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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.

The 2018 World Cup in Russia served as a high‑profile platform for Vladimir Putin, showcasing his nation and bolstering his personal legitimacy. The tournament was effectively a diplomatic bow to the Kremlin’s ambitions.Fast‑forward to the summer of 2026, and the buildup to the event has taken on a distinctly American flavour, with the competition becoming a backdrop for Donald Trump’s political narrative.The next edition, slated for 2034 in Saudi Arabia, presents a fresh set of challenges. Despite the kingdom’s controversial human‑rights record, the event offers Crown Prince Mohammed bin Salman an opportunity to polish his and the nation’s image. FIFA’s current reluctance to enforce independent oversight of migrant‑worker conditions raises fears that construction could be as deadly as the 2022 Qatar experience.These developments underscore a pressing need to insulate the World Cup from the whims of powerful leaders. One proposed solution is to fragment the tournament—treating it like a monopoly that has become too dominant.Evidence that this approach is feasible already exists: the 2026 World Cup will be co‑hosted by three nations, and the 2030 edition is set to span six countries across three continents (Spain, Portugal, Morocco, Argentina, Paraguay, Uruguay).Building on that, the author suggests a radical redesign: allocate each group stage to a different global city—Paris, Rio de Janeiro, Tokyo, Sydney, Johannesburg, London, the Basque Country, and so on. Knock‑out rounds could be broken into three‑match clusters and scattered worldwide, with the semi‑finals, final, and third‑place match awarded to the highest‑bidding venue.Carbon‑footprint concerns are addressed by noting that teams already travel long distances to a single host nation; distributing groups based on the median distance to participating teams would not significantly increase emissions.Financially, the cost of staging a traditional, single‑host World Cup has ballooned, limiting the pool of viable bidders to those seeking political or economic leverage. A decentralized format would dilute any single leader’s ability—whether Trump, Putin, or the Saudi crown prince—to manipulate the event for personal gain.Decentralisation would still align with FIFA’s stated objectives: expanding the sport’s reach, creating a truly global spectacle, and bringing football closer to fans worldwide.While FIFA claims a fiduciary duty to maximise revenue for its 211 member associations—justifying steep ticket prices and controversial sponsorships—the proposed model could actually enhance revenue by turning each small cluster of matches into premium, high‑value events.Precedent exists in the form of Euro 2020, which, despite being postponed by the pandemic, successfully unfolded across 11 European cities, delivering record‑breaking goal tallies and strong attendance figures.In sum, the most effective way to protect the World Cup’s cultural significance and prevent its exploitation by authoritarian figures may be to deconstruct and disperse it globally, turning a single‑host behemoth into a series of interconnected, locally hosted celebrations of the sport.

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.

Australian sprint prodigy Gout Gout stunned the athletics community on Sunday at the national championships in Sydney, clocking a legal 19.67 seconds over 200 m. The performance not only smashed his own previous national record of 20.02 seconds but also made him the first Australian to dip below the coveted 20‑second barrier. Gout’s coach and mentor, Di Sheppard, summed up the achievement with a wry grin: “How long’s a piece of string?” – a nod to the seemingly limitless potential the teenager now displays. The run placed Gout ahead of his compatriot Aidan Murphy, who finished a close second, and sparked immediate comparisons with Jamaican legend Usain Bolt. While Bolt’s all‑time best stands at 19.19 seconds (set in 2009), Gout’s 19.67 at the age of 18 already eclipses the Jamaican great’s performance at the same age, according to his camp. Only one other under‑20 athlete has ever posted a faster time – Erriyon Knighton – whose 2022 effort remains unratified after a subsequent ban. James Templeton, the 18‑year‑old’s manager, said the result was “thrilling but not shocking”, recalling that Gout ran 19.84 seconds the previous year with a marginal wind assistance, a time the team always considered his realistic benchmark. Gout himself has been fixated on breaking the sub‑20 mark ever since an illegal run earlier in his career. “I wrote down 19.75 and kept telling myself I’d hit it,” he explained. “Then I hit 19.67 – gotta love it.” Despite the historic run, the teenager shows no intention of slowing down. “I’ve just turned 18, so I definitely think I can go faster,” he said. “It’s about building consistency and there’s no pressure – I’m the only one out there.” Looking ahead, Gout will compete in the under‑20 junior championships this week, opting to skip the 200 m in Queensland and focus on the 100 m. He will then travel overseas for a high‑profile showdown with Olympic champion Noah Lyles over 150 m at the Golden Spike meet in Ostrava, scheduled for June. Should Gout continue his upward trajectory, the athletics world may soon witness a new challenger to Bolt’s long‑standing age‑group record, reshaping expectations for the next generation of sprint talent.

