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People who are bad with numbers often find it harder to make ends meet – even if they are not poor

<div class="theconversation-article-body"><em><a href="https://theconversation.com/profiles/wandi-bruine-de-bruin-275600">Wändi Bruine de Bruin</a>, <a href="https://theconversation.com/institutions/usc-dornsife-college-of-letters-arts-and-sciences-2669">USC Dornsife College of Letters, Arts and Sciences</a> and <a href="https://theconversation.com/profiles/paul-slovic-359838">Paul Slovic</a>, <a href="https://theconversation.com/institutions/university-of-oregon-811">University of Oregon</a></em></p> <h2>The big idea</h2> <p>People who are bad with numbers are more likely to experience financial difficulties than people who are good with numbers. That’s according to <a href="https://doi.org/10.1371/journal.pone.0260378">our analyses</a> of the <a href="https://wrp.lrfoundation.org.uk/explore-the-poll">Lloyd’s Register Foundation World Risk Poll</a>.</p> <p>In this World Risk Poll, people from 141 countries were asked if 10% was bigger than, smaller than or the same as 1 out of 10. Participants were said to be bad with numbers if they did not provide the correct answer – which is that 10% is the same as 1 out of 10. <a href="https://doi.org/10.1371/journal.pone.0260378">Our analyses</a> found that people who answered incorrectly are often among the poorest in their country. Prior studies in the <a href="https://doi.org/10.1111/j.1468-0297.2010.02394.x">United States</a>, <a href="https://doi.org/10.1111/j.1475-5890.2007.00052.x">United Kingdom</a>, <a href="https://doi.org/10.1016/j.joep.2016.02.011">the Netherlands</a> and <a href="https://doi.org/10.1111/joca.12294">Peru</a> had also found that people who are bad with numbers are financially worse off. But <a href="https://doi.org/10.1371/journal.pone.0260378">our analyses of the World Risk Poll</a> further showed that people who are bad with numbers find it harder to make ends meet, even if they are not poor.</p> <p>When we say that they found it harder to make ends meet, we mean that they reported on the poll that they found it difficult or very difficult to live on their current income, as opposed to living comfortably or getting by on their current income.</p> <p><a href="https://doi.org/10.1371/journal.pone.0260378">Our analyses</a> also indicate that staying in school longer is related to better number ability. People with a high school degree tend to be better with numbers than people without a high school degree. And college graduates do even better. But even among college graduates there are people who are bad with numbers – and they struggle more financially.</p> <p><iframe id="yOIiX" class="tc-infographic-datawrapper" style="border: 0;" src="https://datawrapper.dwcdn.net/yOIiX/3/" width="100%" height="400px" frameborder="0" scrolling="no"></iframe></p> <p>Of course, being good with numbers is not going to help you stretch your budget if you are very poor. <a href="https://doi.org/10.1371/journal.pone.0260378">We found</a> that the relationship between number ability and struggling to make ends meet holds across the world, except in low-income countries like Ethiopia, Somalia and Rwanda.</p> <p><iframe id="RejA1" class="tc-infographic-datawrapper" style="border: 0;" src="https://datawrapper.dwcdn.net/RejA1/8/" width="100%" height="400px" frameborder="0" scrolling="no"></iframe></p> <h2>Why it matters</h2> <p>The ability to understand and use numbers is also called <a href="http://doi.org/10.1093/oso/9780190861094.001.0001">numeracy</a>. Numeracy is <a href="https://doi.org/10.1787/1f029d8f-en">central to modern adult life</a> because numbers are everywhere.</p> <p>A lot of well-paying jobs involve working with numbers. People who are bad with numbers often perform worse in these jobs, including <a href="https://doi.org/10.1111/ecin.12873">banking</a>. It can therefore be hard for people who are bad with numbers to <a href="http://www.doi.org/10.1108/00400919710164125">find employment and progress in their jobs</a>.</p> <p>People who are bad with numbers are less likely <a href="https://www.pnas.org/content/116/39/19386.short">to make good financial decisions</a>. Individuals who can’t compute how interest compounds over time <a href="https://doi.org/10.1111/j.1540-6261.2009.01518.x">save the least and borrow the most</a>. People with poor numerical skills are also more likely <a href="https://doi.org/10.1037/0022-3514.41.3.586">to take on high-cost debt</a>. If you’re bad with numbers, it is hard to <a href="https://doi.org/10.1017/S1474747215000232">recognize</a> that paying the US$30 minimum payment on a credit card with a $3,000 balance and an annual percentage rate of 12% means it will never be paid off.</p> <h2>What still isn’t known</h2> <p>It is clear that people who are bad with numbers also tend to struggle financially. But we still need to explore whether teaching people math will help them to avoid financial problems.</p> <h2>What’s next</h2> <p>In her book “<a href="http://doi.org/10.1093/oso/9780190861094.001.0001">Innumeracy in the Wild</a>,” Ellen Peters, director of the Center for Science Communication Research at the University of Oregon, suggests that it is important for students to take math classes. American high school students who had to <a href="https://doi.org/10.3368/jhr.51.3.0113-5410R1">take more math courses</a> than were previously required had better financial outcomes later in life, such as avoiding bankruptcy and foreclosures.</p> <p>Successfully teaching numeracy also means helping students gain confidence in using numbers. People with <a href="https://doi.org/10.1073/pnas.1903126116">low numerical confidence</a> experience bad financial outcomes, such as a foreclosure notice, independent of their numeric ability. This is because they may not even try to take on complex financial decisions.</p> <p>Numerical confidence can be boosted in different ways. Among American <a href="https://doi.org/10.1037/0022-3514.41.3.586">elementary school children</a> who were bad with numbers, setting achievable goals led to better numerical confidence and performance. Among American <a href="https://doi.org/10.1371/journal.pone.0180674">undergraduate students</a>, a writing exercise that affirmed their positive values improved their numerical confidence and performance.</p> <p>Other important next steps are to find out whether training in numeracy can also be provided to adults, and whether training in numeracy improves the financial outcomes of people who do not live in high-income countries.<!-- Below is The Conversation's page counter tag. Please DO NOT REMOVE. --><img style="border: none !important; box-shadow: none !important; margin: 0 !important; max-height: 1px !important; max-width: 1px !important; min-height: 1px !important; min-width: 1px !important; opacity: 0 !important; outline: none !important; padding: 0 !important;" src="https://counter.theconversation.com/content/172272/count.gif?distributor=republish-lightbox-basic" alt="The Conversation" width="1" height="1" /><!-- End of code. If you don't see any code above, please get new code from the Advanced tab after you click the republish button. The page counter does not collect any personal data. More info: https://theconversation.com/republishing-guidelines --></p> <p><a href="https://theconversation.com/profiles/wandi-bruine-de-bruin-275600"><em>Wändi Bruine de Bruin</em></a><em>, Professor of Public Policy, Psychology and Behavioral Science, USC Sol Price School of Public Policy, <a href="https://theconversation.com/institutions/usc-dornsife-college-of-letters-arts-and-sciences-2669">USC Dornsife College of Letters, Arts and Sciences</a> and <a href="https://theconversation.com/profiles/paul-slovic-359838">Paul Slovic</a>, Professor of Psychology, <a href="https://theconversation.com/institutions/university-of-oregon-811">University of Oregon</a></em></p> <p><em>Image credits: Shutterstock </em></p> <p><em>This article is republished from <a href="https://theconversation.com">The Conversation</a> under a Creative Commons license. Read the <a href="https://theconversation.com/people-who-are-bad-with-numbers-often-find-it-harder-to-make-ends-meet-even-if-they-are-not-poor-172272">original article</a>.</em></p> </div>

Money & Banking

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‘Girl math’ may not be smart financial advice, but it could help women feel more empowered with money

