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Wisden Cricketers' Almanack has severely criticized England's Test team for their tumultuous Ashes tour, labeling their campaign as 'feckless, reckless and legless'. The criticism comes after England suffered a 4-1 defeat in Australia.The editor of Wisden, Lawrence Booth, expressed his dismay at England's performance, stating it is 'hard to think of a privilege so carelessly squandered, a chance so blithely spurned'. Booth highlighted several factors contributing to the team's downfall, including poor preparation, lurching tactics, and an unprofessional approach off the field.The Ashes tour was marred by incidents such as Harry Brook's altercation with a nightclub bouncer in New Zealand and a mid-series break in Noosa, which drew significant criticism. In contrast, Australian bowler Mitchell Starc was praised for his discipline, choosing to abstain from alcohol during the series, which helped him secure 31 wickets and earn the title of Wisden's leading men's cricketer in the world.The awards section of Wisden showed a strong Indian flavor, with Shubman Gill, Rishabh Pant, Ravindra Jadeja, and Mohammed Siraj recognized for their performances. Haseeb Hameed was the sole Englishman among the five players of the year.

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.

Liverpool FC is gearing up for a crucial Champions League showdown against Paris Saint-Germain, with manager Arne Slot expressing confidence in his team's ability to turn the tide in their favor. The Reds are facing a daunting task, having lost 2-0 in the first leg at Parc des Princes.Slot emphasized that his team must deliver a great performance to overcome the European champions, stating that while the task is complicated, it is not impossible. He drew on his team's past successes, highlighting that in 36 of their 50 home games under his management, Liverpool has scored two or more goals.The Liverpool head coach is instilling belief in his players, citing examples of their ability to perform at a high level, even against strong opponents. He noted that his team has shown resilience in the face of adversity, such as coming back from 4-0 down against Manchester City in the FA Cup.Dominik Szoboszlai, Liverpool's midfielder, echoed Slot's sentiments, urging his teammates to go 'all in' from the first minute to the final whistle to knock out PSG. Szoboszlai expressed his desire to secure a win, stating that anything can happen at Anfield in a one-off game.Meanwhile, PSG's manager, Luis Enrique, warned his players not to underestimate Liverpool, cautioning that there could be pitfalls and that the game can change quickly. He emphasized the importance of taking care of details and not allowing Liverpool to benefit from their home crowd and noise.

World Aquatics, the governing body for swimming, diving, and water polo, has lifted restrictions on Russian and Belarusian athletes, allowing them to compete under their own flag and anthem for the first time since 2022. This decision has been met with outrage in Ukraine and joy in Russia, adding momentum to Russia's bid to participate in the 2028 Los Angeles Olympic Games. Ukrainian athletes have expressed their disappointment and anger over the decision. Vladyslav Heraskevych, a Ukrainian skeleton star, described the move as 'unacceptable and disgraceful', highlighting the ongoing conflict between Russia and Ukraine and its impact on Ukrainian athletes and sports facilities. The decision by World Aquatics follows a similar move by judo last year and comes as the International Olympic Committee (IOC) considers removing restrictions on Russian and Belarusian athletes for international events. The IOC recommended allowing Russians to compete under national flags in December, while the International Paralympic Committee has already permitted Russians to compete under their own flag and anthem. Russia has welcomed the decision, with Dmitry Mazepin, head of the Russian Aquatics Federation, stating that competing as a neutral athlete was 'an insult'. This development has significant implications for international sports and the participation of Russian athletes in future competitions.

Manchester United interim manager Michael Carrick strongly criticized the red card decision given to defender Lisandro Martínez during the team's 2-1 loss to Leeds United at Old Trafford. Martínez was sent off in the 56th minute for pulling the hair of Dominic Calvert-Lewin, a decision Carrick described as 'shocking' and one that may prompt an appeal.The red card could result in a three-match ban for Martínez, potentially sidelining him for United's upcoming fixtures against Chelsea, Brentford, and Liverpool. This comes at a critical time as Harry Maguire is also facing a possible suspension for his second yellow card in as many games.Carrick questioned the severity of the red card, stating, 'The arm [is] in the face of Lisandro and he is off balance and grappling. He goes to touch his shirt and gets a red card for it.' He emphasized that the incident did not constitute aggressive behavior, adding, 'It is not aggressive, there is no jolt, no tug.'The manager also expressed concern over another incident involving Noah Okafor's goal for Leeds, suggesting that Dominic Calvert-Lewin impeded Leny Yoro in the buildup. 'The goal, Leny Yoro gets a forearm smash in the back of the head. I don’t know how that doesn’t get overturned,' Carrick remarked.Leeds United's manager, Daniel Farke, reflected on the historic victory, stating, 'I feel tired, relieved, proud of the boys. The first league win here in over 40 years is amazing.'

