Martínez was shown a red card in the 56th minute for yanking Dominic Calvert‑Lewin’s ponytail. Martínez now faces a three‑match ban, with United considering an appeal.Noah Okafor proved decisive, netting a brace. His first goal arrived five minutes after the red card when a Jayden Bogle cross was flicked on by Leny Yoro and finished by Okafor. The Swiss striker celebrated with a calm, hands‑folded pose as the crowd chanted “Yorkshire, Yorkshire”. He added a second, long‑range strike later in the half, sealing the win.Leeds dominated the early exchanges, creating several chances through wing‑back Gabriel Gudmundsson and forward Jayden Bogle. United’s response was limited to a consolation header from Casemiro, but they could not threaten Leeds’ lead.The result has major implications: Leeds now sit comfortably in the Champions League race, while United’s relegation worries intensify. A win against Wolves on Saturday could further distance Leeds from the drop zone, especially if Tottenham falters against Brighton.Post‑match, Leeds manager Daniel Farke and his players celebrated exuberantly, kneeling on the pitch and shouting “We are Leeds”. The three points are described as “vital” for the club’s season ambitions.

Arsenal's recent defeat to Bournemouth has sent shockwaves through the football world, with manager Mikel Arteta expressing his disappointment and frustration with his team's performance. The 2-0 loss has raised concerns about the team's mental fortitude and ability to cope with pressure.Arteta's side has been criticized for their risk-averse playing style, which has led to a series of underwhelming performances. The team's inability to beat Bournemouth's press and create scoring opportunities was a major concern, with Arteta admitting that his team's display was 'a big punch in the face'.Despite the setback, Arteta remains committed to his approach, which he believes will ultimately lead to success. However, with Manchester City breathing down their necks in the Premier League table, the pressure is mounting on Arteta to deliver results.The defeat has also sparked debate about the team's mental preparation and ability to handle the pressure of being top of the league. With a crucial match against Manchester City looming, Arteta will need to find a way to motivate his team and prevent another disappointing performance.

Marie‑Louise Eta will take the touchline for Union Berlin’s upcoming Bundesliga match against Wolfsburg, becoming the first woman to coach a men’s team in one of Europe’s top‑five leagues. The 34‑year‑old was promoted on an interim basis after the dismissal of Steffen Baumgart, who was sacked following a 3‑1 defeat to bottom‑placed Heidenheim.Union sit seven points clear of the relegation‑playoff zone with five games remaining, but a dismal run of two wins in 14 matches has left the club teetering near the drop‑zone. Club officials turned to Eta, citing her continuity and proven tactical acumen, to halt the slide.Eta’s appointment is the latest milestone in a rapid rise through Union’s ranks. In the 2023‑24 season she became the Bundesliga’s first female assistant manager under Nenad Bjelica, and earlier in 2024 she briefly commanded the men’s side, overseeing a win, a draw and a loss while Bjelica served a suspension. Her prior success with Union’s under‑19 men’s squad further cemented her reputation as a forward‑thinking coach.Speaking in a 2023 interview, Eta emphasized that she wants to “convince with quality and substance” rather than rely on tokenism. Former England women’s manager Sarina Wiegman hailed her as a “trailblazer”, noting that such progress reflects football’s broader societal shift toward gender equality.Germany is already seeing more women in senior coaching roles: Sabrina Wittmann leads third‑tier side FC Ingolstadt, while Corinne Diacre previously managed Ligue 2 club Clermont Foot in France. In England, Hannah Dingley made history as caretaker of Forest Green Rovers before moving to Manchester City’s academy.Eta’s current stint with the men’s team is expected to be short‑lived. She has already signed a contract to become head coach of Union Berlin’s women’s side next season, where she will continue to develop talent in the Frauen‑Bundesliga. Nonetheless, her presence on the technical area this weekend offers a powerful visual for aspiring female coaches worldwide.Social media reactions have been mixed. While a minority of users resorted to sexist trolling, Union’s official X account defended Eta vigorously, dubbing her a “football goddess” and firing back at detractors. Eta, a former Champions League winner with Turbine Potsdam, said she draws motivation from messages sent by young women and girls she has inspired.The upcoming match will not only test Union Berlin’s fight against relegation but also serve as a symbolic moment in the ongoing effort to break the “grass ceiling” in professional football.