<div class="theconversation-article-body"><em><a href="https://theconversation.com/profiles/ylva-baeckstrom-1463175">Ylva Baeckstrom</a>, <a href="https://theconversation.com/institutions/kings-college-london-1196">King's College London</a></em></p> <p>If you’ve ever calculated cost per wear to justify the price of an expensive dress, or felt like you’ve made a profit after returning an ill-fitting pair of jeans, you might be an expert in <a href="https://www.standard.co.uk/news/world/girl-maths-tiktok-trend-its-basically-free-b1100504.html">“girl math”</a>. With videos about the topic going viral on social media, girl math might seem like a silly (<a href="https://www.glamourmagazine.co.uk/article/girl-math-womens-spending-taken-seriously">or even sexist</a>) trend, but it actually tells us a lot about the relationship between gender, money and emotions.</p> <p>Girl math introduces a spend classification system: purchases below a certain value, or made in cash, don’t “count”. Psychologically, this makes low-value spending feel safe and emphasises the importance of the long-term value derived from more expensive items. For example, girl math tells us that buying an expensive dress is only “worth it” if you can wear it to multiple events.</p> <p>This approach has similarities to <a href="https://www.investopedia.com/terms/m/modernportfoliotheory.asp">portfolio theory</a> – a method of choosing investments to maximise expected returns and minimise risk. By evaluating how each purchase contributes to the shopping portfolio, girl math shoppers essentially become shopping portfolio managers.</p> <h2>Money and emotions</h2> <p>People of all genders, rich or poor, feel anxious when dealing with their personal finances. Many people in the UK do not understand pensions or saving enough to <a href="https://www.ons.gov.uk/employmentandlabourmarket/peopleinwork/workplacepensions/articles/pensionparticipationatrecordhighbutcontributionsclusteratminimumlevels/2018-05-04">afford their retirement</a>. Without motivation to learn, people avoid dealing with money altogether. One way to find this motivation, as girl math shows, is by having an emotional and tangible connection to our finances.</p> <p>On the surface, it may seem that women are being ridiculed and encouraged to overspend by using girl math. From a different perspective, it hints at something critical: for a person to really care about something as seemingly abstract as personal finance, they need to feel that they can relate to it.</p> <p>Thinking about money in terms of the value of purchases can help create an <a href="https://www.thetimes.co.uk/article/every-time-i-use-my-card-my-phone-buzzes-and-that-stops-me-shopping-ps0fjx6nj">emotional relationship</a> to finance, making it something people want to look after.</p> <figure><iframe src="https://www.youtube.com/embed/GPzA7B6dcxc?wmode=transparent&amp;start=0" width="440" height="260" frameborder="0" allowfullscreen="allowfullscreen"></iframe></figure> <h2>The girl math we need</h2> <p>Women are a consumer force to be reckoned with, controlling <a href="https://www.forbes.com/sites/bridgetbrennan/2015/01/21/top-10-things-everyone-should-know-about-women-consumers/#7679f9d6a8b4">up to 80%</a> of consumer spending globally. The girl math trend is a demonstration of women’s mastery at applying portfolio theory to their shopping, making them investment powerhouses whose potential is overlooked by the financial services industry.</p> <p><a href="https://www.theguardian.com/world/2019/oct/28/women-paid-less-than-men-over-careers-gender-pay-gap-report">Women are disadvantaged</a> when it comes to money and finance. Women in the UK earn on average £260,000 less than men during their careers and the retirement income of men is twice as high as women’s.</p> <p>As I’ve found in <a href="https://www.routledge.com/Gender-and-Finance-Addressing-Inequality-in-the-Financial-Services-Industry/Baeckstrom/p/book/9781032055572">my research</a> on gender and finance, women have lower financial self-efficacy (belief in their own abilities) compared to men. This is not helped by women feeling patronised when seeking financial advice.</p> <p>Because the world of finance was created by men for men, its language and culture are <a href="https://www.routledge.com/Gender-and-Finance-Addressing-Inequality-in-the-Financial-Services-Industry/Baeckstrom/p/book/9781032055572">intrinsically male</a>. Only in the mid-1970s did women in the UK gain the legal right to open a bank account without a male signature and it was not until 1980 that they could apply for credit independently. With the law now more (<a href="https://www.worldbank.org/en/news/press-release/2023/03/02/pace-of-reform-toward-equal-rights-for-women-falls-to-20-year-low">but not fully</a>) gender equal, the financial services industry has failed to connect with women.</p> <p>Studies show that 49% of women are <a href="https://www.ellevest.com/magazine/disrupt-money/ellevest-financial-wellness-survey">anxious about their finances</a>. However they have not bought into patronising offers and <a href="https://www.fa-mag.com/news/gender-roles-block-female-financial-experience--ubs-says-73531.html">mansplaining by financial advisers</a>. This outdated approach suggests that it is women, rather than the malfunctioning financial system, <a href="https://www.theguardian.com/commentisfree/2020/sep/16/women-are-not-financially-illiterate-they-need-more-than-condescending-advice">who need fixing</a>.</p> <p>Women continue to feel that they do not belong to or are able to trust the world of finance. And why would women trust an industry with a <a href="https://www.ons.gov.uk/employmentandlabourmarket/peopleinwork/earningsandworkinghours/bulletins/genderpaygapintheuk/2019">gender pay gap</a> of up to 59% and a severe lack of women in senior positions?</p> <p>Girl math on its own isn’t necessarily good financial advice, but if it helps even a handful of women feel more empowered to manage and understand their finances, it should not be dismissed.</p> <p><!-- End of code. If you don't see any code above, please get new code from the Advanced tab after you click the republish button. The page counter does not collect any personal data. More info: https://theconversation.com/republishing-guidelines --></p> <p><em><a href="https://theconversation.com/profiles/ylva-baeckstrom-1463175">Ylva Baeckstrom</a>, Senior Lecturer in Finance, <a href="https://theconversation.com/institutions/kings-college-london-1196">King's College London</a></em></p> <p><em>Image credits: Getty Images </em></p> <p><em>This article is republished from <a href="https://theconversation.com">The Conversation</a> under a Creative Commons license. Read the <a href="https://theconversation.com/girl-math-may-not-be-smart-financial-advice-but-it-could-help-women-feel-more-empowered-with-money-211780">original article</a>.</em></p> </div>

Money & Banking

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How Aussie maths whiz won the lotto 14 times

<p>Winning the lotto is more than likely a once-in-a-lifetime chance, but Aussie man Stefan Mandel defied the odds when he won the golden ticket 14 times using basic maths.</p> <p>The Romanian-Australian mathematician, joined by a small team of investors, discovered a remarkably easy way to hack the system in the 1980s and 1990s.</p> <p>Mandel’s first two wins were secured in his home country of Romania, where he was saving up to escape the then-Soviet Union before he won another dozen times in Australia.</p> <p>Surprisingly, Mandel’s system was not only straightforward but relied on very little of his mathematical training.</p> <p>The odds of winning the jackpot in the Australian Powerball are about one in 76,767,600, according to lotto land. If you want to double your chances with two tickets, the odds are still a mere 2 in 76,767,600.</p> <p>Mandel observed that in certain lotteries, the jackpot prize was much higher than the cost of purchasing every possible combination of numbers. Given he buys every ticket, he was almost guaranteed a return on his investment – so long as the winnings were split between several golden ticket holders.</p> <p>So, Mandel did just that.</p> <p>While it’s not completely against the rules, snatching up every ticket doesn’t quite resonate with the spirit of the game, and his winnings were astronomical.</p> <p>Mandel, now 89, convinced a group of investors to buy into the scheme over several years.</p> <p>He created algorithms that were able to generate and print the millions of different ticket groups required, which some lotteries allowed people to do at the time.</p> <p>With his pile of tickets printed and ready to go, Mandel and his team waited for a hefty jackpot, where they would purchase those tickets in shops.</p> <p>Mandel secured 12 wins on smaller lotteries Down Under before he sought out jackpots in the US with a sum far larger than anything he had won so far.</p> <p>While he won millions of dollars with his scheme, aiming for massive lotteries in the US proved to be his downfall.</p> <p>Mandel specifically had his sights set on the Virginia lottery, which was new at the time and only used numbers 1-44 in its draws. That meant there were 7,059,052 possible combinations, much less than the 25 million or higher that his team was used to.</p> <p>When the jackpot was high enough, around US$15.5 million, Mandel ordered thousands of investors to buy out the tickets in bulk.</p> <p>To Mandel’s dismay, some investors pulled out. After two days of purchases, the group secured about 6.4 million of the possible 7 million combinations needed to guarantee them the jackpot. Fortunately, the odds remained in his favour as he won the Virginia Lottery too.</p> <p>The FBI and CIA launched an investigation into Mandel, but no wrongdoing was found. Virginia Lottery had no choice but to pay up.</p> <p>Mandel won millions of dollars in the Virginia Lottery, including bringing home most of the smaller prizes.</p> <p>He later disbanded his team and retired to a beach house in Vanuatu, where he still lives.</p> <p>While Mandel’s scheme was legal at the time, it resulted in new rules for the lottery. Many countries, including the US and Australia, have since passed laws that stopped punters from buying lottery tickets in bulk or printing them at home, in turn rendering his methods impossible.</p> <p><em>Image credit: Twitter / Youtube</em></p>

