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At the Metropolitano, Barcelona appeared to be in control early on, with Lamine Yamal delivering a pinpoint cross that set up a near‑certain goal for Fermín López. The strike was thwarted by a spectacular save from Juan Musso, leaving López drenched in claret. Had the ball found the net, Barcelona would have taken a 3‑0 lead and an advantage in the tie after already scoring through Yamal and Ferran Torres in the opening half‑hour.The deadlock was broken when Charlton‑trained forward Ademola Lookman netted the decisive goal, sending Atlético Madrid into the Bigger Cup semi‑finals. The victory sparked an exuberant reaction from coach Diego Simeone, who praised his side’s enthusiasm and readiness for the next challenge, hinting at a possible showdown with Arsenal or Sporting.In the aftermath, Barcelona winger Raphinha launched a scathing critique of referee Clément Turpin, alleging that the officiating had robbed his team not only in the second leg but also in the first. The Brazilian warned that his comments could land him on UEFA’s disciplinary “naughty step,” with precedent suggesting a suspension of at least three matches for such language.The controversy deepened as Turpin refrained from issuing any bookings to Atlético players and denied Barcelona what they believed were two clear penalty opportunities across both legs. Musso, who had earlier saved López’s chance, dismissed the accusations, emphasizing that the match was decided on the pitch and that disciplinary actions are part of the game’s reality.Further coverage of the European fixtures, including live updates from the Bigger Cup quarter‑finals and analysis from Guardian experts, is available on the publication’s football portal.

The IMF has cautioned that the ongoing conflict in the Middle East, particularly the escalation of tensions between Iran and Israel, poses a substantial risk to global economic stability. The fund's half-yearly fiscal monitor report highlights that global debt levels are on track to increase due to the war's impact on energy and food prices, higher government borrowing costs, and slower economic growth.Against this volatile backdrop, the IMF has warned that governments may be forced to choose between cushioning the cost of living shock and maintaining sound public finances. The fund's report notes that global debt levels have already risen to almost 94% of GDP and are projected to reach 100% by 2029, a level not seen since the aftermath of World War II.The IMF emphasizes that any energy support schemes to shield households and businesses from the impact of higher energy prices should be targeted and temporary, focusing on those most exposed and least able to absorb price increases. The fund also cautions against using further borrowing to cushion the blow, suggesting that governments should instead reallocate spending within existing limits and prioritize crisis-related spending.The report highlights the risks associated with higher debt and interest costs, which could eventually force governments to make tougher choices or destabilize debt markets. The IMF points to the UK's experience with Liz Truss's 2022 mini-budget as an example of how market confidence can be lost when fiscal policies are perceived as unsustainable.

Spanish cyclist Jaume Guardeno continues to fight for his life in the intensive care unit (ICU) of Tauli Hospital in Sabadell, two weeks after a severe training accident. The 23-year-old rider from Spain was involved in a collision with a vehicle on March 31, which resulted in serious head injuries.Guardeno's condition remains critical but stable, with his team, Caja Rural-Seguros RGA, providing regular updates on his progress. He is under constant monitoring and is scheduled to undergo further medical procedures in the coming days to aid his recovery.The young cyclist had shown promise in the sport, finishing 14th in the Spanish Vuelta last year and 29th in the Volta a Catalunya just days before the accident. His team is set to make its Tour de France debut this year, highlighting Guardeno's potential.Cycling has seen a resurgence in popularity with riders like Tadej Pogacar, Mathieu van der Poel, and Wout van Aert, but the sport still carries significant risks. Recent incidents include Olympic champion Tom Pidcock pulling out of the Volta a Catalunya after a crash and Italian cyclist Debora Silvestri being hospitalized after a crash during the women's Milan-San Remo.

