TheGuardian.com News Feeds

  • Did you solve it? Clueless sudoku
    by Alex Bellos on July 26, 2021 at 3:59 pm

    The solutions to today’s puzzlesEarlier today I set you three ‘clueless’ Sudoku and an ‘almost clueless’ Killer Sudoku. For discussion and tips you can read the original column here.For a printable page of all the puzzles click here. Scroll down for the solutions. Continue reading…

  • Can you solve it? Clueless sudoku
    by Alex Bellos on July 26, 2021 at 6:10 am

    Puzzles where less is moreUPDATE: Solutions now available here.Sudoku is an extremely elegant puzzle, and this crucial to its appeal. The rules are simple to understand and the grid – with given numbers usually presented in a symmetric pattern – is striking. Yet perhaps Sudoku is not elegant enough. Perhaps the numbers on the starting grid are an unforgivable blemish, a needless sullying of the page.Or so argue a group of mathematicians, who have come up with a new puzzle genre: ‘clueless Sudoku’, which are Sudoku-style puzzles with a pristine starting grid. These puzzles literally don’t have a (numerical) clue. Continue reading…

  • Did you solve it? Oxford university admissions questions
    by Alex Bellos on July 12, 2021 at 4:00 pm

    The answers to today’s logical conundrumsEarlier today I set the following three puzzles, which have all been set during Oxford university admissions interviews for joint philosophy courses. In each case, there is an initial question, which almost all candidates answer correctly. The follow-up questions are more challenging.1. Stephanie’s surprise.Sheila knows the shape of the tile.Colin knows the colour of the tile.small red boxmedium red boxlarge black boxsmall blue boxlarge blue boxXOXXOOOXX Continue reading…

  • Can you solve it? Oxford university admissions questions
    by Alex Bellos on July 12, 2021 at 6:23 am

    Brainteasers for budding philosophersUPDATE: Solutions can now be read here.Do you have what it takes to study philosophy at Oxford? Today’s three puzzles are ‘epistemic logic puzzles’, that is, puzzles concerned with reasoning about knowledge. But I know you know I know you know that.All three puzzles have been set in recent years during Oxford university admissions interviews for joint philosophy degrees. In each case, there is an initial question. Almost all candidates will answer this correctly, and I hope you will too. I’ve also included a sample of the follow-up questions. Only the best candidates will get everything right. Best of luck!Sheila knows the shape of the tile.Colin knows the colour of the tile.small red boxmedium red boxlarge black boxsmall blue boxlarge blue box Continue reading…

  • Pure folly: Turing family join fight to save ‘blue-skies maths’ from neglect
    by Michael Savage on July 11, 2021 at 8:50 am

    As hard-pressed universities axe abstract study, the codebreaker’s great niece and top mathematicians are fighting backAlmost exactly 80 years ago, British codebreakers made a crucial breakthrough. Using methods developed by the mathematical genius of Alan Turing, they were able to decipher the Enigma code that the Nazis were using on the eastern front in the second world war, gaining another crucial advantage for the allies.Yet even as Turing’s contribution has begun to be accorded its proper importance, there are growing concerns among Britain’s most prominent mathematicians – and Turing’s own family – that a search for the Turings and Newtons of the future is being dented by declining opportunities to study pure mathematics. Continue reading…

  • Did you solve it? Carl Friedrich Gauss, money saving expert
    by Alex Bellos on June 28, 2021 at 4:00 pm

    The answers to today’s puzzlesEarlier today I set you the following two puzzles, inspired by a money-saving trick devised by Carl Friedrich Gauss. (Click to the original for the explanation of the trick, and what it has got to do with Gauss).1. The double bill. Continue reading…

  • Can you solve it? Carl Friedrich Gauss, money saving expert
    by Alex Bellos on June 28, 2021 at 6:04 am