Money & Banking

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Movie myths meet movie maths

<p dir="ltr">Some moments on the screen stay with us forever, but not always for the right reasons. </p> <p dir="ltr">For some avid film and TV fans, there are certain scenes that have left us scratching our heads, inspecting from every angle, and making frame-by-frame comparisons to try and come up with an answer that tells us what we want to hear. </p> <p dir="ltr">After all, we’ve all had our say over that infamous door and those two fated souls in the middle of the ocean, haven’t we?</p> <p dir="ltr">Luckily, those in the know - mathematicians - have put their brains to the task of solving it for us, sharing their findings as they debunk some of the screen world’s more memorable moments. </p> <ol> <li dir="ltr" aria-level="1"> <p dir="ltr" role="presentation">The door, <em>Titanic </em>(1997)</p> </li> </ol> <p dir="ltr">Could Jack have fit on the door too? Could Rose have saved him?</p> <p dir="ltr">Such questions have sat with fans of the blockbuster film <em>Titanic</em> since its release, when the end of the film saw Rose and Jack trying to save themselves with a scrap of the ship’s debris - a door - in the middle of the freezing North Atlantic Sea.  </p> <p dir="ltr">As anyone who’s seen the film could tell you, Jack gave up his spot so that Rose might survive, but many have refused to accept that this was necessary. They believe, instead, that Jack could have fit there with her, ultimately saving them both from further tragedy. </p> <p dir="ltr">And a group of girls at school in Adelaide believe they know exactly how it could have been done. </p> <p dir="ltr">The solution? Sliding their life jackets beneath the door.</p> <p dir="ltr">“We looked at how buoyant the door would have been, and how that would have changed if there were people on top of that,” 15-year-old Abigail explained to<em> The Daily Telegraph</em>, adding that “there was a lot of exploring and testing, and we had to fiddle with different buoyancies and look at what materials were realistic for that time.”</p> <ol start="2"> <li dir="ltr" aria-level="1"> <p dir="ltr" role="presentation">The jump, <em>Speed </em>(1994)</p> </li> </ol> <p dir="ltr">From start to finish, <em>Speed </em>is a wild ride. And while many questions about the logistics of the high-speed action bus ride have arisen since the film’s release, one tops the list more often than not - could Jack really have made that jump? </p> <p dir="ltr">At one point in the film, Jack and his runaway bus - which he must keep travelling at a speed of just over 80km/h to prevent the entire thing from exploding - are faced with an incomplete road, and he is forced to make the jump over the gap to give himself and his passengers any hope of survival. </p> <p dir="ltr">While the film’s characters succeed, and make it out of there alright, the people at ZME Science were not quite so eager to leave it at that. </p> <p dir="ltr">Instead, they have studied the scene, and put the likelihood of survival in such a situation to the test. With a few handy equations and crucial bits of info - the gap was 15m, their speed 108km/h - they came to the conclusion that the bus more than likely would have fallen into the gap, rather than landing safely on the other side. </p> <p dir="ltr">This, of course, means that the detonation would have occurred, and the outcome would have been drastically different to what transpired on the screen. </p> <ol start="3"> <li dir="ltr" aria-level="1"> <p dir="ltr" role="presentation">The bullet, <em>The Matrix </em>(1999)</p> </li> </ol> <p dir="ltr">While <em>The Matrix</em> is held in high regard by many cinema enthusiasts, from its concept alone to its iconic fight scenes, there are those who’ve come out of the films with a few more questions than what its creators ever intended. </p> <p dir="ltr">Namely, questions over how exactly Neo managed to dodge that bullet. </p> <p dir="ltr">While attempting to save Morhepus from Agent Smith, Neo goes head-to-head against agents in a rooftop fight. A shot is made at Neo, and he deftly dodges the potentially fatal wound by bending all the way back, with the bullet clearing the air above him, leaving him unscathed. </p> <p dir="ltr">It’s a scene that wowed audiences worldwide with its slow motion approach, and its attention to detail, but for one mathematician, it was exactly this that drew her curiosity. Could Neo actually have pulled that off? </p> <p dir="ltr">According to Kerry Cue, the answer is no. </p> <p dir="ltr">After working out the distance between Neo and the agent (roughly 12m), the logistics of the weapon, and the speed at which it was moving, Kerry worked her way to her conclusion. </p> <p dir="ltr">The bullet itself would take 0.04 seconds to get to Neo. And as a human’s average reaction time is 0.25 seconds, it’s impossible that Neo would have been able to make that impressive save in the real world.</p> <ol start="4"> <li dir="ltr" aria-level="1"> <p dir="ltr" role="presentation">The sofa,<em> Friends </em>(1994-2004)</p> </li> </ol> <p dir="ltr">Would pivoting really have helped Ross, Rachel, and Chandler get that unfortunate sofa up the stairwell of their New York apartment building? </p> <p dir="ltr">In the heat of the moment, Ross certainly seemed to think so, but as fans of the sitcom know, their efforts were in vain. Unable to complete their mission, the friends opted to cut it up instead. </p> <p dir="ltr">Some weren’t satisfied with this ‘easy’ way out, and one mathematician put her brain to the test trying to prove that it would have been a possible feat to accomplish.</p> <p dir="ltr">And it was - if only the trio had bothered to take measurements. </p> <p dir="ltr">Caroline Zunckel - a data science consultant - ran approximately 10,000 different simulations using various measurements for both the stairs and the couch, all to prove her point. Luckily for her, she discovered that she was right, and that the furniture only required some tilting upwards to get around that problem corner. </p> <p dir="ltr"><em>Images: Shutterstock</em></p>

Movies

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“Love doesn’t know math”: Cher defends 40-year age gap