Plans to alter the size of HS2 trains, aimed at maximizing capacity, may result in increased costs and fewer seats, potentially leading to slower services north of Birmingham. A senior government and rail industry figure, Chris Gibb, has warned against changing the train order.The original £2bn order for 54 high-speed trains, to be built by a joint venture of Alstom and Hitachi, was placed in 2021. However, the project has been under review since the cancellation of the northern leg of HS2 by Rishi Sunak in 2023. The initial plan was for the 200-metre, eight-carriage units to double into 16-carriage trains, similar in size to a Eurostar. But this will only be feasible on the new line between London and Birmingham, as existing stations like Manchester Piccadilly cannot accommodate a 400-metre train.Gibb, a non-executive director of DfT Operator, expressed concerns that if HS2 opens with eight-coach trains, they would be full, leaving people behind. He suggested that instead of varying the train order, which could incur extra costs and delays, the government should retain the original order and plan to replace the current Pendolino fleet with longer, faster, modern versions around 2040.This approach, Gibb argued, would provide a significant increase in capacity, revenue, and a reduction in journey times on all routes without the need for further railway construction. Lord McLoughlin, former transport secretary, and Lord Berkeley, a long-term HS2 sceptic, have backed Gibb's idea, emphasizing the importance of consistent rolling stock for future use.A spokesperson for HS2 Ltd stated that no changes have been made to the original order, and they are still working closely with the manufacturer and the DfT to finalize train designs. The trains will be built in Derby and Newton Aycliffe.

Goldman Sachs's chief executive, David Solomon, has expressed heightened awareness of the capabilities of Anthropic's Mythos AI model and is collaborating closely with the tech firm following warnings about the cybersecurity risk it poses.The US bank has been closely monitoring the rapid advancements in artificial intelligence, including large language models (LLMs), as part of broader efforts to protect itself from hackers.“Obviously the LLMs are making rapid progress and we’re hyper-aware of the enhanced capabilities of these new models with the help of the US government and the model publishers,” Solomon told analysts on an earnings call on Monday.Anthropic, the company behind the Claude family of AI tools, claimed last week that its latest model, Mythos, posed an unprecedented risk due to its ability to expose flaws in IT systems. The company warned that AI models have reached a level of coding capability where they can surpass all but the most skilled humans at finding and exploiting software vulnerabilities.Solomon emphasized that Goldman Sachs is working closely with Anthropic and all of its security vendors to harness frontier capabilities. “We are very focused on supplementing our cyber and infrastructure resilience. And this is part of our ongoing capabilities that we have been investing in, and are accelerating our investment in.”The news comes after the US Treasury secretary, Scott Bessent, summoned Solomon and other big American bankers to Washington to discuss the Mythos model last week. The meeting focused on heads of so-called systemically important banks, where regulators believe that a major disruption to their operations, or their potential collapse, would put financial stability at risk.On Monday, the UK government’s AI Security Institute (AISI) warned that Mythos was a “step up” over previous models in terms of the cyber threat it posed. AISI said Mythos could carry out attacks that required multiple actions and discover weaknesses in IT systems without human intervention.

Dr. James Noyes, a prominent advocate for gambling reform, has urged the UK government to pause the implementation of affordability checks for online gamblers. Noyes, who initially proposed the idea of affordability checks in 2020, expressed concerns that the current pilot scheme has raised serious questions that need to be addressed before proceeding.Noyes' call for a pause echoes similar concerns raised by senior figures in the horse racing industry, which fears that the checks could disproportionately affect racing bettors and cost the industry tens of millions of pounds in revenue.The Gambling Commission launched a pilot study on financial risk assessments in September 2024 to assess a two-tier system of checks. However, Noyes and others have raised concerns over the lack of transparency and inconsistent data in the pilot scheme.Noyes emphasized that while affordability checks were initially proposed as a worthy idea, their implementation must be carefully considered to avoid impeding the majority of gamblers from engaging in a lawful activity. He also highlighted the need for a gambling ombudsman to ensure proper treatment of consumer redress and rights.A spokesperson for the Gambling Commission stated that the regulator is working on financial risk assessments with a focus on removing friction for consumers. The Commission has yet to publish a final report on the pilot and has not issued an update on its progress since the spring of 2025.

Rory McIlroy has revealed that weeks of preparation at 'home course' Augusta National played a crucial role in his successful Masters defence. The Northern Irish golfer spent considerable time at Augusta in the lead-up to the Masters, rather than participating in PGA Tour events, despite struggling with a back injury.McIlroy's preparation involved simulating a tournament by playing with a single ball, a strategy inspired by advice from golf legend Jack Nicklaus. This approach allowed him to feel comfortable with the course and make informed decisions about his shots.After securing his sixth major win, McIlroy expressed his satisfaction with his preparation, stating, “I joked last week that this place feels like my home course”. He emphasized the importance of getting to know the course and being prepared for various situations.McIlroy's victory joins an exclusive group of golfers who have retained the Green Jacket, including Jack Nicklaus, Nick Faldo, and Tiger Woods. With this win, McIlroy believes he can focus on playing his game and increasing his chances of winning more majors.The article also mentions Scottie Scheffler's comments on the course conditions, particularly on Friday afternoon when McIlroy birdied six out of Augusta's closing seven holes. Scheffler suggested that the firmness of the course was not equal on Thursday and Friday, but acknowledged that the weather and wind conditions also played a role.