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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.

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.

Acclaimed director Ken Loach revisits his 2016 film I, Daniel Blake, a poignant portrayal of poverty and the struggles faced by those in need. The film, which sparked controversy upon its release, shed light on the cruel realities of a system that vilifies the vulnerable.Loach reveals that the film was born out of a time of 'mean-spiritedness,' where those who needed support were met with punishment. The story follows Daniel Blake, a character who desperately wants to work but is thwarted by a system designed to fail him.The film's screenwriter, Paul Laverty, conducted extensive research, including a visit to a Glasgow food bank, where he encountered a young man who had not eaten in two to three days. This harrowing experience inspired a pivotal scene in the film, where Katie, played by Hayley Squires, is forced to eat cold baked beans from a tin.Loach notes that at the time of the film's release, the notion of food banks as an institution was unimaginable. However, food banks are now a normalized part of society, with many people relying on them to survive. The film's portrayal of poverty and hunger was met with resistance from some, including Damian Green, who claimed it was a work of fiction. Loach counters that while the characters are fictional, the stories are rooted in truth.Hayley Squires, who played Katie, shares her experience working on the film. She was drawn to the project after meeting Loach and was impressed by his authenticity and warmth. The film's shooting process was unique, with Squires and her co-star Dave Johns working chronologically and improvising scenes.Squires also recounts her preparation for the food bank scene, which included visiting a real food bank and cutting back on food to better understand the experience of hunger. The scene was shot only once, with Loach and the cinematographer Robbie Ryan working to create a sense of empathy and realism.

Rory McIlroy has made history by winning his second Masters title, holding off a strong challenge from world No 1 Scottie Scheffler to claim a one-shot victory at Augusta.This impressive win cements McIlroy's status as one of golf's all-time greats, making him only the fourth player in the tournament's 90-year history to win successive titles at Augusta. McIlroy's sixth major puts him level with Nick Faldo and one beyond the great Spaniard Seve Ballesteros, who won five.Donald Trump, the former US President who has played golf with McIlroy in the past, was quick to congratulate the Northern Irishman on his achievement. Using his Truth Social platform, Trump wrote: 'Congratulations to Rory McIlroy on another Great Championship, The Masters! He performed tremendously under intense pressure, something which few people would be able to even think about doing. With each year, Rory is becoming more and more a LEGEND!'Trump also expressed his excitement for McIlroy's next appearance at the Cadillac Championship at Trump National Doral in Miami later this month, praising the quality of professional golfers today.

Hungary's longtime Prime Minister Viktor Orban has conceded defeat in the country's parliamentary election after partial official results showed Peter Magyar's Tisza party winning a landslide victory.With 53.45% of precincts counted, Tisza stood at 52.49% and Orban's Fidesz at 38.83%. In a victory speech, Magyar said his voters had rewritten history, stating, 'Tonight, truth prevailed over lies. Today, we won because Hungarians didn’t ask what their homeland could do for them – they asked what they could do for their homeland.'The partial count showed Tisza ahead in 95 of Hungary's 106 constituencies, with the party projected to win more than 130 mandates in the 199-seat parliament. This comfortable two-thirds majority could allow Tisza to amend Hungary's constitution.Orban's defeat will have significant implications not only for Hungary but also for the European Union, Ukraine, and beyond. It may spell an end to Hungary's adversarial role inside the EU, possibly opening the way for a €90 billion ($105bn) loan to war-battered Ukraine, which was blocked by Orban.Orban's exit could also mean the eventual release of EU funds to Hungary that the bloc had suspended due to what Brussels said was Orban's erosion of democratic standards. Additionally, it would deprive Russian President Vladimir Putin of his main ally in the EU and send shockwaves through Western right-wing circles.

The light‑heavyweight division entered a new chapter on Saturday night in Miami when Carlos Ulberg secured the vacant UFC title by delivering a decisive left hook to former champion Jiri Prochazka. President Donald Trump watched from the cageside as Ulberg’s strike landed at the 3:45 mark of the opening round, ending the bout with a knockout and awarding him the undisputed belt. Ulberg entered the fight with a professional record of 14‑1 in MMA (10‑1 in the UFC), while Prochazka held a 32‑6‑1 MMA record (6‑3 in the UFC). Early in the first round Ulberg felt a knee give way, yet he persisted, capitalising on Prochazka’s hesitation to land the winning blow. “I blew out my knee, but I never counted myself out,” Ulberg said afterward. “I knew I needed one clean shot, and when I saw Jiri pulling back, I threw my left hand and it landed.” Prochazka, who has gone 1‑3 in UFC title fights since June 2022, reflected on the loss: “I felt sorry for him, and this is one of the biggest lessons in my life. The fight was in my hands, I saw his injury, and I’ll be back.” The championship was vacant after former champion Alex Pereira vacated the belt to pursue an interim heavyweight title at UFC Freedom 250, a bout scheduled for the White House on Donald Trump’s 80th birthday. Trump promoted the event on his Truth Social account and arrived at the Kaseya Center accompanied by UFC president Dana White, Secretary of State Marco Rubio, and U.S. ambassador to India Sergio Gor. A Kid Rock track blared as Trump took his seat beside the officials. In the co‑main event, Azamat Murzakanov knocked out Paulo Costa with a right round‑house at 1:23 of the third round, extending his perfect UFC record to 17‑0‑0. After his victory, Murzakanov shook hands with Trump, who praised the fighter. Murzakanov acknowledged the president during his post‑fight interview with Joe Rogan. The heavyweight showdown between Josh Hokit and Curtis Blaydes turned into a gritty slugfest, with Hokit prevailing by unanimous decision (29‑28 on all three cards). Trump cheered loudly as the fighters exchanged blows. Following Hokit’s win, UFC chief Dana White announced on social media that a bout between Hokit and Derrick Lewis would be added to the UFC Freedom 250 card, noting that President Trump helped bring the matchup together.