<p dir="ltr">Cher has defended the massive 40-year age gap between her and her new and much younger beau. </p> <p dir="ltr">The 76-year-old singer is currently in a relationship with 36-year-old music producer Alexander Edwards.</p> <p dir="ltr">Despite the 40-year age gap, Cher is not shying away from the “blossoming romance” and answered fans’ questions about the relationship along with a cheeky photo of Alex in his boxers.</p> <p dir="ltr">“He’s 36 and in end he came after me. I’m the skittish one. We love each other …. LADIES NEVER GIVE UP. Must say he was different for me,” she wrote. </p> <blockquote class="twitter-tweet"> <p dir="ltr" lang="en">A.E.Hanging Ot <a href="https://t.co/TB5XXJqlxk">pic.twitter.com/TB5XXJqlxk</a></p> <p>— Cher (@cher) <a href="https://twitter.com/cher/status/1595612020325240832?ref_src=twsrc%5Etfw">November 24, 2022</a></p></blockquote> <blockquote class="twitter-tweet"> <p dir="ltr" lang="en">On paper This Looks<br />strange (Even 2 ME)<br />A.E Says ♥️Doesn’t<br />Know Math</p> <p>— Cher (@cher) <a href="https://twitter.com/cher/status/1595690505576161281?ref_src=twsrc%5Etfw">November 24, 2022</a></p></blockquote> <blockquote class="twitter-tweet"> <p dir="ltr" lang="en">BABE,SOME MARCH 2 A DIFFERENT DRUMMER,I Dance 2 One</p> <p>— Cher (@cher) <a href="https://twitter.com/cher/status/1595695842584731648?ref_src=twsrc%5Etfw">November 24, 2022</a></p></blockquote> <p dir="ltr">“He’s kind, smart, hilarious … and we (kiss emoji) like teenagers,” she responded to a question asking about her favourite quality about Alex.</p> <p dir="ltr">“On paper this looks strange (even to ME) AE says love ️doesn’t know math,” Cher tweeted shortly after.</p> <p dir="ltr">The pair sparked rumours earlier this month when they were seen holding hands outside the West Hollywood restaurant Craig's where they met with rapper Tyga for dinner.</p> <p dir="ltr">During the night, Alex was seen kissing Cher’s hand as they drove off together. </p> <p dir="ltr">It was only days after the dinner that Cher confirmed the relationship on Twitter.</p> <p dir="ltr"><em>Image: Getty</em></p>

Relationships

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Retiree figures out how to win the lotto

<p dir="ltr">A retired couple have beaten possibly all odds when it comes to winning the lottery thanks to “simple math”.</p> <p dir="ltr">Jerry and Marge Selbee from Evart, Michigan, are multimillionaires because of a loophole in the gambling game.</p> <p dir="ltr">After retiring in 2003, Jerry decided to follow the lotto closely and discovered that it's easier than he thought to win, saying, “Anyone could have done it.”</p> <p dir="ltr">The retiree inspected the game called WinFall and found that if no one won the jackpot of US$5 million ($7 million AUD), then the money would go to ticket holders with fewer winning numbers.</p> <p dir="ltr">"I looked at the probabilities of the game and it said that when the WinFall actually occurred and no one won the jackpot, that the prize level would go up by a factor of 10," Jerry said on <a href="https://9now.nine.com.au/60-minutes/jerry-and-marge-go-large-lotto-tips-selbee-how-retired-couple-won-39-million/1e5093b5-be35-400f-a142-8ecdf0c289d0" target="_blank" rel="noopener">60 Minutes</a>.</p> <p dir="ltr">"US$50 for a three-number winner and US$1,000 for a four-number winner and the odds were one in, one in 56 and a half for a three-number winner and one in 1032 for a four-number winner."</p> <p dir="ltr">Jerry went on to explain that part of the problem when it comes to playing the lotto is that people think it is structured.</p> <p dir="ltr">"I did not have to be lucky to win. I had to be unlucky to lose."</p> <p dir="ltr">Almost akin to placing a bet on himself, Jerry decided to test his theory and realised that he was right – and quickly came clean to his wife Marge who was all for it.</p> <p dir="ltr">The couple would buy hundreds of thousands of tickets for the WinFall game – but disaster eventually struck when no more tickets were sold in their hometown.</p> <p dir="ltr">Soon the pair had to drive 15 hours to Massachusetts to keep winning a similar style of lottery with the same "loophole" structure, but it was something they were both keen to do.</p> <p dir="ltr">Eventually, they were caught out by investigators but Jerry and Marge were in fact not doing anything illegal.</p> <p dir="ltr">Their story eventually became well known to the point that a film is being made for streaming service Paramount+ and will feature Breaking Bad’s Bryan Cranston.</p> <p dir="ltr">Despite their lifetime of winnings – in the many tens of millions over the years – Jerry and Marge remain quite humble, spending their money on education for their grandchildren and great-grandchildren.</p> <p dir="ltr"><em>Images: Nine</em></p>

Money & Banking

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The better you are at math, the more money seems to influence your satisfaction