Tanya Khovanova has long been a leading voice in the world of recreational mathematics, authoring a popular blog and running the Number Gossip site where enthusiasts can inquire about any number.She now debuts her first book, Mathematical Puzzles and Curiosities, co‑written with fellow puzzle‑enthusiasts Ivo David and Yogev Shpilman. Published by World Scientific, the volume offers fresh challenges and inventive twists on classic problems.To give readers a taste, Khovanova selected three puzzles for the Guardian column:1. Battleships – As a naval admiral you must choose between sending a single vessel with a success probability of P % or two vessels each with a P/2 % chance, where the mission succeeds if at least one ship does. Which strategy maximises the odds?2. The Two Oracles – You face two respondents, Randie, who answers randomly, and Rando, who randomly decides to tell the truth or lie before each answer. Is there a method to distinguish them?3. Bad Maths – A student computes 5548 − 5489 as 59, claiming the “548” cancels out. He then experiments with a subtraction of the form XXYZ − XYZW (distinct digits) and observes the result is XW. How many digits in the new expression match those in the original calculation?Solutions to the trio were later posted online (update), but readers were urged to avoid spoilers until the scheduled reveal.Khovanova also reminds fans that she has been curating puzzles for the Guardian every other Monday since 2015 and welcomes new submissions via email.

According to the latest Tottenham Hotspur financial statements, former executive chair Daniel Levy received £5.76 million in remuneration for the year ending 30 June 2025. That figure represents a 54% increase on his 2024 earnings and, as noted by football‑finance analyst Kieran Maguire, made him the highest‑paid director in the Premier League for the season. In stark contrast, the club’s women’s team—comprising 64 players and staff—had a combined salary and bonus total of £3.73 million, a 23% rise from the previous year. After accounting for social security and pension contributions, the overall wage bill reached £4.3 million, with an average annual earnings of roughly £58,000 per employee. This places Tottenham Women below several WSL rivals that have disclosed their 2024‑25 accounts, such as Brighton (£5 million), Manchester United (£5.88 million), and Arsenal (£11.3 million), but above Liverpool (£3.12 million). The women’s side recorded a post‑tax loss of £2.83 million, marginally higher than the £2.73 million loss reported in 2024. The deficit persisted despite a notable surge in commercial revenue, which more than doubled from £1.46 million to £3.34 million. Broadcast income remained static at £267,414, while prize‑money earnings fell by approximately £600,000. On the pitch, Tottenham Women finished the 2024‑25 campaign in 11th place in the Women’s Super League. However, the current 2025‑26 season shows a marked turnaround, with the team sitting fifth with three matches remaining and having nearly doubled their league victories compared with the previous term. Sources indicate that an internal review has repositioned women’s football as a strategic priority for the club, a shift that is expected to be reflected in the forthcoming 2025‑26 accounts.

King Charles's upcoming visit to the White House to meet with Donald Trump is poised to be a delicate diplomatic situation. The king will have to navigate a complex web of potential insults and controversies, including Trump's past comments about the UK's military assets, his criticism of British politicians, and his unconventional social media posts.Historically, Charles has had his share of awkward encounters with US presidents. During his visit to President Nixon in 1970, officials awkwardly presented Nixon's daughter Tricia as a potential match for the then-young prince. Later, during a visit to Ronald Reagan, Charles was handed a cup of tea with the bag still in it, leaving him unsure of how to proceed.In contrast, Charles's meetings with the Clintons and Bushes were uneventful, and his 2015 meeting with Obama was notable for his frank discussion on climate change, which, although not necessarily polite, was a significant moment.However, the current situation with Trump is particularly challenging. Trump has publicly criticized the UK's military assets, including the HMS Queen Elizabeth and HMS Prince of Wales, bearing the names of members of the royal family. Additionally, Trump has made derogatory comments about Pope Francis, which could complicate relations between the US and the Vatican.The king will also have to address Trump's recent social media post featuring an AI-generated image of himself as Jesus, which could be seen as blasphemous or insensitive. Given Trump's unpredictable nature, it's uncertain what he might say or do during the visit.While it would be unprecedented for the king to cancel the visit, the situation is already out of the ordinary. It remains to be seen how Charles will navigate this complex diplomatic situation and maintain the dignity of his office.