Gordon Ramsay's latest reality TV venture, Secret Service, has taken the Kitchen Nightmares formula to new heights by sending the famously fiery chef undercover to expose the horrific conditions at a struggling Washington DC restaurant, Parthenon. Ramsay arrived at the Parthenon in the early hours of the morning, donning a baseball cap and driving a SUV. He had been contacted by a whistleblower from within the restaurant, who arranged for him to break in overnight to investigate the kitchen's state. Upon entering, Ramsay was met with a scene that looked like the aftermath of a crime, with fatty burnt-orange goo covering the prep surfaces and a black light scan revealing a kitchen in a shocking state of disarray. The kitchen's condition was so bad that Ramsay predicted "rats the size of my grandmother's cat" could be present. He then descended into the sticky horror of the basement, where he found a bandsaw used to slice racks of lamb with fleshy residue on it, and a plastic bag of raw chicken sitting in bloody ice-water. A bacteria expert later confirmed the presence of tiny things wriggling in the samples. The next day, Ramsay sat in a broadcast truck, monitoring the restaurant's service via a wall of monitors and headphones. He directed the filming, barking orders and reacting to the listeria-flavoured fiasco unfolding before him. The footage was then edited with special spy effects, including a green light blinking in the corner and the name of the room displayed at the top of the screen. Ramsay's team also sent in two young chef pals to pose as diners, wearing body-mounted cameras to gather evidence. When they ordered the bandsaw lamb, Ramsay shouted into their earpieces, "Don't eat those lamb chops!", before bursting into the restaurant to confront the staff. The intervention led to a dramatic showdown with the restaurant's owner, Pete, and his family. Ramsay's tough love approach and emotional truths helped to bring about a watershed moment in their lives. The restaurant was subsequently refitted and a new menu implemented, with Pete's son Mikey taking charge. The show's mix of kitchen reality and cheesy espionage did not detract from the emotional impact of the transformation, as Pete tearfully thanked Ramsay for his intervention. The identity of the secret insider who contacted Ramsay was also revealed, adding a gripping mystery to the episode.

The UK's culture secretary, Lisa Nandy, has cleared Axel Springer's £575m takeover of the Telegraph titles, paving the way for the end of almost three years of uncertainty over the ownership of the newspapers. Nandy stated that she does not believe there are grounds to intervene and refer the deal to the media regulator, Ofcom, for an in-depth regulatory investigation. The culture secretary has the power to call in mergers for further scrutiny on public interest grounds, as well as the new foreign state influence regime. Axel Springer, a German media group, had tabled a significantly superior offer to Lord Rothermere's Daily Mail and General Trust (DMGT), prompting the United Arab Emirates-backed group that controls the Telegraph to seek UK government approval to switch the permission to sell the right-to-buy option to Axel Springer. The Telegraph titles will add to Axel Springer's media portfolio, which includes Europe's biggest newspaper, Bild, Politico, and Business Insider. Axel Springer CEO, Mathias Döpfner, has promised to invest in the Telegraph to make it the “leading centre-right media outlet in the English-speaking world”, with a rapid expansion planned for the US supported by the expertise of Politico and Business Insider. The sale of the newspapers was kicked off in 2023 when the Barclay family lost control of the group over £1.16bn of unpaid debts owed to Lloyds bank. RedBird IMI, which is 75% controlled by Sheikh Mansour bin Zayed Al Nahyan, the vice-president of the UAE and the owner of Manchester City, took control of the publishing group after agreeing to pay the Barclays' debts.

The UK government's ambitious plans to create 400,000 green jobs by 2030 seem to be failing to deliver for young people in England's coastal communities. Despite being surrounded by offshore windfarms, 44% of the UK's offshore windfarms are located in the east of England, areas like Lowestoft and Great Yarmouth are struggling with high unemployment and limited job opportunities.Jake Snell, a 19-year-old from Lowestoft, is a prime example. With high grades in maths and physics A-levels, a distinction in BTEC engineering, and work experience at an engineering company, he seemed like the perfect candidate for a role in the green energy sector. However, out of his 14-person cohort, only two people ended up with apprenticeships, and only one of these was in engineering.Rachel Wilde, a social anthropologist at University College London, notes that the term 'green jobs' is nebulous and that there is little concrete evidence of what these jobs actually are. She argues that there is a gap between politicians and policymakers promoting green jobs and people on the ground trying to talk to young people about job opportunities.Avril Keating, a professor of youth studies at UCL, suggests that the focus on high-profile roles in green energy is misleading and that more investment in continuing careers support for people in coastal and economically deprived areas is urgently needed.The government has announced plans to establish five technical excellence colleges that will focus training around the green energy sector, which could provide hope for the next generation of young people in these areas. However, for now, many young people like Snell are struggling to find employment and are feeling frustrated and disillusioned with the lack of opportunities.