<p>Your grade school math teacher probably told you that being good at math would be very important to your grownup self. But maybe the younger you didn’t believe that at the time. A lot of research, though, has shown that <a rel="noopener" href="https://theconversation.com/people-who-are-bad-with-numbers-often-find-it-harder-to-make-ends-meet-even-if-they-are-not-poor-172272" target="_blank">your teacher was right</a>.</p> <p>We are two researchers who study decision-making and how it relates to wealth and happiness. In a study published in November 2021, we found that, in general, people who are better at math <a rel="noopener" href="https://doi.org/10.1371/journal.pone.0259331" target="_blank">make more money and are more satisfied with their lives</a> than people who aren’t as mathematically talented. But being good at math seems to be a double-edged sword. Although math-proficient people are very satisfied when they have high incomes, they are more dissatisfied, compared to those who aren’t as good at math, when they don’t make a lot of money.</p> <p>Many researchers have suggested that more money only increases <a rel="noopener" href="https://qz.com/1503207/a-nobel-prize-winning-psychologist-defines-happiness-versus-satisfaction/" target="_blank">life satisfaction and happiness</a> up to a certain point. Our research modifies this idea by showing that satisfaction derived from income relates strongly to how good a person is at math.</p> <p><a href="https://images.theconversation.com/files/441600/original/file-20220119-27-1kh4idi.jpg?ixlib=rb-1.1.0&amp;q=45&amp;auto=format&amp;w=1000&amp;fit=clip"><img src="https://images.theconversation.com/files/441600/original/file-20220119-27-1kh4idi.jpg?ixlib=rb-1.1.0&amp;q=45&amp;auto=format&amp;w=754&amp;fit=clip" alt="A person holding a pencil above a sheet of paper." /></a> <em><span class="caption">Nearly 6,000 people responded to a survey that asked about math skills, income and life satisfaction.</span> <span class="attribution"><a rel="noopener" href="https://www.gettyimages.com/detail/photo/student-taking-math-quiz-cropped-royalty-free-image/97612935?adppopup=true" target="_blank" class="source">PhotoAlto/Odilon Dimier via Getty Images</a></span></em></p> <p><strong>A math and happiness test</strong></p> <p>We investigated the relationship between math ability, income and life satisfaction, using surveys sent to 5,748 diverse Americans as part of the <a rel="noopener" href="https://uasdata.usc.edu/index.php" target="_blank">Understanding America Study</a>.</p> <p>The study included two questions and one test relevant to our research. One question asked participants about their household yearly income. Another one asked respondents to rate how satisfied they are with their lives on a scale of zero to 10.</p> <p>Finally, people answered eight math questions that varied in difficulty to get a sense of their math skills. For example, one of the moderately difficult questions was: “Jerry received both the 15th highest and the 15th lowest mark in the class. How many students are in the class?” The correct answer is 29 students.</p> <p>We then combined the results to see how they all related to one another.</p> <p>Math skills and income also are tied to <a rel="noopener" href="https://theconversation.com/money-buys-even-more-happiness-than-it-used-to-141766" target="_blank">level of education,</a> so, in our analyses, we controlled for education, verbal intelligence, personality traits and other demographics.</p> <p><strong>Connecting math skills to income and satisfaction</strong></p> <p>On average, the better a person was at math, the <a rel="noopener" href="https://doi.org/10.1371/journal.pone.0259331" target="_blank">more money they made</a>. For every one additional right answer on the eight-question math test, people reported an average of $4,062 more in annual income.</p> <p>Imagine you have two people with the same level of education, one of whom answered none of the math questions correctly and the other answered all of them correctly. Our research predicts that the person who answered all of the questions correctly will earn about $30,000 more each year.</p> <p>The survey also showed that people who are better at math were, on average, also more satisfied with their lives than those with lower math ability. This finding agrees with <a rel="noopener" href="https://doi.org/10.1257/0002828041464551" target="_blank">a lot of other research</a> and suggests that income influences life satisfaction.</p> <p>But prior research has shown that the relationship between income and satisfaction is not as straightforward as “more money equals greater happiness.” It turns out that how satisfied a person is with their income often depends on how they feel it <a rel="noopener" href="https://doi.org/10.1177/0956797610362671" target="_blank">compares to other people’s incomes</a>.</p> <p>Other research has also shown that people who are better at math tend to make <a rel="noopener" href="https://doi.org/10.1093/oso/9780190861094.001.0001" target="_blank">more numerical comparisons</a> in general than those who are worse at math. This led our team to suspect that math-proficient people would compare incomes more, too. Our results seem to show just that.</p> <p><a href="https://images.theconversation.com/files/439268/original/file-20220104-15-15r038f.png?ixlib=rb-1.1.0&amp;q=45&amp;auto=format&amp;w=1000&amp;fit=clip"><img src="https://images.theconversation.com/files/439268/original/file-20220104-15-15r038f.png?ixlib=rb-1.1.0&amp;q=45&amp;auto=format&amp;w=754&amp;fit=clip" alt="A graph correlating math skills to life satisfaction and income." /></a><em> <span class="caption">This chart shows that people who scored highest on the math test (red line) appear to be happiest when they make a lot of money (top right of graph), but also the least satisfied when they make less money (bottom left of graph). Different color lines correspond to the number of math questions answered correctly.</span> <span class="attribution"><span class="source">Ellen Peters, Pär Bjälkebring</span>, <a rel="noopener" href="http://creativecommons.org/licenses/by-nd/4.0/" target="_blank" class="license">CC BY-ND</a></span></em></p> <p>Simply put, the better a person was at math, the <a rel="noopener" href="https://doi.org/10.1371/journal.pone.0259331" target="_blank">more they cared about how much money they make</a>. People who are better at math had the highest life satisfaction when they had high incomes. But deriving satisfaction from income goes both ways. These people also had the lowest life satisfaction when they had lower incomes. Among people who aren’t as good at math, income didn’t relate to satisfaction nearly as much. Thus, the same income was valued differently depending on a person’s math skills.</p> <p><strong>Money does buy happiness for some</strong></p> <p>An often-quoted fact – backed up by research – says that once a person makes around $95,000 a year, <a rel="noopener" href="https://doi.org/10.1038/s41562-017-0277-0" target="_blank">earning more money doesn’t dramatically increase satisfaction</a>. This concept is called <a rel="noopener" href="https://www.nature.com/articles/s41562-017-0277-0?mod=article_inline" target="_blank">income satiation</a>. Our research challenges that blanket statement.</p> <p>Interestingly, the people who are best at math did not seem to show income satiation. They were more and more satisfied with more income, and there didn’t appear to be an upper limit. This did not hold true for people who weren’t as talented at math. The least math-proficient group gained more satisfaction from income only until about $50,000. After that, earning more money made little difference.</p> <p>For some, money does seem to buy happiness. While more work needs to be done to really understand why, we think it may be because math-oriented people compare numbers – including incomes – to make sense of the world. And maybe that’s not always a great thing. In comparison, those who are worse at math appear to derive life satisfaction from sources other than income. So if you are feeling dissatisfied with your income, maybe seeing beyond the numbers will be a winning strategy for you.<!-- Below is The Conversation's page counter tag. Please DO NOT REMOVE. --><img style="border: none !important; box-shadow: none !important; margin: 0 !important; max-height: 1px !important; max-width: 1px !important; min-height: 1px !important; min-width: 1px !important; opacity: 0 !important; outline: none !important; padding: 0 !important; text-shadow: none !important;" src="https://counter.theconversation.com/content/173720/count.gif?distributor=republish-lightbox-basic" alt="The Conversation" width="1" height="1" /><!-- End of code. If you don't see any code above, please get new code from the Advanced tab after you click the republish button. The page counter does not collect any personal data. More info: https://theconversation.com/republishing-guidelines --></p> <p><em><a rel="noopener" href="https://theconversation.com/profiles/par-bjalkebring-1289840" target="_blank">Pär Bjälkebring</a>, Assistant Professor of Psychology, <a rel="noopener" href="https://theconversation.com/institutions/university-of-gothenburg-1351" target="_blank">University of Gothenburg</a> and <a rel="noopener" href="https://theconversation.com/profiles/ellen-peters-812268" target="_blank">Ellen Peters</a>, Director, Center for Science Communication Research, <a rel="noopener" href="https://theconversation.com/institutions/university-of-oregon-811" target="_blank">University of Oregon</a></em></p> <p><em>This article is republished from <a rel="noopener" href="https://theconversation.com" target="_blank">The Conversation</a> under a Creative Commons license. Read the <a rel="noopener" href="https://theconversation.com/the-better-you-are-at-math-the-more-money-seems-to-influence-your-satisfaction-173720" target="_blank">original article</a>.</em></p> <p><em>Image: Getty Images</em></p>

Money & Banking

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How maths can help you get a good deal at the bank

