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Match details: Atletico Madrid will meet Barcelona on Tuesday at 21:00 CET (19:00 GMT) in the Metropolitano Stadium for the Champions League quarter‑final second leg. The fixture decides which side advances to the semi‑finals. After a 2‑0 first‑leg triumph at Camp Nou, Atletico enter the tie as favourites despite trailing Barcelona in the La Liga table. Their advantage stems from goals by Julian Alvarez and Alexander Sörloth, who capitalised on a red card for Barcelona defender Pau Cubarsi. Barcelona, the reigning Spanish champions, are desperate to overturn the deficit. They bolstered their domestic campaign with a 4‑1 win over Espanyol, extending their lead over Real Madrid to nine points. Ferran Torres netted a brace, assisted by teenage prodigy Lamine Yamal, while Marcus Rashford added the fourth. Atletico’s weekend league performance was less convincing, suffering a 2‑1 loss to Sevilla after heavy rotation by Diego Simeone. The loss left them fourth in La Liga with 57 points, four behind Villarreal. Historical context: The two clubs have met 251 times, with Barcelona winning 115 matches, Atletico 79 and 57 draws. Their recent knockout encounters include Atletico’s victories in the 2014 and 2016 quarter‑finals, both decided over two legs. Team news: Atletico will miss Marc Pubill (suspension) and have Jose Giménez, Pablo Barrios and David Hancko listed as doubtful. Barcelona’s defender Pau Cubarsi is suspended, replaced by Ronald Araujo. Injuries rule out Marc Bernal, Raphinha and Andreas Christensen. Predicted line‑ups: Atletico – Musso; Molina, Le Normand, Lenglet, Ruggeri; Llorente, Koke; Simeone, Griezmann, Lookman; Alvarez.Barcelona – Joan Garcia; Koundé, Araujo, Martín, Cancelo; Eric Garcia, Pedri; Yamal, Fermin, Rashford; Lewandowski. Managerial insights: Simeone stressed the need to stay focused on the objective of advancing, while Barcelona coach Hansi Flick highlighted the quality of his squad and the importance of collective effort. With a slim margin separating the sides, the second leg promises a tactical battle that could see either club secure a coveted place in the Champions League semi‑finals.

Australia announced that Lieutenant General Susan Coyle will assume the role of chief of the Australian Army in July, marking the first time a woman has held the post in the service’s 125‑year history.Coyle, currently chief of joint capabilities, brings nearly four decades of experience, including senior command roles in Afghanistan and the Middle East, and expertise in cyber‑warfare. She will succeed Lieutenant General Simon Stuart, who took the position in July 2022.Prime Minister Anthony Albanese hailed the appointment as a historic breakthrough, stating, "From July, we will have the first ever female chief of army in the Australian Army’s 125‑year history." Defence Minister Richard Marles called the move a "deeply historic moment" and emphasized its symbolic power: "You cannot be what you cannot see."The appointment arrives as the Australian Defence Force (ADF) intensifies efforts to raise female participation. Women currently constitute about 21 % of the ADF and 18.5 % of senior leadership roles, with a target of 25 % overall participation by 2030.In October, a class‑action lawsuit alleged that the ADF failed to protect thousands of women officers from systematic sexual assault, harassment, and discrimination, underscoring the urgency of cultural reform alongside the leadership change.Alongside Coyle’s promotion, Vice Admiral Mark Hammond, the incumbent chief of the navy, will become the head of the ADF, succeeding Admiral David Johnston. Rear Admiral Matthew Buckley is set to replace Hammond as navy chief.The army is also undergoing a major transformation, investing in long‑range firepower, drones, and other modern combat tools. Coyle’s background in cyber‑warfare is expected to bolster the force’s capability to operate in increasingly digitised battlefields.

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.