The US has announced plans to blockade the Strait of Hormuz, a vital waterway through which about 20% of global oil passes. This move comes after ceasefire talks with Iran ended without an agreement over the weekend. The blockade, threatened by President Donald Trump, aims to pressure Iran into reopening the strait, which has been effectively closed since February 28. Trump's announcement on social media stated that the US Navy will begin the process of blockading any and all ships trying to enter or leave the Strait of Hormuz. He accused Iran of 'WORLD EXTORTION' and threatened that any person who attacked US vessels would be 'BLOWN TO HELL!' However, the blockade's scope appears to have been scaled down, with US Central Command (Centcom) stating it would be confined to vessels transiting through Iranian ports, permitting passage of ships headed to ports belonging to America's Gulf allies. The blockade is set to come into effect at 10am ET (2pm GMT). The UK will not be involved in any blockade of the strait, and Australian Prime Minister Anthony Albanese has stated that his country was not asked to participate. Oil prices have surged following Trump's announcement, with US crude increasing 8% to $104.24 a barrel and Brent crude oil rising 7% to $102.29. Experts warn that the blockade could lead to higher oil prices, but much depends on its 'scope and implementation.' The managing director of research at ClearView Energy Partners, Kevin Book, noted that leaner volumes generally mean tighter markets and higher prices. Iranian and/or Houthi reprisals against Gulf producers' alternative routes could drive prices still higher. The blockade could cut off one of the Iranian regime's major sources of funding but might also have a short-term negative effect on global prices. About 100 tankers have transited the strait since the US and Israel started bombing Iran, most carrying Iranian oil products bound for China and India. Iran's Revolutionary Guards have stated that any warships approaching the strait to enforce a blockade would be considered in breach of the current ceasefire and would be dealt with strongly. Trump floated the possibility of a resumption of US strikes inside Iran, citing missile factories as one possible target.

The United States is set to implement a blockade on ships traversing the Strait of Hormuz, a vital passage for global oil exports. This move was announced by former US President Donald Trump. The Strait of Hormuz is a critical waterway, with a significant portion of the world's oil supply passing through it.The blockade could have substantial implications for global oil markets and international trade, potentially leading to increased tensions in the region. The Strait of Hormuz is a key route for oil shipments from the Middle East to the rest of the world.

President Donald Trump declared that the U.S. Navy will commence a blockade of the Strait of Hormuz immediately after peace talks between Washington and Tehran in Pakistan ended without an agreement. In a social‑media post, Trump labeled Iran’s actions as “extortion” and warned that American warships would hunt down and interdict any ship that has paid Iran a toll to traverse the waterway, while also beginning mine‑clearing operations. Iran’s Revolutionary Guard responded that civilian vessels may still cross the strait under “specific regulations,” but any military craft attempting entry would be deemed a breach of the cease‑fire and would be “dealt with severely.” Since the February 28 war launched by the United States and Israel, Iran has effectively taken control of the strategic chokepoint, a route that carries about 20% of the world’s oil and liquefied natural gas shipments. Traffic has now dwindled to a trickle, sending shockwaves through the global economy and raising alarm among Gulf Cooperation Council (GCC) states. Al Jazeera correspondents noted that the rhetoric from the White House has amplified “alarm bells” across the GCC, where leaders had hoped the two‑week ceasefire would evolve into a longer‑term peace framework. Oman’s foreign minister, Badr Albusaidi, urged on social media that the ceasefire be extended and that all parties make “painful concessions” to avoid a return to war. Trump’s statements also included a stark threat: any Iranian forces that fire on U.S. or “peaceful” vessels would be “blown to hell.” He claimed the blockade would involve “other countries” and that the United Kingdom, along with “a couple of other nations,” were dispatching minesweeper vessels to assist – a claim the British government has not confirmed. Domestic criticism emerged quickly. Democratic Senator Mark Warner told CNN he “doesn’t see how blockading the strait will compel Iran to open it,” questioning the strategic logic behind the move. Iran denied U.S. allegations that two of its warships had recently passed through the strait for mine‑clearing, warning that any military vessel attempting such a passage would meet a “strong response.” Tehran officials have floated the idea of instituting a post‑conflict toll system for vessels using the waterway, a prospect that could further entrench Iran’s leverage over global energy flows. Analysts warn that heightened tensions in the Hormuz corridor could push oil prices higher, amplifying inflationary pressures worldwide. As the situation unfolds, mediators continue to press both sides to resume diplomatic talks and avoid a broader escalation.