<div class="copy"> <p>Few people love mathematics.</p> <p>A common refrain among students is, “Why do I have to learn this stuff? When will I need it?” But having a working knowledge of the basic concepts is essential in daily life as an adult.</p> <p>We use them when counting cash, calculating mortgage payments and filling out tax returns.</p> <p>In fact, it was financial matters such as loans, interest payments and gambling that spurred the development of a lot of early mathematics.</p> <p>Negative numbers, for example, were needed to represent debt, and the mathematical rules for their use were worked out in India and the Islamic world by the 7th century.</p> <p>One money problem that was carefully analysed in the 17th century concerned compound interest – a familiar enough concept today.</p> <p>Just like modern banks, the money lenders of the day competed for customers using interest rates as incentives.</p> <p>But when making comparisons the customer always has to be careful of the small print.</p> <p>Interest rates are normally expressed on an annual basis.</p> <p>For example, a simple 5% annual interest means that $100 investment becomes $105 at the end of one year.</p> <p>But if interest is credited, say, every six months, the customer gets a higher overall annual return.</p> <p>To keep the arithmetic simple, imagine a bank that paid 100% annual interest (that would be nice!).</p> <p>If credited annually, that rate of interest would turn $100 into $200 at the end of the year.</p> <p>But if credited every six months, then $50 gets credited to the account after six months, so at the end of the year the original capital has earned $100, but the $50 credited after six months will itself earn $25 interest over the second half of the year.</p> <p>So by offering biannual compound interest, the bank would pay the customer $125 interest at the end of one year rather than $100.</p> <p>A customer who started with $100 would now have $225 in the account.</p> <p>If the interest is paid quarterly, the deal is even better, amounting to a little over $244 at the end of the year.</p> <p>The more often the interest is credited, the higher the final total.</p> <p>But it is a process of diminishing returns: the total goes up by a smaller and smaller amount the more frequently you credit the interest.</p> <p>Crediting every day would yield a bit over $271. That is to say, the original capital will have been boosted 2.71 times.</p> <p>All of which raises the question: what would be the upper limit to this compounding process?</p> <p>Mathematicians were pondering this even back in the 17th century.</p> <p>In 1683, the mathematician Jacob Bernoulli found the answer: 2.7182818… (the ellipsis indicates that this number is an unending decimal).</p> <p>It is an <a href="https://cosmosmagazine.com/mathematics/the-square-root-of-2">irrational number</a> and, like π<span style="font-family: inherit;">, proved to be a fundamental mathematical constant that turns up in fields as diverse as accounting, physics, engineering, statistics and probability theory. </span></p> <p><span style="font-family: inherit;">It is such an important number it is given a letter all its own: e. </span></p> <p><span style="font-family: inherit;">Peruse any textbook on science, engineering or economics, and you will see the symbol e scattered throughout. </span></p> <p><span style="font-family: inherit;">It is most often used in connection with “exponential growth” – a term that has entered the popular lexicon, though it is often misused. </span></p> <p><span style="font-family: inherit;">The correct meaning refers to a specific type of rapid, runaway growth in which a quantity doubles in a fixed time, and then doubles again, and again, ad infinitum. </span></p> <p><span style="font-family: inherit;">The population of bacteria in a dish, for example, will increase exponentially if their growth is unrestrained. </span></p> <p><span style="font-family: inherit;"> One familiar example of exponential growth is Moore’s Law, named after Gordon Moore, co-founder of Intel. </span></p> <p><span style="font-family: inherit;">After noticing in 1965 that the size of transistors was rapidly shrinking, which meant more of them could fit onto a computer chip, he predicted that processing power would double roughly every two years (and the price would drop by half). </span></p> <p><span style="font-family: inherit;">Remarkably, this exponential growth has remained more or less consistent for several decades, though nobody expects it to go on forever. </span></p> <p><span style="font-family: inherit;">And e makes a surprise appearance in less obvious places, too. </span></p> <p><span style="font-family: inherit;">My favourite example is e’s application to the secretary problem. </span></p> <p><span style="font-family: inherit;">Imagine there are 100 applicants </span><span style="font-family: inherit;">to be randomly interviewed </span><span style="font-family: inherit;">for a secretarial job. </span></p> <p><span style="font-family: inherit;">At the end of each interview, the interviewer must give the applicant an irrevocable decision as to whether they’ve got the job. </span></p> <p><span style="font-family: inherit;">It would be risky to see them all, dismissing the first 99, because the 100th interviewee would have to be given the job regardless of quality.</span></p> <p><span style="font-family: inherit;">The conundrum is this: to maximise the probability of getting the best candidate, how many should be interviewed before selecting the first remaining candidate who trumps the ones already seen? </span></p> <p><span style="font-family: inherit;">It turns out the answer is 100/e, or about 37. This result is worth remembering by people who like to play the dating game methodically. </span></p> <p><span style="font-family: inherit;">So mathematical knowledge isn’t just useful at tax time. </span></p> <p><span style="font-family: inherit;">Perhaps if more people knew maths could help them find love, more would be willing to embrace it.</span></p> <p><em><span style="font-family: inherit;">Image credit: Shutterstock</span><span style="font-family: inherit;"></span></em></p> <p><em><span style="font-family: inherit;">This article was originally published on <a rel="noopener" href="https://cosmosmagazine.com/science/mathematics/explore-the-potential-of-exponential-growth/" target="_blank">cosmosmagazine.com</a> by Paul Davies. </span></em></p> </div>

Money & Banking

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Prince William reveals the worst gift he's given Kate Middleton

<div class="post_body_wrapper"> <div class="post_body"> <div class="body_text "> <p>Prince William has revealed the worst gift he's ever given Kate Middleton in a new podcast.</p> <p>He appeared on <em>BBC Radio Five Live's That Peter Crouch Podcast</em>, and explained just how bad the gift was.</p> <p>"That was early on in the courtship that was. I wrapped them. They were really nice," William said, according to <a rel="noopener" href="https://people.com/royals/prince-william-shares-curry-snacks-and-beers-to-talk-soccer-and-mental-health-see-the-picture/" target="_blank" class="_e75a791d-denali-editor-page-rtflink"><em>People</em></a>. </p> <p>"I was trying to convince myself about it. I was like, ‘But these are really amazing, look how far you can see!’ </p> <p>"She was looking at me going, ‘They’re binoculars, what’s going on?’ It didn’t go well. Honestly, I have no idea why I bought her a pair of binoculars."</p> <p>Luckily, the pair seemed to work things out as they got married and have three beautiful children.</p> <blockquote style="background: #FFF; border: 0; border-radius: 3px; box-shadow: 0 0 1px 0 rgba(0,0,0,0.5),0 1px 10px 0 rgba(0,0,0,0.15); margin: 1px; max-width: 540px; min-width: 326px; padding: 0; width: calc(100% - 2px);" class="instagram-media" data-instgrm-permalink="https://www.instagram.com/p/CBrAw7GFOv6/?utm_source=ig_embed&amp;utm_campaign=loading" data-instgrm-version="12"> <div style="padding: 16px;"> <div style="display: flex; flex-direction: row; align-items: center;"> <div style="background-color: #f4f4f4; border-radius: 50%; flex-grow: 0; height: 40px; margin-right: 14px; width: 40px;"></div> <div style="display: flex; flex-direction: column; flex-grow: 1; justify-content: center;"> <div style="background-color: #f4f4f4; border-radius: 4px; flex-grow: 0; height: 14px; margin-bottom: 6px; width: 100px;"></div> <div style="background-color: #f4f4f4; border-radius: 4px; flex-grow: 0; height: 14px; width: 60px;"></div> </div> </div> <div style="padding: 19% 0;"></div> <div style="display: block; height: 50px; margin: 0 auto 12px; width: 50px;"></div> <div style="padding-top: 8px;"> <div style="color: #3897f0; font-family: Arial,sans-serif; font-size: 14px; font-style: normal; font-weight: 550; line-height: 18px;">View this post on Instagram</div> </div> <p style="color: #c9c8cd; font-family: Arial,sans-serif; font-size: 14px; line-height: 17px; margin-bottom: 0; margin-top: 8px; overflow: hidden; padding: 8px 0 7px; text-align: center; text-overflow: ellipsis; white-space: nowrap;"><a style="color: #c9c8cd; font-family: Arial,sans-serif; font-size: 14px; font-style: normal; font-weight: normal; line-height: 17px; text-decoration: none;" rel="noopener" href="https://www.instagram.com/p/CBrAw7GFOv6/?utm_source=ig_embed&amp;utm_campaign=loading" target="_blank">A post shared by Duke and Duchess of Cambridge (@kensingtonroyal)</a> on Jun 20, 2020 at 2:30pm PDT</p> </div> </blockquote> <p>Despite being members of the royal family, the Duke and Duchess of Cambridge have had to adjust to the challenges of homeschooling during the coronavirus pandemic.</p> <p>Prince William admitted that it hasn't been easy.</p> <p>"My patience is a lot shorter than I thought it was... and my wife has a lot of patience."</p> <p>He joked about his lack of math knowledge as he tried to help out his children with their homework.</p> <p>"I was a bit embarrassed about my maths knowledge—I can’t do Year 2 Maths!"</p> </div> </div> </div>

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How to cut queues at immigration – with maths