At 19,000 miles above the lunar surface, the Artemis II astronauts heard the voice of Apollo‑13 commander Jim Lovell greeting them from beyond the grave, a message recorded shortly before his death at 97. Mission control transmitted the tribute on the morning of 6 April, when astronaut Reid Wiseman held a silk square bearing the original Apollo 8 patch—handed to him by Lovell’s son—before the crew’s launch. Launch director Charlie Blackwell‑Thompson secured a unanimous "go" from every console, a moment the author describes as a snapshot of humanity’s capacity to honor the past while reaching for the future. The ceremony stood in stark contrast to the Pentagon’s agenda. Two decades after a 2006 Iraqi kill‑board note reading “Let the bodies hit the floor,” the current defense chief pledged “death and destruction from the sky all day long” against Iran, a stance legal scholars warn could constitute a war crime. That rhetoric accompanies a proposed $1.5 trillion defense budget, including an additional $200 billion earmarked for operations against Iran—figures that dwarf NASA’s entire annual budget of $24.4 billion. Amid this fiscal disparity, crew members reflected on their place in history. Victor Glover, the first Black astronaut to travel deep space, described the view of Earth as an "oasis" in the void, while Christina Koch, the first woman to orbit the Moon, pressed her face to the window and formed a heart with her hands, calling the mission’s spirit "humility." Reid Wiseman watched the planet rotate beneath him, noting the sight of Africa, Europe, and the aurora‑lit north, saying it "paused all four of us in our tracks." Canadian astronaut Jeremy Hansen broke Jim Lovell’s 56‑year distance record and asked mission control to name a lunar feature after his late wife, Carroll. The crew agreed, designating a bright spot on the Moon as "Carroll," a tribute that will endure beyond any single lifetime. When Koch announced the spacecraft’s descent, she radioed, "We are now falling to the moon rather than rising away from Earth," a poetic reversal that underscored the mission’s symbolic return. The article recalls the author’s 2022 reflection on the James Webb Space Telescope, noting how humanity’s finest inventions now aim outward, seeking answers to our origins rather than turning inward toward conflict. Artemis II’s vessel, named Integrity, carried four breathing humans who, in a moment of collective grief, pressed their faces to the glass and imagined the faces of every loved one ever lived, captured in a single frame. Beyond the spacecraft, cultural threads wove through the mission: Hansen’s patch displayed the Seven Sacred Teachings of the Anishinaabe people, and the Chinese myth of Chang’e reminded viewers of the Moon’s timeless allure. As Carl Sagan famously wrote, "We are made of star‑stuff," the Artemis crew embodied that sentiment—not as passive observers, but as active participants in a fragile, hopeful narrative that rises above the relentless tally of bodies on Earth’s battlefields.

A federal judge in Miami has dismissed former President Donald Trump’s defamation lawsuit against the Wall Street Journal and News Corp, granting the former president a two‑week deadline to refile the case. Trump’s suit, filed last summer, alleged that a lewd drawing featured in a July 2025 article—purportedly a “bawdy” birthday letter to the late financier Jeffrey Epstein—was fabricated, and that the newspaper published it with actual malice. The complaint also named media mogul Rupert Murdoch, whose News Corp owns the Journal, as a defendant. Judge Darrin P. Gayles ruled that the complaint “fails to adequately allege actual malice,” the legal standard required for defamation actions by public figures. He noted that the Journal had conducted a “significant” inquiry into the authenticity of the drawing and that Trump’s assertion of falsity alone does not prove the newspaper acted with “serious doubts” about the story’s truth. In his opinion, the judge wrote: “Because President Trump has not plausibly alleged that defendants published the article with actual malice, both counts must be dismissed.” He also observed that Trump’s team had not presented evidence of special damages. Under the order, Trump may refile the lawsuit by April 27 with additional proof that the Journal knowingly published false material. A spokesperson for Trump’s legal team confirmed they will pursue a revised filing, emphasizing the administration’s intent to “hold accountable those who traffic in fake news.” The Wall Street Journal and its parent company, Dow Jones, welcomed the decision. A Dow Jones representative said, “We stand behind the reliability, rigor and accuracy of The Wall Street Journal’s reporting.” The dismissal underscores the stringent “actual malice” requirement for defamation suits involving public officials, a threshold that continues to shape media‑law battles in the United States. It also leaves Trump with ongoing litigation against the BBC and other media outlets over separate First Amendment disputes.

Tottenham Hotspur have lost their captain Cristian Romero for the remainder of the 2025‑26 Premier League campaign after sustaining medial knee‑ligament damage in a clash with Sunderland striker Brian Brobbey. The injury, expected to require around eight weeks of rehabilitation, forces Romero off the pitch for the final six matches that will decide whether the club remains in the top flight.Romero left the Stadium of Light in tears after 70 minutes of a 1‑0 defeat, the goal coming from his own goalkeeper Antonín Kinský following the collision. The Argentine defender’s absence adds to an already extensive injury list that includes James Maddison, Dejan Kulusevski, Wilson Odobert and Mohammed Kudus. Goalkeeper Guglielmo Vicario is also sidelined after a hernia operation, leaving Kinský as the starter.Spurs sit 18th after a season that has seen them lose 16 league games and fail to register a domestic win in 2026. Manager Roberto De Zerbi admitted the blow could be “a big problem” but stressed the need for the squad to rally: “He’s a good guy, a top player, and we need him to finish the season and achieve our goal.”The incident also sparked a backlash against Brobbey, who was targeted with racist abuse on social media. Sunderland issued a statement pledging full support for the striker and confirming that the matter has been reported to the Premier League, relevant platforms and the police.With the relegation battle intensifying, Tottenham’s ability to replace Romero’s defensive leadership will be crucial as they fight to stay in the Premier League.

