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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.

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.

The Olivier Awards, a prestigious event in the theatre world, recently took place, and among the many memorable moments were the quotes shared by the winners. Host Nick Mohammed kicked off the ceremony with a lighthearted remark about the opening gondola scene from Phantom of the Opera, joking that it wasn't Cunard's boat, but rather Andrew Lloyd Webber's mode of transportation.Cole Escola, playwright of Oh, Mary!, expressed gratitude to a rather unconventional recipient: "my amazing husband, who doesn’t exist". This humorous comment set the tone for a night filled with both laughter and heartfelt acknowledgments.Elaine Paige, a special award winner, shared the secret to her long-lasting career, attributing her success to her father's motto: "perseverance furthers". This insight into her personal life added a touching element to the evening.Rachel Zegler, winner of the best actress in a musical for her role in Evita, recalled her experience performing in the Palladium balcony, calling it "the honour of a lifetime". Her sentiment encapsulated the pride and gratitude felt by many of the winners.Rosamund Pike, best actress winner, reflected on the challenges of balancing life and art, acknowledging the support of her family and partner. Her words resonated with the audience, highlighting the importance of a strong support system.The ceremony also saw Jack Holden win the surprise best actor award, who, upon hearing his name, jokingly asked, "It was definitely me, was it?". This lighthearted moment brought humor to the event.Throughout the evening, winners shared their appreciation for their loved ones and mentors. James Hameed thanked his dad, who had come to London to chase his dreams, showcasing the impact of family on one's journey to success.

Euphoria's third season has been a long-awaited return, but unfortunately, it's absolutely not worth the wait. The show's creator, Sam Levinson, has taken a darker and more desperate approach, focusing on the characters' bleak lives and struggles with sex work, drugs, and trauma.The season picks up five years after the end of season two, with recovering addict Rue (Zendaya) drawn into the world of drug dealer Laurie (Martha Kelly). Her life as a mule between Mexico and the US is depicted in gritty and intense cinematic sequences, drawing on westerns and blaxploitation.Meanwhile, Cassie (Sydney Sweeney) is on the cusp of trad wifedom with toxic jock Nate (Jacob Elordi), but their relationship is marred by Nate's crumbling business and Cassie's OnlyFans content. The show's handling of her cam girl ambitions feels bafflingly dated and voyeuristic.The performances are mostly good, with standout performances from Zendaya, Sweeney, and Adewale Akinnuoye-Agbaje. However, the show's grim and humorless tone makes it feel like a chore to watch.Levinson's approach to exploring the devastating impact of synthetic opioids on ordinary Americans feels heavy-handed and desperate. The show's focus on brainrot bimbo-ism and male perversion also detracts from its once unapologetically queer heart.Overall, Euphoria season three is a disappointing and grubby addition to the series, feeling like a contractual obligation rather than a passion project.

Ghanaian winger Dominic Frimpong was tragically killed at the age of 20 in an armed robbery attack on his team's bus. The incident occurred on Sunday as Berekum Chelsea was returning from a Ghana Premier League match against Samartex.The club reported that six masked men, armed with guns and assault rifles, blocked the road. As the bus attempted to reverse away from danger, the robbers opened fire. Staff and players fled the vehicle, but Frimpong was struck in the head. He was taken to hospital but succumbed to his wounds, becoming the only reported casualty. The bus was carrying 30 players and officials.The Ghana Football Association (GFA) expressed profound shock and deep sorrow over Frimpong's passing. In a statement, the GFA described him as a promising young talent whose dedication and passion embodied the spirit of the league. This season, Frimpong had scored two goals in 13 appearances.This incident is not isolated; several teams in Ghana, including FC Savannah, Wa All Stars, Legon Cities, and AshantiGold, have reported similar attacks in recent years. Local police have deployed additional personnel and crime scene experts, vowing to arrest the perpetrators within the shortest possible time.