<p>When going on holiday to a foreign country, there’s one part of the journey that everybody dreads: border control. Everyone has to have their passport checked by an immigration official when entering a new country – and even when leaving some – so queues are almost inevitable.</p> <p>At Heathrow airport – <a href="https://www.internationalairportreview.com/article/32311/top-20-largest-airports-world-passenger-number/">one of the largest in the world</a> – many arriving passengers are <a href="http://www.dailymail.co.uk/travel/travel_news/article-6030399/BA-boss-criticises-two-hour-queues-Heathrow-Airport-border-farce.html">experiencing waiting times</a> of up to two hours at passport control. Border control officials seek to manage these queues through staff rosters – and when there aren’t enough staff rostered on to meet the number of arriving passengers, then queues at passport control can become excessively long.</p> <p>Staff rostering presents what’s known in industry as an “optimisation problem”. It is used in hospitals for nurses, in call centres and even in schools, <a href="http://www.optimisationintherealworld.co.uk/2018/04/13/challenges-in-producing-a-staff-roster/">for playground supervision</a>. The main goals are typically to ensure that services are completed in a reasonable amount of time, and to reduce the cost of staff.</p> <p>But these two goals are often contradictory – since paying more staff usually leads to better service. And because of this contradiction, staff rostering can be a very difficult optimisation problem to solve.</p> <p><strong>Meeting requirements</strong></p> <p>To balance these two aspects of staff rostering, organisations or regulatory bodies typically impose “service requirements”, in the form of expected service times. At Heathrow airport, the <a href="https://www.heathrow.com/company/company-news-and-information/performance/airport-operations/border-force">service requirements</a> state that 95% of passengers should be processed at passport control within 25 minutes for EEA citizens and 45 minutes for everyone else.</p> <p>Unfortunately, the border force at Heathrow has been unable to meet the services requirements for non-EEA immigrants since February 2018. July saw the worst performance, with 24.5% of all passengers entering the UK through terminals three and four experiencing waiting times of more than 45 minutes at passport control. In <a href="https://www.express.co.uk/travel/articles/977533/british-airways-heathrow-airport-passport-control-queues-UK">June</a>, <a href="https://www.express.co.uk/news/uk/991733/summer-holiday-travel-delay-Heathrow-airport-luton-airport-manchester-airport">July</a> and <a href="http://www.dailymail.co.uk/travel/travel_news/article-6030399/BA-boss-criticises-two-hour-queues-Heathrow-Airport-border-farce.html">August</a>, there have been reports of passengers waiting longer than two hours.</p> <p>Having lots of valid data is critical to making a good roster and reducing waiting times. The main components of staff rostering are modelling demand, scheduling days off and assigning staff to shifts or tasks. If the demand is known exactly in advance – for example, if the number of playground supervision tasks are the same every day throughout the school year – then staff rostering only needs to consider the last two components.</p> <p>In more dynamic environments, such as airport arrivals, demand modelling plays a crucial role in staff rostering. In an airport, the demand for passport control is directly related to the arrival times of aircraft, which can in turn be delayed. For example, in May 2015 only <a href="https://www.caa.co.uk/Data-and-analysis/UK-aviation-market/Flight-reliability/Datasets/Punctuality-data/Punctuality-statistics-2018/">75.93%</a> of flights arriving into Heathrow airport were on time. <a href="https://www.caa.co.uk/Data-and-analysis/UK-aviation-market/Flight-reliability/Datasets/Punctuality-data/Punctuality-statistics-2018/">Of the remaining flights</a>, 17% were delayed by less than an hour, and about 7% were delayed by longer. Since <a href="https://www.heathrow.com/company/company-news-and-information/company-information/facts-and-figures">94% of passengers</a> are international travellers, border control is massively affected by flight delays.</p> <p><strong>Digging into the data</strong></p> <p>One of the worst options, in regard to meeting service requirements, is to roster staff according to the scheduled arrival time of all flights. Although this would be relatively cheap, it ignores the fact that air travel is routinely subject to delays.</p> <p>A better way for border force to reduce delays at passport control is to roster staff so that the largest expected demand can be served within the set service requirements. Basically, this would mean opening as many booths at passport control as possible, at the busiest time for arrivals – taking into account any expected delays.</p> <p>But this is a very impractical and expensive solution, and there are limitations with respect to the number of available staff – especially since <a href="https://publications.parliament.uk/pa/cm201719/cmselect/cmhaff/421/42105.htm">border force is already struggling</a> with insufficient numbers of staff. Fortunately, there is lots and lots of data relating to air travel, which can be used to model demand more accurately, and roster staff and employ other available technologies accordingly.</p> <p>Historical records of flight arrivals, the number of EEA and non-EEA citizens arriving and the demand at passport control are all available. Through the use of statistical and data science techniques, such as <a href="https://en.wikipedia.org/wiki/Forecasting">forecasting</a>, a sophisticated model of demand at passport control can be developed.</p> <p>Performing staff rostering with such a demand model may be conservative, meaning a higher overall cost, but it will be more likely to fit with the reality of air transportation. Yet proper demand modelling can also highlight situations – periods of time when predominately EEA citizens are arriving – where automatic passport scanners could provide flexibility in rostering staff, and which could decrease costs.</p> <p>Given the excessive delays reported at Heathrow border control, we can only assume that there is significant limitations to the demand model currently being used for staff rostering. By making better use of statistical techniques and drawing on the large amount of data that is available, it’s possible to significantly reduce the waiting time for passport control – even when flights are delayed.<!-- Below is The Conversation's page counter tag. Please DO NOT REMOVE. --><img style="border: none !important; box-shadow: none !important; margin: 0 !important; max-height: 1px !important; max-width: 1px !important; min-height: 1px !important; min-width: 1px !important; opacity: 0 !important; outline: none !important; padding: 0 !important; text-shadow: none !important;" src="https://counter.theconversation.com/content/100988/count.gif?distributor=republish-lightbox-basic" alt="The Conversation" width="1" height="1" /><!-- End of code. If you don't see any code above, please get new code from the Advanced tab after you click the republish button. The page counter does not collect any personal data. More info: http://theconversation.com/republishing-guidelines --></p> <p><em>Written by <span>Stephen J Maher, EPSRC Research Fellow, Lancaster University</span>. Republished with permission of </em><a rel="noopener" href="https://theconversation.com/how-to-cut-queues-at-immigration-with-maths-100988" target="_blank"><em>The Conversation</em></a><em>. </em></p>

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Maths hack goes viral and blows people’s minds: "You've changed my life"

<p>A UK copywriter has shared an arithmetic trick that makes calculating a lot easier.</p> <p>Ben Stephens took to Twitter to share his “fascinating little life hack” for doing percentage calculations.</p> <p>He showed that by flipping numbers and multiplying them as per usual will result in the sum you are looking for.</p> <p>“So, for example, if you needed to work out 4 per cent of 75 in your head, just flip it and and do 75 per cent of 4, which is easier,” Stephens wrote.</p> <blockquote class="twitter-tweet" data-lang="en-gb"> <p dir="ltr">Fascinating little life hack, for doing percentages:<br /><br />x% of y = y% of x<br /><br />So, for example, if you needed to work out 4% of 75 in your head, just flip it and and do 75% of 4, which is easier.</p> — Ben Stephens (@stephens_ben) <a href="https://twitter.com/stephens_ben/status/1102167046115262466?ref_src=twsrc%5Etfw">3 March 2019</a></blockquote> <p>People on the Internet have been amazed by the simple maths hack, with Stephens’ post accumulating more than 4,000 retweets and 11,000 likes at the time of writing.</p> <p>“You’ve changed my life,” a man simply replied.</p> <p>Another man commented that he was “furious” for not knowing this sooner. “I'm 30 and have avoided knowing this until some hero on Twitter tweeted it.”</p> <p>One wrote, “How could maths teachers let us live without this!”</p> <p>The tweet also inspired some teachers who had not been aware of the switching technique. </p> <p>“I teach Maths at primary level and had never realised this,” one wrote. “50 per cent blown away/50 per cent going DOH!”</p> <p>A woman chimed in, “I used to teach maths for reporters as a part of journalism school and wish I’d had this explanation in my back pocket. I had other tricks for mathsphobes but this is far more elegant.”</p> <p>Some complained that the trick is a simple mathematics rule rather than some little-known hack.</p> <p>“Do you really think people don’t understand such a simple concept enough to know this? Good grief,” one wrote.</p> <p>“Those of us who studied basic arithmetic at school are scratching our heads as to why this is a revelation,” another added. “Next you’ll be telling us that x+y = y+x and that xy = yx.”</p> <p>Stephens defended his post, saying it was meant as a way to pique people’s interest in numbers. He admitted that he also just learned about the ‘switcheroo’ fact.</p> <p>“I almost think stuff like this would be lost on a kid at school,” he wrote. “It has way more impact a couple of decades later when you see it and you're like OMG IT WAS SITTING RIGHT THERE THE WHOLE TIME.”</p> <p>Did you know this maths trick? Let us know in the comments.</p>

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Can you solve this math problem for primary students?