Islamabad transformed into a security zone on Saturday as the city imposed a lockdown, sealing roads, establishing checkpoints, and deploying over 10,000 security personnel ahead of the anticipated US‑Iran ceasefire talks. The Iranian delegation arrived quietly late on Friday night, traveling through Balochistan before a Pakistani Air Force aircraft switched off its call sign. By the next afternoon, the American team touched down at Nur Khan Air Base, a site India once claimed was damaged during last year’s brief conflict. On the tarmac, three distinctive tail fins—one American, two Iranian—caught the eye, a subtle reminder of the region’s reliance on symbolism. Both delegations were escorted along pre‑cleared routes to the Serena Hotel, which had been emptied and secured days earlier, turning the former luxury venue into a tightly controlled diplomatic arena. This marked the first direct, high‑level engagement between post‑revolution Iran and the United States on foreign soil. Clashing worldviews in the negotiation room Inside, the talks juxtaposed an American “peace through strength” stance with Iran’s “resistance with dignity” perspective. Pakistani Prime Minister Shahbaz Sharif warned the night before that the meeting was a make‑or‑break moment for lasting peace. Iran’s chief negotiator, Mohammad Bagher Ghalibaf, set pre‑conditions: any dialogue required progress on a Lebanon ceasefire—where Israel’s campaign has killed over 2,000 people—and the unfreezing of Iranian assets held abroad, which have crippled Tehran’s economy. Within hours of arrival, bilateral side‑talks began, offering a tentative thaw for Pakistani officials facilitating the process. Although previous rounds in Muscat, Vienna, Geneva and Abu Dhabi suffered from deep mistrust, this was the first occasion that the United States’ vice‑president JD Vance and Iran’s parliamentary speaker Ghalibaf faced each other face‑to‑face. Pakistan’s strategic mediating role Pakistan leveraged its unique position—close ties to Gulf states, a shared border with Iran, proximity to the Strait of Hormuz, and a strategic partnership with China—while not hosting US military bases. This allowed Islamabad to engage all parties without overt alignment. The marathon 21‑hour session Officials described the talks as continuous yet uneven. The first session lasted under two hours, followed by a brief procedural pause during which dinner was served but informal discussions continued. Subsequent rounds involved multiple draft exchanges and rapid redrawing of red lines, with constant communication to Washington—including President Donald Trump—and Tehran. Pakistani leaders, including Prime Minister Sharif, Foreign Minister Ishaq Dar, and Army Chief Asim Munir, worked around the clock, aiming not for a final pact but for a framework to prevent further escalation. Why the talks stalled As the session entered its final phase, the United States signaled an abrupt end. JD Vance summed up the outcome: “We had substantive discussions, but no agreement.” He emphasized the US demand for an affirmative, long‑term commitment from Iran not to pursue nuclear weapons, describing Washington’s proposal as its “final and best offer.” Iran’s ambassador in Islamabad framed the meeting as “not an event, but a process,” claiming it laid groundwork for future dialogue, while state‑affiliated outlets criticized the US stance as overly demanding. A senior Iranian foreign‑ministry spokesperson noted that, for Tehran, diplomacy is a continuation of its broader struggle, and any progress hinges on the other side’s “seriousness and good faith.” Pakistan’s cautious post‑talk posture Finance Minister Dar thanked both sides and pledged continued facilitation, avoiding any claim of victory or admission of failure. Behind the scenes, officials acknowledged pressure from multiple fronts—including Israel, whose prime minister Benjamin Netanyahu is perceived by some sources as a major obstacle to peace. Aftermath in Islamabad The city did not immediately revert to normal; security checkpoints and traffic diversions persisted, and the Serena Hotel remained under tight control. Journalists reported a disciplined environment with limited leaks, suggesting a deliberate effort to contain information. As the delegations departed, the door on diplomatic engagement remained open, albeit without a concrete agreement. The talks, though inconclusive, demonstrated that high‑level US‑Iran dialogue is possible under Pakistan’s mediation, preserving a channel that could prove pivotal in future regional negotiations.

The article features three brainteasers with their respective solutions. The first puzzle involves a Navy admiral choosing between sending one ship with a P per cent chance of success or two ships each with a P/2 per cent chance of success. The solution reveals that sending one ship is always the better option.The second puzzle introduces two oracles, Randie and Rando, who answer questions differently. Randie responds randomly, while Rando decides to tell the truth or lie. The solution explains how to distinguish between them by asking a specific question that yields the same answer from both a liar and a truthteller.The third puzzle involves a mathematical problem where Johnny calculates 5548-5489 = 59 by incorrectly canceling out digits. A similar calculation XXYZ - XYZW is analyzed, and the solution reveals that Z and W are 8 and 9, respectively.

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.