West Bromwich Albion has denied any wrongdoing regarding the EFL's financial rules, despite growing fears of a points deduction that could significantly impact their relegation battle in the Championship. The Daily Telegraph reported that the EFL's Club Financial Reporting Unit (CFRU) had filed a compliance report against West Brom, alleging a breach of the loss limits for the 2024-25 season under the profitability and sustainability rules (PSR). If a points penalty were imposed, it would affect West Brom in the current campaign, with the club currently sitting 20th in the Championship, just two points above the relegation zone. West Brom responded by stating, “The club considers that it has fully complied with the rules.” They emphasized their commitment to cooperating with the EFL and resolving the matter, while also thanking fans for their support. Under PSR rules, Championship clubs are required to keep losses under £39m over a three-year assessment period. Certain expenditures, such as investments in infrastructure, youth, and women’s football, are ‘added back’ in the PSR calculation. West Brom, having competed in the Championship last season, was required to submit their annual accounts for 2024-25 by December 31. The EFL has declined to comment on the matter, and decisions on sanctions by the Club Financial Reporting Panel (CFRP) are typically published after discussions between the club and the EFL remain confidential.

German club Union Berlin broke new ground on Sunday by appointing Marie‑Louise Eta as interim manager, the first female to head a Bundesliga side and the inaugural woman to coach a top‑flight men’s team in a major European league. Eta, 34 years old, previously made history as the Bundesliga’s first female assistant coach. She will steer the team for the remainder of the campaign after the dismissal of Steffen Baumgart, whose tenure ended following a 3‑1 loss to bottom‑placed Heidenheim that underscored a stagnant second half of the season. In a statement, Eta expressed her enthusiasm: “I am delighted the club has entrusted me with this challenging task.” Sporting director Horst Heldt welcomed the decision, noting that Eta will transition to lead Union’s women’s Bundesliga squad in the summer as originally planned. Union’s recent form has been troubling: the side has secured only two victories since Christmas and currently sits seven points above the relegation playoff zone. Heldt described the situation as “absolutely disappointing” and emphasized the urgent need for points to avoid a drop. Eta brings a distinguished playing résumé, having won the 2010 UEFA Women’s Champions League and three Bundesliga titles with Turbine Potsdam. Her coaching résumé includes stepping in for head coach Nenad Bjelica during a three‑game suspension in 2024, showcasing her readiness for senior responsibilities. While women have managed men’s teams in Germany’s lower tiers—such as Sabrina Wittmann at Ingolstadt FC—Eta’s appointment marks the first instance at the top level. France’s former second‑division side Clermont also benefited from a female coach, Corinne Diacre, between 2014 and 2017. The historic move not only reflects Union Berlin’s immediate need for a turnaround but also signals a broader shift toward gender diversity in elite football management.

Day 44 of the US‑Iran war ended without a peace deal as a marathon 21‑hour session in Islamabad collapsed, jeopardising the fragile cease‑fire that has held since the conflict began over six weeks ago.Vice President JD Vance, leading the US delegation, told reporters that the lack of an agreement was "bad news for Iran much more than it’s bad news for the United States of America," before departing Pakistan.Pakistan’s Foreign Minister Ishaq Dar pledged that Islamabad would continue to facilitate dialogue between the two longtime adversaries.In Iran, officials downplayed expectations, noting that no one anticipated a settlement in a single session. State‑run IRIB quoted ministry spokesperson Esmaeil Baghaei saying the talks were never expected to conclude quickly. Meanwhile, Tehran residents expressed a mix of scepticism and hope after weeks of air attacks that have left a nation of 93 million people reeling; more than 2,000 Iranians have been killed in the US‑Israel‑Iran conflict.In the United States, Vance reiterated that the delegation left with a "final and best offer" for Iran, emphasizing that Washington had communicated its position repeatedly during the talks. He cited multiple conversations with President Donald Trump, Secretary of State Marco Rubio, Treasury Secretary Scott Bessent, and Central Command head Brad Cooper. Trump, however, maintained that the US had already "won" on the battlefield by eliminating Iranian leaders and key infrastructure, stating that a deal would not alter the outcome.The US military reported that two destroyers transited the Strait of Hormuz ahead of planned mine‑clearing operations – a first since hostilities began – though Iran’s state media claimed the joint command denied the movement.Academic David Des Roches of the Thayer Marshall Institute told Al Jazeera that while Washington clarified its stance, it did not shift its core demand: preventing Iran from acquiring a nuclear weapon.In Lebanon, Israel continued strikes, claiming to have hit a "loaded and ready‑to‑launch rocket launcher" in Jouaiya, southern Lebanon. Protests have erupted in Beirut against any direct Israel‑Lebanon negotiations. The Lebanese Ministry of Public Health reported at least 2,020 deaths and 6,436 injuries from Israeli attacks since March 2.In Israel, Channel 12 reported that a drone launched from Lebanon triggered sirens in the Upper Galilee before being intercepted.The stalemate has kept global oil and gas prices soaring, underscoring the broader economic ripple effects of a war that shows no sign of abating.