<p>A homework question that was intended for an 8-year-old has left parents clueless.</p> <p>The question, which was shared on parenting website <a href="https://www.mumsnet.com/Talk/_chat/3245037-Can-someone-help-with-this-KS2-homework?messages=100&amp;pg=1#prettyPhoto" target="_blank"><strong><em><span style="text-decoration: underline;">Mumsnet</span></em></strong></a>, asks students to solve a riddle that involves working out what time various lighthouses will shine their lights.</p> <p>The answer is achieved by working out the common multiples between the schedules of the lighthouses.</p> <p>Can you solve the homework riddle?</p> <p style="text-align: center;"><img width="500" height="650" src="https://oversixtydev.blob.core.windows.net/media/7818287/1_500x650.jpg" alt="1 (136)"/></p> <p>The question has been criticised as being “ridiculous” for primary students to answer. </p> <p>The puzzle reads, “On the coast there are three lighthouses. The first light shines for 3 seconds then it is off for three seconds. The second light shines for 4 seconds then it is off for 4 seconds. The third light shines for 5 seconds then it is off for 5 seconds. All three lights have just come on together.</p> <p>“When is the first time that all three of the lights will be off together?</p> <p>“When is the next time that all three lights will come on at exactly the same moment?”</p> <p>The math question left parents baffled but they eventually arrived at the same answer that the lights would be off together at six seconds, and they would come on together at 120 seconds.</p> <p>Parents found that the problem was easiest worked out by finding the time they were off and then finding out when they were off at the same time.</p> <p style="text-align: center;"><img width="500" height="289" src="https://oversixtydev.blob.core.windows.net/media/7818288/2_500x289.jpg" alt="2 (78)"/></p> <p>The first light house comes on every 6 seconds, the second every 8 and the third every 10, so you have to work out the lowest number that can be divided by all those numbers – which is 120.</p> <p>The question frustrated many parents by the level of difficulty being given to students in Year 4.</p> <p>“That is a ridiculous question and I'm only here to learn something,” one wrote.</p> <p>Did you solve the problem? Let us know in the comments below.</p>

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Can you solve this tricky maths riddle in one second?

<p>A 13-year-old genius solved this tricky maths riddle in just one second. How long will it take you?</p> <p>The headscratcher comes from the Mathcounts National Mathematics competition in the United States, which is like a maths version of a national spelling bee.</p> <p>The 2017 competition was won by 13-year-old Luke Robitaille of Texas, who took less than a second to answer this riddle.</p> <p><strong>Riddle:</strong> In a barn, 100 chicks sit peacefully in a circle. Suddenly, each chick randomly pecks the chick immediately to its left or its right. Each chick pecks only once, and is not affected by which way its neighbours peck. What is the most likely number of unpecked chicks?</p> <p>Mathematical genius <span style="text-decoration: underline;"><strong><a href="https://www.adamspencer.com.au/" target="_blank">Adam Spencer</a></strong></span>, whose new book The Number Games is out now, offers this hint.</p> <p>“Imagine you are one of the chickens in the circle. What are all the possible ‘peckings’ that could happen to you, including not getting pecked, and what are the odds of each of those ‘peckings’ happening? Run these odds out over the 100 chickens and what number of ‘no pecks’ do you get?” he tells news.com.au.</p> <p>Still haven’t got it yet? Here’s the answer, as explained by Spencer.</p> <p><strong>Answer:</strong> For every chicken, the odds of getting pecked from the right is 0.5 and the odds of not getting pecked from the right is 0.5. Obviously the odds are the same for getting pecked from the left. So the odds of getting ‘double pecked’ are 0.5 x 0.5 = 0.25. The odds of getting ‘not pecked’ are also 0.5 x 0.5 = 0.25. The odds of getting ‘single pecked’ are 0.5 (0.25 from the left plus 0.25 from the right). Across 100 chickens you’d expect 25 to remain unpecked — you’d also expect 25 to be double pecked and 50 to be pecked once only.</p> <p> </p> <p> </p>

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Are you smarter than an 8-year-old?

<p>A US mum has shared a photo of a maths question from her third-grade child’s homework to <a href="https://www.reddit.com/r/funny/comments/79rc0f/this_3rd_grade_math_problem/" title="www.reddit.com">Reddit</a> – and it’s left the internet collectively scratching their heads.</p> <p>Not only does it appear that the child’s homework is insanely long (there’s at least 45 questions!) but it seems the maths query in question doesn’t actually have a clear answer.</p> <p>Question 44 reads: “Janell had 15 marbles. She lost some of them. How many does Janell have now?”</p> <p><img width="441" height="331" src="http://cdn.newsapi.com.au/image/v1/07bd39c6a4cd1361bccd4582d2e50c9d" alt="What does this mean?" style="display: block; margin-left: auto; margin-right: auto;"/></p> <p>Neither mum Dusty Sappington, who posed the photo of the question, nor the 800 internet users who commented could say for sure what the correct answer is.</p> <p>One popular comment suggested that the correct answer is “&lt; 15” (less than 15).</p> <p>However, if you want to be technical, the answer isn’t absolutely correct as it would include negative numbers of marbles — which would be impossible.</p> <p>So the real answer is closer to “0 &lt; x &lt; 15”.</p> <p>Even so, it’s unlikely the third grade teacher would have set such a difficult question so perhaps the answer is, as some commentators suggested, is simply “some”.</p> <p>What’s more likely though is the teacher who set the homework left out the vital information in the question. Perhaps they need to find their own marbles?</p> <p>The mother updated Reddit saying her daughter has yet to receive the marked homework back.</p> <p>“I haven’t found out the answer, but hope to see her graded paper soon,” she wrote. </p>

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Can you work out the TWO answers to this simple maths challenge?

<p>A seemingly simple maths challenge is sweeping the internet – and leaving many people scratching their heads in the process.</p> <p>Created by Go Tumble and shared on <a href="https://wikr.com/can-solve-new-viral-iq-test-1-1000-can/?utm_source=family&amp;utm_medium=rpost&amp;utm_campaign=ep" target="_blank">Wikr,</a> the test asks people to “'think outside the box” by working out two different but correct answers to a series of equations.</p> <p>“Firstly, think outside the box! This maths riddle is not that simple. Even though there’s usually one right answer for maths problems, two common solutions are causing heated debates all over the world,” the makers of the test tease.</p> <p>According to them, only one in 1,000 people can figure out the second possible answer to the test, so can you?</p> <p> <img width="546" height="410" src="http://cdn.newsapi.com.au/image/v1/b3e8f3777662ea4caccffe06bcc5e1ce" alt="There are two different ways of solving these equations, can you find them both?" style="display: block; margin-left: auto; margin-right: auto;"/></p> <p><strong>Answer 1</strong></p> <p>Most people will begin by adding 1 + 4 to reach the answer 5.</p> <p>Then they'll add 2 + 5 to the sum of 5 to get an answer of 12.</p> <p>Following this logic, most people will use the same process in the next line, adding 3 + 6 to get 9, and add to this to 12 to get 21.</p> <p>In the last stage, they will add 8 + 11 to get 19, before adding it to the sum of the previous line (21) to get 40.</p> <p>With the test creators say 40 is the correct answer, there's another answer – and only a select few will reach it.</p> <p><strong>Answer 2</strong></p> <p>The game makers say that while of course, 1 + 4 = 5, you can also reach 5 by adding 1 to 4 x 1.</p> <p>With this rule, they'll then add 2 to 2 x 5 to get 12.</p> <p>On the third line, they’ll add 3 to 6 x 3 to get 21.</p> <p>And to reach the final and alternate answer, they'll add 8 to 11 x 8 to get 96.</p> <p>Did you get both answers?</p>

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