The U.S. Central Command (CENTCOM) reported that the destroyers USS Frank E. Peterson and USS Michael Murphy "transited the Strait of Hormuz and operated in the Arabian Gulf" as part of a mission to clear sea mines allegedly laid by Iran’s Islamic Revolutionary Guard Corps (IRGC).Admiral Brad Cooper hailed the operation as a turning point in the U.S.–Israeli campaign against Iran, saying the navy was establishing a "new passage" to restore safe commercial flow. Iran’s Khatam al‑Anbiya Central Headquarters immediately rejected the claim, stating that any vessel movement in the strait remains under the "Armed Forces of the Islamic Republic of Iran" and that the U.S. report is "strongly denied." The strait, a narrow chokepoint through which roughly 20% of the world’s oil and natural gas transits, has been a flashpoint since the February 28 U.S.–Israel attacks that prompted Iran to restrict passage to pre‑approved ships. The closure spiked global fuel prices and disrupted both commercial and military traffic. Analysts, such as Maria Sultan of the South Asian Strategic Stability Institute, argue that any U.S. navigation would require Tehran’s explicit permission, underscoring the strategic leverage Iran holds over the waterway. Simultaneously, senior delegations from the United States and Iran met in Islamabad for historic face‑to‑face talks—the highest‑level engagement since the 1979 Islamic Revolution. The negotiations, sparked by a preliminary ceasefire announced earlier in the week, focus on contentious issues including Iran’s nuclear program, frozen assets, and the future of Israeli operations in Lebanon. Both parties acknowledge that control of the Strait of Hormuz remains a major point of disagreement. Iran has signaled willingness to temporarily reopen the channel for commercial shipping but insists on maintaining leverage, proposing tolls to compensate for war damages. The United States, however, deems continued Iranian control a "non‑starter." U.S. President Donald Trump used his Truth Social platform to assert that Iran is "losing big" and to downplay the strait’s importance to the United States relative to its allies, claiming the mine‑clearing effort benefits nations such as China, Japan, South Korea, France, and Germany. Al Jazeera’s on‑the‑ground correspondents noted that despite a "deficit of trust," negotiators are working late into the night to bridge gaps, though fundamental disagreements over the strait’s governance persist.

The British government announced that it is putting on hold a bill that would return the Chagos Islands to Mauritius, after President Donald Trump signaled a lack of US support for the arrangement.A UK spokesperson told Reuters and AFP that the deal would only move forward with American backing, stating, "We have always said we would only proceed with the deal if it has US support." The statement added that the islands, particularly Diego Garcia, remain a critical military asset for both nations.Last May, London and Port Louis unveiled a plan under which Britain would cede full sovereignty of the 60‑plus islands to Mauritius while retaining a 99‑year lease on Diego Garcia to preserve the US‑run base that anchors American power in the Indian Ocean.Trump dismissed the proposal in January as an "act of great stupidity," arguing that relinquishing the archipelago would undermine the strategic partnership. In response, the UK reiterated that the base’s long‑term security is the primary reason for the agreement and that it continues to engage with both Washington and Mauritius.At an Indian Ocean conference in Mauritius, Foreign Minister Dhananjay Ramful pledged that his government would "spare no effort" to pursue every diplomatic and legal avenue to complete the decolonisation of the Chagos archipelago, calling the issue a matter of justice.After an initial softening of tone following a February conversation with Prime Minister Keir Starmer, Trump later resumed his criticism on Truth Social, labeling the cession a "big mistake" and a "blight on our Great Ally." The dispute has unfolded against a backdrop of strained US‑UK relations over the ongoing US‑Israel conflict in Iran and the UK's leadership of a 30‑nation coalition protecting shipping in the Strait of Hormuz without US participation.Former senior civil servant Simon McDonald told BBC Radio that Trump’s hostility has forced the agreement into a "deep freeze," noting that when the US president is openly opposed, the British government must reassess its position.Britain has administered the Chagos Islands since 1814, even after Mauritius gained independence in the 1960s. The Diego Garcia base has been pivotal in US operations in Vietnam, Iraq and Afghanistan. The displaced Chagossian community continues to seek compensation, and a 2019 International Court of Justice advisory opinion recommended that the archipelago be returned to Mauritius.

The online prediction market platform Polymarket has seen a surge in users betting on global events, including war and politics. With over $500,000 staked on whether Russia will capture Kostyantynivka, Ukraine, and millions more bet on the US-Iran conflict, the platform's influence is growing.Users, often anonymous and operating in groups on messaging apps like Discord, debate and strategize on how to profit from these events. Some critics argue that this gamification of war is immoral and can lead to manipulation of broader markets.Polymarket views itself as a source of truth, providing data on the future by allowing the public to bet on it. The platform has gained attention from major investors, including the Intercontinental Exchange, which has invested up to $2bn.However, concerns arise about the platform's decision-making process, which relies on an anonymous group of people holding a cryptocurrency token called UMA. This has led to disputes over the outcome of events and accusations of corruption.Experts warn that Polymarket's influence could extend beyond the platform, potentially manipulating larger markets and affecting institutions and pension funds.