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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.

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.

World champion boxer Terence Crawford was found guilty of careless driving on Monday and ordered to pay a $75 fine stemming from a traffic stop last year that led to a gunpoint incident. The incident occurred on September 28, hours after Crawford's hometown of Omaha held a parade to celebrate his unanimous-decision victory over Canelo Álvarez in a super middleweight championship fight.Crawford was stopped by police after officers observed his vehicle driving recklessly. During the stop, Crawford's head of security informed an officer that he was carrying a legal firearm, and seconds later, another officer spotted a gun on the floorboard. With guns drawn, officers ordered everyone out of the vehicle. Crawford claimed he had leaned over to tell the officer that he also had a legal firearm, but the officer didn't hear him. Police confirmed that all occupants of the vehicle were legally permitted to carry firearms.The traffic stop led to an internal investigation by the Omaha police chief into the officers' actions, which was found to have been lawful. In addition to the $75 fine, Crawford was ordered to pay $49 in court costs. This incident comes after Crawford announced his retirement in December with a 42-0 record and 31 knockouts, making him the first male boxer to capture three unified division titles.

Meta, the company behind Facebook and Instagram, is reportedly working on an AI version of its CEO, Mark Zuckerberg. This AI clone is being trained on Zuckerberg's mannerisms, tone, and public statements to allow employees to interact with a digital version of their boss.The rationale behind this project is to make Meta's 79,000 employees feel more connected to one of the most influential figures in Silicon Valley. The AI character will be developed using images and the voice of Zuckerberg, with the CEO reportedly taking part in the training process.This move is part of Meta's broader effort to integrate AI into its business operations. The company aims to use AI to lower costs and accelerate work pace. Zuckerberg has emphasized the importance of efficiency, stating that the goal is to 'get more done' by elevating individual contributors and flattening teams.The development of this AI character follows Meta's previous experiments with digital avatars. In 2022, Zuckerberg shared his own avatar in the metaverse, which received public criticism for its graphic quality. The company has since scaled back its metaverse vision, focusing on AI-generated 3D characters for everyday conversations.Meta's investment in AI is part of a larger strategy to remain competitive with tech rivals. The company is pouring billions of dollars into AI research to create 'superintelligence,' a system capable of performing any cognitive task far better than a human.

Rory McIlroy, the world's No 2 golfer, secured his second Masters win at Augusta National, a triumph he largely attributes to the support of his parents, Rosie and Gerry McIlroy. In a heartwarming display of family devotion, McIlroy had to convince his parents to attend the tournament, as they feared their presence might jinx his title defense. The McIlroy family has a remarkable story of sacrifice and dedication. Rory's parents worked multiple jobs, including graveyard shifts, to support their son's golfing ambitions. Gerry, 66, managed a bar and worked as a cleaner, while Rosie, 65, worked late nights at a factory. Their unwavering support and refusal to pressure Rory into playing golf have been instrumental in his success. During his final round, McIlroy admitted to thinking about his parents and fighting back tears. After securing his win, he turned to his family, including his wife Erica and daughter Poppy, and expressed his gratitude to his parents. 'Mum and Dad, I owe everything to you. You’re the most wonderful parents,' he said, visibly emotional. This victory cements McIlroy's stature as one of golfing's greats, with his sixth major win. His parents' presence at the tournament made the moment even more special, with Rosie sporting a handbag adorned with newspaper reports from his 2025 win. As McIlroy looks to the future, he hopes to emulate his parents' example, stating, 'If I can be half the parent to Poppy as you were to me then I’ll know I’ve done a good job.'

Justin Rose secured a joint‑third place at the 2026 Masters, ending the tournament two shots behind defending champion Rory McIlroy. The result marked Rose’s third top‑six finish in his last eight major appearances. After a heartbreaking playoff loss to McIlroy at Augusta in 2025, Rose entered Sunday’s final round with the lead on the back‑nine but ultimately carded a final‑round 70 following a stumble at the famed Amen Corner. Reflecting on his performance, Rose said, "In the last two years I’ve really re‑kicked and re‑energised my career. I now have a lot of belief that there’s plenty of runway ahead." The 45‑year‑old, who claimed a PGA Tour victory in February, believes his recent form positions him to compete for future major titles. Rose emphasized that the majors are the events that drive his preparation: "These are the tournaments I focus on, the ones that make me put in that extra mile to show up and stay in these great arenas." His record at Augusta is notable, with eight top‑10 finishes and two runner‑up finishes, underscoring his affinity for the course. Rose cited veterans such as Freddie Couples and Bernhard Langer as inspirations, noting that the layout of Augusta rewards deep course knowledge and a personal playing style. Englishman Tyrrell Hatton also made headlines, posting a spectacular final‑round 66 that included six birdies and an eagle, propelling him to a joint‑third finish – his best performance in a major to date. Hatton explained his approach: "I try not to treat majors any differently – I go out every day, every round, every shot, and give it my best. I’m looking at ways to fine‑tune my preparation, perhaps more putting early in the week, to feel even more ready." Now in his tenth Masters, Hatton highlighted his steady improvement, citing recent top‑10 finishes at the U.S. Open and a rise from a tied‑fourteenth to a tied‑ninth in the last three years at Augusta.