    Take the 2021 envelope challenge!UPDATE: To read the answers click hereFinancially well-informed readers may have recently learned about a money-saving trick that uses a formula supposedly devised by Carl Friedrich Gauss, the 19th century maths colossus. The viral 100 envelope challenge is based on an apocryphal story that Gauss, when a young boy, outwitted his teacher by adding the numbers from 1 to 100 almost instantly.The child genius had realised that if you group the numbers from 1 to 100 in pairs, the sum is equal to (1 + 100) + (2 + 99) + (3 + 98) + … In other words, 101 + 101 + 101 + … Since there are 50 pairs of numbers, the sum is 101 x 50 = 5050. Continue reading…

  • Did you solve it? Ace of spades
    by Alex Bellos on June 14, 2021 at 4:04 pm

    The solutions to today’s headbangersEarlier today I set you the following two puzzles:1. Deck dilemmais the card red?is the card a face card? (Jack, Queen or King)is the card the ace of spades? Continue reading…

  • Ailsa Land obituary
    by Georgina Ferry on June 14, 2021 at 11:32 am

    Researcher into mathematical approaches to real-world problems who seized on the increased possibilities offered by computersYou’re moving house and you want to pack the largest possible number of different sized items into a box, but don’t want the box to end up too heavy to lift. Or you have a series of related jobs to do, and you need to know what order to do them in so that you finish by a certain time. These are optimisation problems, and they were the kind of problem that fascinated Ailsa Land, who has died aged 93.Before computers were widely available, Land devised pencil and paper methods to solve such problems without resorting to the “brute force” approach of trying every possible solution one by one. As soon as she could, she also grasped the opportunity computers offered to automate such methods, structuring data effectively and devising strategies to produce computer code that was as efficient as possible.The branch and bound method organised potential optimal solutions of a problem as a tree of branching possibilities Continue reading…

  • Can you solve it? Ace of spades
    by Alex Bellos on June 14, 2021 at 6:10 am

    Head-scratchers for headbangersUPDATE: To read the solutions click hereIn the immortal words of Lemmy from Motörhead: “I don’t share your greed, the only card I need is the ace of spades.”Whether or not this was in response to the following puzzle is for you to decide.is the card red?is the card a face card? (Jack, Queen or King)is the card the ace of spades? Continue reading…

  • The Guardian view on the god of science: a divine but rational disagreement | Editorial
    by Editorial on June 6, 2021 at 5:25 pm

    A key maths tool during the pandemic came about because of an 18th-century debate about Christianity. The lesson we can draw today is that moral philosophy mattersDo the laws of science and mathematics explain everything, without any need to bring God into it? The pious once believed that wrathful deities could unleash plagues. As reason emerged in the temple of thinking, there was a move to claim God was behind the advance of reason. In this struggle between beliefs, new pathways of thought emerged, to the benefit of humanity.The fruits of this theological and scientific collision have been revealed during Covid. The work of Thomas Bayes, an 18th-century clergyman and mathematician, has become central to understanding the pandemic. Bayes’ theorem shows how to calculate the accuracy of lateral flow tests used to map the spread of coronavirus. The maths is used to work out the conditional probability that a person is not infected, given a positive test. This is just the tip of the Bayesian spear. David Spiegelhalter and Anthony Masters wrote in April that many complex pandemic analyses “have been ‘Bayesian’, including modelling lockdown effects, the ONS infection survey, and Pfizer-BioNTech’s vaccine trial”. Continue reading…

  • Did you solve it? Gods of snooker
    by Alex Bellos on May 31, 2021 at 3:59 pm

    The solution to today’s puzzleEarlier today I set you the following puzzle:Baize theorem Continue reading…

  • Can you solve it? Gods of snooker
    by Alex Bellos on May 31, 2021 at 6:11 am

    Your turn to break offUPDATE: To read the solution click hereMy cultural highlight of recent weeks has been the brilliant BBC documentary Gods of Snooker, about the time in the 1980s when the sport was a national obsession. Today’s puzzle describes a shot to malfunction the Romford Robot (above left) and put the Whirlwind (above right) in a spin.Baize theorem Continue reading…

  • Did you solve it? Are you smart enough to opt out of cookies?
    by Alex Bellos on May 17, 2021 at 4:00 pm

    The solutions to today’s puzzlesEarlier today I set three puzzles from Terms & Conditions Apply, a free online game about website deviousness (that I made with Jonathan Plackett.) The puzzles in the game exaggerate the tricks websites use to extract our data. 1. Naughty negatives Continue reading…