Tehran – Iranian officials warned that the United States must increase pressure for any peace agreement while urging their supporters to keep the streets under control.Parliament speaker Mohammad Bagher Ghalibaf said the US delegation in Islamabad “failed to gain the trust of the Iranian delegation” during the marathon talks.US President Donald Trump announced an immediate naval blockade of the Strait of Hormuz and declared that US forces are “locked and loaded” to finish Iran at the “appropriate moment.”Iran hailed the delegation’s refusal to accept Washington’s core demands – ending nuclear enrichment and relinquishing control of the Strait – as a sign of defiant resolve.Judiciary chief Gholam‑Hossein Mohseni‑Ejei thanked the Islamabad team for “guarding the rights” of government supporters, including paramilitary forces that have been gathering in Tehran’s main squares for more than six weeks.State television aired an IRGC aerospace officer urging flag‑waving crowds not to worry, stating, “If the enemy does not understand, we will make them understand,” which was met with cheers demanding more missile and drone attacks.Iranian officials blamed Trump’s “excessive demands” for the talks’ failure, noting the Ministry of Foreign Affairs did not expect an agreement after a single day of negotiations.Hard‑line parliamentarians expressed satisfaction with the stalemate, viewing Iran as holding the upper hand. Deputy speaker Hamidreza Haji‑Babaei said only a UN Security Council resolution signalling US surrender would lift sanctions on Iran.Lawmaker Amir Hossein Sabeti of the Paydari faction thanked the negotiating team for standing by red lines and called for “resistance in the field against these evildoers.”The sudden announcement of a two‑week cease‑fire left pro‑state voices disappointed; local media reported the Iranian delegation numbered over 85 members, including state‑affiliated journalists and factional analysts.The talks confirmed that a diplomatic breakthrough was not imminent and hinted at further escalation, though not necessarily a return to full‑scale fighting.National security commission head Ebrahim Azizi dismissed Trump’s blockade threats as “excessive talk.”The IRGC warned it would meet any vessel passing the Strait of Hormuz with “full force” and rejected US claims that two warships had already transited the waterway.Russian President Vladimir Putin told Iranian President Masoud Pezeshkian he remains ready to facilitate a Middle‑East peace settlement.Pezeshkian, focused on domestic affairs, reaffirmed support for Supreme Leader Ayatollah Ali Khamenei and announced that schools and universities will continue online via a limited intranet.Iran’s economy continues to suffer from chronic inflation, rising unemployment and a near‑total internet shutdown, deepening public hardship.

The recent ceasefire talks between the United States and Iran have ended without a breakthrough, with Iran's chief negotiator, Mohammad Bagher Ghalibaf, blaming the US for the failure of the talks held in Islamabad, Pakistan. The talks, which were the first direct engagement between the two countries at this level since the 1979 Iranian Revolution, exposed deep divisions on core issues.The US framed the lack of a breakthrough primarily around Iran's alleged refusal to meet its core demand: a firm commitment not to develop nuclear weapons. US Vice President JD Vance said Washington had made its 'red lines' clear and presented what he described as a 'final and best offer'. However, Iran downplayed expectations and blamed the US for making unreasonable demands.The main sticking points between Tehran and Washington are:Iran's nuclear programme: The US wants a clear and enforceable commitment that Iran will not develop nuclear weapons – or even the capability to do so quickly. Iran has consistently rejected accusations that it seeks to build nuclear weapons but said it is willing to negotiate limits on its nuclear activities if sanctions are removed.Strait of Hormuz: Who gets to control this strategic waterway, through which almost all of the oil and natural gas exports from the Gulf nations pass, has become a major flashpoint. Iran has floated the idea of charging transit fees to allow ships to pass through the strait, while the US is adamant the strait is reopened free of any tolls.The near shutdown of shipping through the strait has sent global energy prices soaring with many countries, especially in Asia, forced to implement unprecedented austerity measures to soften the impact of fuel shortages. Experts said the near-closure of the strait has caused the worst economic shock since the 1973 oil embargo.