Experts are closely monitoring climate patterns in the Pacific Ocean, which indicate a high chance of El Niño developing this summer. A strong El Niño event could lead to severe weather conditions, including super-charged rainstorms and droughts, depending on the region. A 'super El Niño' could push 2027 to break global heat records, according to climate scientists. This phenomenon occurs when ocean surface temperatures in the central and eastern tropical Pacific Ocean warm up, leading to significant impacts on global weather patterns. El Niño is characterized by warming of the ocean surface in the central and eastern tropical Pacific Ocean. It's one of three states scientists observe: La Niña, conversely, happens when sea surface temperatures are below average, and neutral conditions are defined when neither El Niño or La Niña are present and surface temperatures are about average. The 'El Niño-southern oscillation' (Enso) tends to develop during spring in the northern hemisphere and shifts every three to seven years. Warming and cooling at sea surface during El Niño and La Niña can range from 1C to 3C, and have enormous effects on precipitation, drought, heat, and climate disasters in different regions. Conditions are currently shifting from La Niña to a neutral pattern, according to the latest outlook from the US Climate Prediction Center. Models show a 62% chance El Niño will emerge this summer and linger until at least the end of the year. A super El Niño that occurred in 2015 brought severe drought in Ethiopia, water supply shortages in Puerto Rico, and smashed records after unleashing a vicious hurricane season in the central North Pacific. A 'super' El Niño means one that is stronger, typically defined by sea surface temperatures spiking up to at least 2C. Noaa scientists have given a 1 in 4 chance that this could happen by fall or winter, with the caveat that spring forecasts are sometimes muddled. Transitions in conditions that happen in the spring can make outcomes a bit harder to predict. Experts warn that a strong or super El Niño could lead to drought and heat across Australia, southern and central Africa, India, and parts of South America. Heavy precipitation, meanwhile, could hit the southern tier of the US, parts of the Middle East, and south-central Asia.

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.”

Oil prices jumped back above $100 a barrel and global stocks fell after weekend talks between the US and Iran ended without an agreement and Donald Trump imposed a blockade of the Strait of Hormuz. The US president announced the blockade on Sunday, targeting Iranian vessels and ships that have paid a toll to Iran for passage through the strait, in an attempt to choke off the flow of Iranian oil.US Central Command said it would start at 10am ET (5.30pm in Iran and 3pm in the UK), blocking all Iranian Gulf ports and coastal areas, in effect seizing control of maritime traffic in the Strait of Hormuz. The news drove oil and gas prices sharply higher again, after the two-week ceasefire between the US and Iran announced on Wednesday prompted a sharp fall in energy prices, and crude ended the week below the psychological $100 a barrel threshold.Brent crude rose by nearly 7% to $101.74 a barrel on Monday morning, while US crude is up more than 8% to $104.69 a barrel. Gas prices also increased, with the British wholesale gas contract for May soaring by 11.7% to 122.5p a therm. Analysts at JPMorgan Chase said last week they expected oil prices to stay high in the second quarter, above $100 a barrel, before easing in the second half of the year.Most Asian stock markets fell on Monday, with Japan’s Nikkei down 0.7% and Hong Kong’s Hang Seng index losing 1%, while Chinese stocks rose slightly. Sentiment was helped by Beijing’s announcement of a 10-initiative strategy aimed at deepening ties with Taiwan. European stocks also fell, led by airlines including Lufthansa, Wizz Air, easyJet and British Airways parent IAG. The FTSE 100 index in London lost 0.4%, dropping 45 points to 10,555. Germany’s Dax fell 1%, Italy’s FTSE MiB slipped 0.7% and Spain’s Ibex was down 1.1%. With oil and gas prices rising sharply higher, energy companies such as BP and Shell are rallying.Priyanka Sachdeva, senior market analyst at the broker Phillip Nova, said: “In today’s environment, every barrel of risk added to oil markets carries an inflation price tag for the global economy.” She added: “The market reaction underscores a simple but powerful reality: Hormuz risk is not theoretical; it is structural, and it is real.”Interest rate expectations have shifted again; investors now see an 84% chance of two rate increases from the Bank of England this year to tackle rising inflation, up from 60% on Friday. Before the Iran war, the central bank was expected to cut rates. The price of gold fell 0.4% to $4,730.75 an ounce as the blockade fuelled inflation concerns, prompting traders to scale back expectations for Federal Reserve rate cuts this year.