Chala Chala Nav Bala (Maze Baal, 1943) marks the debut of Asha Bhosle, who entered the film world at ten years old. Paired with her sister Lata Mangeshkar, her bright falsetto captures the youthful innocence of the Marathi romance, foreshadowing the emotive style that would define her career. Aaiye Meherbaan (Howrah Bridge, 1958) showcases Bhosle’s rise during Hindi cinema’s golden age, thanks to her partnership with composer O.P. Nayyar. The song’s sultry vibrato and lush orchestration set the tone for the film’s noir atmosphere, establishing her as a leading‑lady playback voice. Aao Huzoor Tumko (Kismat, 1968) became a chart‑topping hit, featuring intricate vocal runs over a flamenco‑style guitar. Bhosle’s lower‑register chorus broke the conventional shrillness of female playback, while her nuanced phrasing added depth to the on‑screen heroine’s drunken allure. Dum Maro Dum (Hare Rama, Hare Krishna, 1971) stands out as her most successful crossover, later sampled by Western rappers. The track, produced with R.D. Burman—her future husband—blends psychedelic Beatles‑inspired grooves with Hindi lyrics, demonstrating her ability to bridge Eastern and Western pop sensibilities. Piya Tu Ab To Aaja (Caravan, 1971) pushes the fusion further into jazz‑cabaret territory, with bold horn sections and cinematic guitar reverb. Bhosle’s breathy, suggestive delivery sparked controversy, yet the performance remains a masterclass in balancing sensuality with technical agility. Chura Liya Hai Tumne Jo Dil Ko (Yaadon Ki Baaraat, 1973) epitomises the “masala” film soundtrack, merging drama, romance, and crime. Over a gentle guitar backdrop, Bhosle’s tender humming conveys quiet longing, contrasting with the film’s high‑octane narrative. In Ankhon Ki Masti (Umrao Jaan, 1981) sees Bhoske venture into Urdu ghazals with composer Khayyam. Her lower, huskier timbre—adjusted a half‑step down—highlights her continued artistic experimentation even as she approached fifty. Bow Down Mister (1991) illustrates her early 1990s foray into international collaborations, lending wordless, soaring vocals to Boy George’s post‑Culture Club project. The track transforms into a rave‑infused anthem, underscoring Bhosle’s versatility across genres. Radha Kaise Na Jale (Lagaan, 2001) pairs Bhosle with a young A.R. Rahman, reaffirming her status as an elder stateswoman of Indian music. The duet with Udit Narayan blends tabla and flute with powerful vocal runs, marrying traditional Hindustani scales to contemporary film scoring. The Way You Dream (2002) features an unexpected partnership with REM frontman Michael Stipe on the 1 Giant Leap project. The eight‑minute piece weaves tabla rhythms, subtle guitar, and a dramatic breakbeat, proving that Bhosle’s voice can seamlessly inhabit New Age and electronic soundscapes.

Sam Neill, the veteran actor celebrated for his memorable performances on screen, is set to answer readers' questions in an upcoming interview with The Guardian. Neill's iconic roles include his portrayal in Jurassic Park, where he famously removes his sunglasses and gazes at a towering Brachiosaurus, a scene that has become etched in cinematic history.Born in Northern Ireland and raised in New Zealand, Neill's diverse filmography showcases his versatility as an actor. He has appeared in a range of films, from period dramas like My Brilliant Career to thrillers such as Dead Calm, which is set to be released in 4K later this year. His recent projects include Godzilla x Kong: Supernova, alongside Kaitlyn Dever and Matthew Modine.Neill's career has been marked by his ability to take on idiosyncratic, director-led projects, often playing characters with a unique blend of gruffness and warmth. His performances in Sweet Country and Rams have been particularly noted for their depth and nuance.In addition to his film work, Neill has also made headlines for his memoir, Did I Ever Tell You This?, in which he openly discusses his experience with stage-three blood cancer and his journey towards remission. When asked about his mortality, Neill expressed a pragmatic view, stating, “I’m not afraid to die, but it would annoy me”.Readers are invited to post their questions for Sam Neill by 6pm BST, Thursday 16 April, and The Guardian will publish his answers in their reader interview series. This provides a unique opportunity for fans to engage with one of cinema's most beloved actors and gain insight into his life and career.

