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The Mathematical ChallengeToday's offering is for fans of the number 4. It's a cute puzzle that offers up its solution in an elegant way.Nose to Tail ProblemThere is a number N beginning with 4 such that moving the 4 to the end of it creates a new number that is a quarter of N.In other words N is of the form 4[…], where […] is a sequence of digits, and N ÷ 4 = […]4What is the lowest possible value of N?Problem-Solving ApproachHINT. Suppose that N has two digits. If you can't find a solution, suppose that N has three digits. Repeat until done.I'll be back at 5pm UK with the solution.PLEASE NO SPOILERS. Instead discuss snouts.Solution and SourcesUPDATE: Solution is here.Source: Moscow Mathematical Olympiad 1983, via @mathematicsproblems and Kevin GatelyPuzzle Column InformationI've been setting a puzzle here on alternate Mondays since 2015. I'm always on the look-out for great puzzles. If you would like to suggest one, email me.

The Lead Hans Niemann, the 22-year-old US grandmaster at the center of a cheating controversy in chess, has achieved a significant victory by winning the $50,000 first prize at the Warsaw Rapid & Blitz in Poland. Niemann's Dominant Performance Niemann, competing as a wildcard, finished with a score of 22.5/36, edging out Fabiano Caruana, the US champion and world No 3, by half a point. He dominated the rapid section, remaining unbeaten, and managed to recover from three consecutive defeats in the blitz section. The Data Analysis Niemann's score: 22.5/36 Caruana's score: 22/36 Wesley So's score: 21/36 Prize money: $50,000 The Impact Analysis This victory marks a significant milestone in Niemann's career, which has been marred by controversy. His game against Magnus Carlsen at the 2022 Sinquefield Cup led to allegations of cheating, a $100m lawsuit, and an out-of-court settlement. A Netflix documentary and a forthcoming book have also highlighted the scandal. The Prediction With this win, Niemann is now a strong candidate for the US Olympiad team and is closing in on a place in the classical world top 10, being only 12 points away in live ratings. His immediate target is to become the US No 1 and potentially a world championship candidate before 2030.

The Unexpected Classical Comeback in MalmöMagnus Carlsen returned to classical chess for the first time since 2025 at the TePe Sigeman tournament in Malmö, Sweden, on May 9, 2026. After a dramatic loss to Jorden van Foreest in round four, Carlsen fought back to a 5/7 tie and secured the overall win via a blitz tiebreak.Carlsen’s Path to the Blitz PlayoffThe tournament unfolded over seven rounds. Carlsen played conservatively against top‑12 opponents before opting for aggressive openings—King’s Indian, Benoni, and Najdorf Sicilian—against lower‑rated players, exploiting the fast classical time control that transitions into rapid‑style play after move 40.Round 4: Lost an 88‑move marathon to Jorden van Foreest.Final round: Tied with Arjun Erigaisi at 5/7.Blitz playoff: Won 2‑1, clinching the tournament.Scoreline and Tournament StatisticsKey results from the final standings:Carlsen: 5 points (tied for first)Arjun Erigaisi: 5 pointsNodirbek Abdusattorov: 4 pointsYagiz Kaan Erdogmus: 4 points (14‑year‑old Turkish talent)Van Foreest: 3.5 pointsCarlsen’s victory came after a decisive blunder by Erdogmus in the final round, allowing Carlsen to force a sudden‑death blitz.Implications for the Upcoming Oslo Chess OlympiadThe win serves as a confidence boost ahead of the Oslo Chess Olympiad starting in two weeks, an event Carlsen has dominated six of the last seven years. His mixed strategy—solid early play followed by sharp counter‑attacks—demonstrates readiness for both classical and rapid formats that will feature in Oslo.What to Expect from Carlsen’s Form Ahead of OsloAnalysts anticipate that Carlsen will continue to leverage his rapid‑chess superiority, especially in the latter phases of classical games where time pressure mounts. If he maintains this blend of caution and aggression, he remains the favorite to retain his world champion title at the upcoming Olympiad.

The End of a Streak England's senior chess team has failed to win a medal in the world senior team championships for the first time in five years. The championships, which took place in Durres, Albania, saw the US and a nominally German team win gold in the over-50 and over-65 categories, respectively. England's Performance In the 50+ category, England finished fourth with 13 match points and 24 game points. Their top scorer was captain John Emms with 5.5/7. In the 65+ category, England finished fourth with 13 match points and 22 game points. The Impact of Team Selection England's failure to win a medal has raised questions about their team selection policy. The team's top player, Michael Adams, had a rare form downturn, and the absence of Nigel Short, who has been a regular in the team, was felt. The Future of English Chess The English Chess Federation should consider reinstating Nigel Short to the team and focus on developing young talent. The return of experienced players like Stuart Conquest and Danny Gormally could also boost the team's performance. Global Chess Scene The world chess scene is heating up with Uzbekistan hosting the Olympiad in September and Magnus Carlsen remaining the world No 1. The upcoming World Cup in August will also feature a $1.5m prize fund.