The 2018 World Cup in Russia served as a high‑profile platform for Vladimir Putin, showcasing his nation and bolstering his personal legitimacy. The tournament was effectively a diplomatic bow to the Kremlin’s ambitions.Fast‑forward to the summer of 2026, and the buildup to the event has taken on a distinctly American flavour, with the competition becoming a backdrop for Donald Trump’s political narrative.The next edition, slated for 2034 in Saudi Arabia, presents a fresh set of challenges. Despite the kingdom’s controversial human‑rights record, the event offers Crown Prince Mohammed bin Salman an opportunity to polish his and the nation’s image. FIFA’s current reluctance to enforce independent oversight of migrant‑worker conditions raises fears that construction could be as deadly as the 2022 Qatar experience.These developments underscore a pressing need to insulate the World Cup from the whims of powerful leaders. One proposed solution is to fragment the tournament—treating it like a monopoly that has become too dominant.Evidence that this approach is feasible already exists: the 2026 World Cup will be co‑hosted by three nations, and the 2030 edition is set to span six countries across three continents (Spain, Portugal, Morocco, Argentina, Paraguay, Uruguay).Building on that, the author suggests a radical redesign: allocate each group stage to a different global city—Paris, Rio de Janeiro, Tokyo, Sydney, Johannesburg, London, the Basque Country, and so on. Knock‑out rounds could be broken into three‑match clusters and scattered worldwide, with the semi‑finals, final, and third‑place match awarded to the highest‑bidding venue.Carbon‑footprint concerns are addressed by noting that teams already travel long distances to a single host nation; distributing groups based on the median distance to participating teams would not significantly increase emissions.Financially, the cost of staging a traditional, single‑host World Cup has ballooned, limiting the pool of viable bidders to those seeking political or economic leverage. A decentralized format would dilute any single leader’s ability—whether Trump, Putin, or the Saudi crown prince—to manipulate the event for personal gain.Decentralisation would still align with FIFA’s stated objectives: expanding the sport’s reach, creating a truly global spectacle, and bringing football closer to fans worldwide.While FIFA claims a fiduciary duty to maximise revenue for its 211 member associations—justifying steep ticket prices and controversial sponsorships—the proposed model could actually enhance revenue by turning each small cluster of matches into premium, high‑value events.Precedent exists in the form of Euro 2020, which, despite being postponed by the pandemic, successfully unfolded across 11 European cities, delivering record‑breaking goal tallies and strong attendance figures.In sum, the most effective way to protect the World Cup’s cultural significance and prevent its exploitation by authoritarian figures may be to deconstruct and disperse it globally, turning a single‑host behemoth into a series of interconnected, locally hosted celebrations of the sport.

England and Spain meet again on Tuesday night in front of more than 70,000 at Wembley in the Women's World Cup 2027 qualifiers. This match comes eight-and-a-half months after they faced off in the Euro 2025 final, which England won.Spain has undergone significant changes since then, with a new head coach, Sonia Bermúdez, and a crop of emerging young players. Despite these changes, they remain unbeaten since the Euros with five wins and a draw in six matches. Bermúdez has already led them to the Nations League title.The visitors have a number of talented young players, including Fiamma Benítez, the 21-year-old Atlético Madrid midfielder, who has made a strong impact with seven goal contributions in the Champions League this season. Another player to watch is Vicky López, the Barcelona winger, who has become a regular starter.England head coach Sarina Wiegman believes that despite the changes, Spain's DNA remains the same: they want to have the ball and play dynamically. Wiegman noted that there might be some tweaks but the principle will be very similar.For England, Leah Williamson is an injury doubt due to a hamstring injury, but she has started training with her international teammates. Keira Walsh is set to win her 100th cap and Wiegman praised her vision and game understanding.England will have to make at least one change from the starting XI that beat Spain in Switzerland, with Ella Toone out injured. Jess Park is likely to start in her place.