Recent CDC data reveal a dramatic 1,200% increase in kratom‑related poisonings across the United States over the last ten years, with the most pronounced surge recorded in 2025. Researchers link this rise to the growing presence of 7‑hydroxymitragynine (7‑OH), a synthetically produced compound that mimics kratom’s effects but carries opioid‑like risks. Walter Prozialeck, pharmacology professor at Midwestern University, said the trend was expected, noting that the synthetic alkaloid has entered the market through energy drinks and other products since 2024. Christopher McCurdy of the University of Florida warned that marketing 7‑OH as “enhanced kratom” blurs the line for consumers, turning poison‑control calls into a conflated metric for both natural and synthetic products. By contrast, natural kratom (Mitragyna speciosa)—a Southeast Asian plant used for centuries as a pain reliever—has demonstrated a relatively favorable safety profile in animal and human studies. A 2018 statement from then‑HHS Secretary Brett Giroir rejected the DEA’s push to schedule kratom as a Schedule I substance, citing insufficient evidence of harm. Despite the scientific distinction, several states have moved to implement or propose blanket bans on all kratom products, prompting concern from clinicians and patient advocates. A recent user survey indicated that about 50% of respondents rely on kratom for chronic pain, while roughly 40% use it during addiction recovery. Personal testimonies underscore the plant’s therapeutic role. Jeff Maslan, a 68‑year‑old Californian with severe osteoarthritis, credits kratom with easing opioid withdrawal after multiple surgeries. Similarly, “Steven,” a disabled California resident, describes how kratom eliminated unbearable oxycodone withdrawal symptoms without producing the euphoric “warm fuzzy” feeling typical of opioids. Researchers emphasize that 7‑OH carries genuine opioid hazards, including addiction, severe withdrawal, and respiratory depression that can lead to fatal overdose. In animal models, 7‑OH demonstrated the same respiratory‑depression risk as classic opioids, whereas kratom’s primary alkaloid did not. Prozialeck and colleagues explain that kratom’s pharmacology is more nuanced: it partially activates opioid receptors while also engaging adrenergic and serotonin pathways, resembling a hybrid of a weak opioid and an SNRI‑type antidepressant. This multimodal action likely accounts for its lower euphoric potential and the reported boost in energy among users. Nevertheless, experts caution that kratom is not without risk. Fatal poisonings often involve co‑ingestion of potent opioids such as fentanyl, suggesting that some users may cycle between kratom and stronger substances, raising overdose danger due to reduced opioid tolerance. Additionally, heavy‑metal contamination has been detected in certain kratom batches, though the source—soil, processing, or storage—remains unclear. Given these complexities, the consensus among scholars like Austin Zamarripa (Johns Hopkins) is that natural kratom should remain accessible, while concentrated 7‑OH products merit stricter regulation. “These products may offer meaningful benefits to some individuals, and those benefits could be lost if access is restricted too broadly,” Zamarripa said, urging a differentiated policy approach. As the debate unfolds, patients like Steven worry that a sweeping ban would ignore the nuanced safety profile of the plant. “There’s corn on the cob, there’s high‑fructose corn syrup, there’s whiskey— all derived from corn but fundamentally different,” he remarked, highlighting the need for targeted, evidence‑based regulation rather than a one‑size‑fits‑all prohibition.

Scientists at London's Institute of Cancer Research and the RCSI University of Medicine and Health Sciences in Dublin have announced a new AI-driven approach to identify how patients with advanced bowel cancer will respond to bevacizumab, a drug recently introduced by the NHS. The method uses PhenMap, an AI tool that integrates complex data on the genetic makeup of tumors, allowing researchers to track patterns of how different patients react to the drug. This development aims to spare potentially thousands of patients from being given drugs that would be ineffective in fighting their cancers. In the UK alone, nearly 10,000 cases of advanced bowel cancer are identified every year, with young adults seeing a particular rise in diagnoses. Bowel cancer has the second-highest mortality rate of any cancer, behind only lung cancer. While survival rates can be as high as 98% when caught early, the five-year survival rate for advanced bowel cancer can be as low as 10%. The study tracked 117 European bowel cancer patients who had been treated with chemotherapy and bevacizumab. Researchers identified a group of patients who all had the same gene mutation and were at a high risk of having negative reactions. The scientists behind the tests now hope to expand the number of patient samples and see if the results can be used in treatments for other types of cancer. Anguraj Sadanandam, a professor in stratification and precision medicine at the ICR, said: “Once bowel cancer spreads to other parts of the body, there are very few treatment options available for patients. It is therefore positive that patients can now access the targeted drug bevacizumab on the NHS. However, we know that the majority of patients won’t benefit from the drug, meaning thousands of people in England could be facing unpleasant side effects unnecessarily.” Sadanandam added that while the findings were encouraging, the tool would need to be tested on a larger cohort to be validated. “In future, I hope this approach will lead to a test that can be used by clinicians, to ensure patients receive personalised care that has the highest chance of working against their cancer.”