  • Can you solve it? Are you smart enough to opt out of cookies?
    by Alex Bellos on May 17, 2021 at 6:00 am

    Puzzles about internet deviousnessUPDATE: Solutions can be read here.It’s a depressing fact of online life that websites are often shameless in using shady practices, like misdirection and obfuscation, to get us to sign up to, or to agree to, something we do not want.Today’s puzzles exaggerate the cunning tricks websites use to extract our personal data – but only just! Continue reading…

  • To infinity and beyond: the spectacular sensory overload of Ryoji Ikeda’s art
    by Cleo Roberts-Komireddi on May 9, 2021 at 2:00 pm

    Incandescent light, the thud of Tokyo nightclubs, particle physics … it all goes into Ryoji Ikeda’s extraordinary sensory symphonies. He talks about his upcoming show at 180 The StrandRyoji Ikeda has delivered some dazzling rushes on the senses over his 25-year career: a beach in Rio de Janeiro bathed in his unique palette of light; New York’s Times Square given over to his black and white flickering patterns. But for his next show, the Japanese artist and composer is taking things underground. Ikeda’s biggest exhibition in Europe to date concerns the exposed underbelly of 180 The Strand in London, which he has reimagined as staves, notes and bar lines – with himself as the conductor, “orchestrat[ing] everything into a symphony”.Beginning with a single light beam piercing the rafters, the exhibition carries the viewer through an incandescent corridor of white light and into a room filled with a ring of immense, super-directional speakers reverberating at concert pitch. To Ikeda, this is “opera” with light and sound. “There’s the intro, the welcome piece, then the crescendo [and] climax. It’s a long journey.” Continue reading…

  • How good are we at predicting the pandemic? | David Spiegelhalter & Anthony Masters
    by David Spiegelhalter and Anthony Masters on May 9, 2021 at 7:00 am

    Models have been useful, especially as humans are far too optimistic and confidentEpidemiological models have been a source of continual controversy from the start of the pandemic, often blamed for fearmongering and inaccuracy. How well have they done?Perhaps the most famous piece of modelling came from Neil Ferguson’s team at Imperial College London in March 2020, credited with provoking the full national lockdown. Unfortunately, there are repeated claims they estimated 510,000 deaths in Great Britain over two years, but that was a projection under the implausible scenario that nothing was done about the virus. Their model was, if anything, rather optimistic. Even short of a full lockdown, they projected maximum deaths in Great Britain of fewer than 50,000 and the actual total has been far higher. Continue reading…

  • Did you solve it? A tray of Portuguese delights
    by Alex Bellos on May 3, 2021 at 4:00 pm

    The solutions to today’s puzzlesEarlier today I set you four puzzles by Paulo Ferro, a Portuguese puzzle maker.1. Trapezium or trap-not-so-easy-um? Continue reading…

  • Can you solve it? A tray of Portuguese delights
    by Alex Bellos on May 2, 2021 at 11:00 pm

    Custard tarts for the brainUPDATE: The solutions are now up here.Today, four tasty treats from Paulo Ferro, a puzzlesmith from Porto.1. Trapezium or trap-not-so-easy-um? Continue reading…

  • Free will debate rages on, or is it all an illusion? | Letters
    by Letters on May 2, 2021 at 3:29 pm

    Readers reflect on the role of chance, randomness and responsibility in their own livesWhat high-quality letters (29 April) on free will. My A-level psychology students always found this fascinating and usually thought that free will was obvious until they had examined their own lives and realised that “soft determinism”, well-expounded by Robert Dimmick, was the likely answer. However, there is a big role for chance.For example, I probably wouldn’t have been born in 1949 if my father hadn’t dropped a large tin of paint and shattered his foot while painting the cruiser that he was on during the second world war. His ship sailed without him and was sunk by Japanese bombers with massive loss of life. My father didn’t choose to drop the paint pot, but thereafter there were broad deterministic tramlines to his and my life.Philip WoodKidlington, Oxfordshire Continue reading…