Javokhir Sindarov sealed the men’s Candidates in Pegeia, Cyprus, with a historic 10 out of 14 points, finishing 1.5 points clear of Anish Giri. The 20‑year‑old Uzbek also posted the highest tally of six wins and eight draws since the current Candidates format began in 2013. In the women’s section, India’s Vaishali Rameshbabu claimed the title by a narrow ½‑point margin over Kazakhstan’s Bibisara Assaubayeva. Sindarov’s play evoked the classic Soviet master Mikhail Botvinnik, with meticulous opening preparation that often anticipated his opponents’ ideas deep into the endgame. When pressure mounted – notably in his second round against world No. 3 and US champion Fabiano Caruana – his defensive technique remained precise and confident. Final standings (14 rounds): Sindarov 10, Giri 8.5, Caruana 7.5, Wei Yi 7, Hikaru Nakamura 6.5, Praggnanandhaa Rameshbabu 6, Matthias Blübaum 6, Andrey Esipenko 4.5. The upcoming world championship match will be a best‑of‑14 showdown, pitting Sindarov against reigning champion Gukesh Dommaraju. Both will be 20 years old when the contest takes place in the second half of 2026, though the venue remains undecided. Gukesh’s recent dip to 15th in the ratings has added intrigue to the encounter. Analysts rate Sindarov as at least a 60 % favourite, while India’s grandmaster cohort – led by former champion Viswanathan Anand – is expected to rally behind Gukesh. Speculation also surrounds Magnus Carlsen, the current world No. 1, who stepped away from the classical crown in 2023. He indicated a willingness to defend only against Alireza Firouzja, but Firouzja’s recent focus on blitz and fashion has left the door open for a possible Carlsen‑Sindarov clash, should the Norwegian be persuaded. Sindarov’s rise is remarkable: he earned the grandmaster title at 12 years 10 months, later fell into a teenage obsession with the video game Counter‑Strike, and refocused on chess after defeating Firouzja at the 2021 World Cup. His resurgence helped Uzbekistan win gold at the 2022 Olympiad. Financial projections suggest a potential $10 million revenue stream for a Carlsen‑vs‑Sindarov title match, a figure that could also bolster Carlsen’s claim as the all‑time No. 1 ahead of Garry Kasparov. Nonetheless, Carlsen’s aversion to the intensive computer‑prep demanded by modern classical play remains a major hurdle. Carlsen may instead target the forthcoming 2027 FIDE World Total Championship Tour, which blends classical, rapid, and blitz formats, offering a more varied competitive landscape. In the Women’s Candidates, Vaishali Rameshbabu staged a stunning turnaround. After a 0‑5 start, she surged to the top after round 11, maintained a one‑point lead despite a round‑12 loss to China’s Zhu Jiner, and clinched the final round with a decisive victory over Kateryna Lagno in a sharp Sicilian Dragon, delivering the winning combination 39 Rd8+! 40 c4! Women’s final scores (14 rounds): Vaishali 8.5, Assaubayeva 8, Aleksandra Goryachkina 7.5, Zhu 7.5, Anna Muzychuk 7, Kateryna Lagno 6.5, Divya Deshmukh 5.5, Tan Zhongyi 5.5. Five‑time women’s world champion Ju Wenjun enters the upcoming title defence as a clear favourite, holding a peak rating above 2600 and currently rated 2559 against Vaishali’s 2470. Elsewhere, English GM Dan Fernandez posted an unbeaten 7/9 at the Menorca Open, achieving a 2601 performance rating and boosting his chances for selection to the England Olympiad squad. Young talents also featured: Argentina’s Faustino Oro and England’s Supratit Banerjee – both 12‑year‑olds – failed to secure their final GM norms, while India’s 10‑year‑old prodigy Aarit Kapil became only the fifth player ever to earn an IM norm before turning 11, later flirting with a historic GM norm. The English Chess Federation will host a 24‑hour chess marathon on Chess.com in memory of coaches GM Jonathan Hawkins and IM Adam Hunt, with proceeds supporting Macmillan Cancer Support. 4020: 1…Bxd4! 2 cxd4 Nf4! 3 Qb3 Qxf1+! 4 Kxf1 Rc1+ 5 Qd1 Rxd1 #