IQ tests offer a formula that allows you to compare yourself to other people and see how average (or above average) your intelligence is. The Cognitive Reflection Test (CRT) is dubbed the world’s shortest IQ test because it consists of just three questions. It assesses your ability to identify that a simple problem can actually be harder than it first appears. The quicker you do this, the more intelligent you appear to be. Here are the three questions: 1. A bat and a ball cost £1.10 in total. The bat costs £1.00 more than the ball. How much does the ball cost? 2. If it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets? 3. In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? Sign up to our free Indy100 weekly newsletter Here is what a lot of people guess: 1. 10 pence 2. 100 minutes 3. 24 days These answers would be wrong. When you're ready, scroll down for the correct answers, and how you get to them: 1. The ball would actually cost 5 pence or 0.05 pounds If the ball costs X, and the bat costs £1 more, then it will be: X+£1 Therefore Bat+ball=X + (X+1) =1.1 Thus 2X+1=1.1, and 2X=0.1 X= 0.05 2. It would take 5 minutes to make 100 widgets. Five machines can make five widgets in five minutes; therefore one machine will make one widget in five minutes too. Therefore if we have 100 machines all making widgets, they can make 100 widgets in five minutes. 3. It would take 47 days for the patch to cover half of the lake If the patch doubles in size each day going forward, it would halve in size going backwards. So on day 47, the lake is half full. In a survey of almost 3,500 people, 33 per cent got all three wrong, and 83 per cent missed at least one. While this IQ test has its shortcomings – its brevity, and lack of variation in verbal and non-verbal reasoning - only 48 per cent of MIT students sampled were able to answer all three correctly. Have your say in our news democracy. Click the upvote icon at the top of the page to help raise this article through the indy100 rankings.

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Amy Dowden has shared “the hardest step” of her cancer journey with fans as she shaved her head. The Welsh dancer, who has competed on Strictly Come Dancing since 2017, was diagnosed with breast cancer in May. She is currently undergoing chemotherapy. Dowden, 33, has been documenting the journey for her fans, and recently described in a candid video how she “cries every day” as her hair falls out due to treatment. On Thursday (21 September), with Dowden over halfway through her chemotherapy, the dancer made the brave decision to “take control” and shave her head. In a montage shared on Instagram, Dowden was shown dabbing at her eyes while her “loved ones” cut off chunks of her hair down to a short, cropped style. The remaining hair was then shaved off, with the Strictly star growing more emotional and pausing to cover her face with her hands. However, she was in the end shown admiring the end results in the m “This too shall pass,” Dowden wrote, before describing the haircut as “the hardest step so far”. “I tried my best to save it. I know it’s only hair but these past few months I’ve had what feels like so much taken away from me that has made me not feel like Amy. I’m missing every possible aspect of dancing. I just wanted to keep my identity with my hair and I tried telling myself it wouldn’t go. But I would dread the pain of waking up to the shredding everyday.” She continued: “I’ve not been able to take control of this journey so far, but as you can see with some of my loved ones I took the courage and CONTROL. “It’s going to take some time to get use to and learn to love and embrace but, I’m now focusing – not on the hair I’m losing but the hair I’m going to get back and the happy dancing, tea lover who talks way to fast whilst rolling every rrrrr who is still there inside with or without hair!” Dowden said that she could now “see the finish line” after shaving her head, explaining: “This for me was a hurdle I couldn’t even bring myself to think or speak about. I’ve done it and I’ve also crossed the halfway chemo line! I’m feeling empowered and positive!” Dowden’s fellow Strictly pro Dianne Buswell commented: You are still all the things you were before, just with added courage, strength and determination. One thing about you is that you don’t let anything take over! “I cannot wait to have you back on the dancefloor with us chatting away, making endless cups of tea! We all love you so much and I’m such a proud friend.” Due to her treatment, Dowden has not been given a professional partner during this series of Strictly Come Dancing. However, the team paid tribute to Dowden during Saturday (16 September) night’s launch show. Host Tess Daly called Dowden their “Welsh dragon” and explained that she would be missing “the start of the series”. Strictly Come Dancing continues Saturday 23 September at 6.15pm on BBC One. Read More Strictly’s Bobby Brazier: ‘I don’t think happiness or fulfilment lies in what TV show I’m gonna do’ Strictly’s Amy Dowden says she ‘cries every day’ as she opens up on losing her hair during cancer treatment Strictly Come Dancing’s biggest stars this year are 50 plus – it’s refreshing to see Stacey Solomon leads tributes to cancer campaigner Nicky Newman who has died aged 35 Yoghurt could be the cure for bad garlic breath, study finds Teenager’s death after drinking too much water was ‘preventable’

Manchester United were made to suffer in Germany after a promising start to their Champions League opener against Bayern Munich. Christian Eriksen should have opened the scoring inside the first five minutes only to be denied by a sharp save from Sven Ulreich. United were quick to transition the ball up the pitch and looked comfortable in the game until a howler from Andre Onana gave the hosts the opening goal. Leroy Sane added a second before the break following a wonderful solo run from Jamal Musiala who took the ball through midfield before pulling it back to Sane for the finish. Rasmus Hojlund netted his first goal for United to give them hope of a comeback after the break but Harry Kane restored the host’s cushion with a beautifully taken penalty. The goals kept on coming with three being scored late. Casemiro bagged a brace either side of a Mathys Tel rocket but United couldn’t get the win. Here’s how all the players rated at the Allianz Arena: Bayern Munich Sven Ulreich - 6. Denied Christian Eriksen an opening goal in the fourth minute after his defenders lost the ball deep in their own half and kept out a wild shot from Marcus Rashford. Could do nothing about Rasmus Hojlund’s or Casemiro’s goals and unfortunate to conced three. Konrad Laimer - 6. Thought primarily about getting forward on the wing and linked up nicely with Leroy Sane to exploit the spaces in behind Sergio Reguilon. Dayot Upamecano - 7. Stayed switched on to cover Laimer’s forward runs, handled Rashford and Hojlund with composure and poise until United’s first goal. Minjae Kim - 6. A top partner for Upamecano against a United attack that lacked persistent bite. Drove the ball up the pitch a couple of times but went to sleep late in the game with the match won. Alphonso Davies - 7. Stuck a foot on the ball first when tackling Facundo Pellestri, stopping the Uruguayan youngster from scoring a simple tap-in early in the match. Joshua Kimmich - 6. Was a valuable link between defence and attack providing pressure high up the pitch towards the end of the game. Leon Goretzka - 6. Commanding in midfield though wasn’t put under enough pressure from United’s attacking personnel. Took umbrage with a tackle on Kane from Lisandro Martinez and got booked. Leroy Sane - 9. His movement off the ball caused real problems and he was Bayern’s biggest threat. Scored the opening goal and curled one past the post in the first half before hitting the post in the second. Jamal Musiala - 8. Developing a solid relationship with Harry Kane making several forward runs when the England captain dropped back. A wonderful solo run and cutback set up Bayern’s second goal. Serge Gnabry - 7. Drifted into space inside the box and slotted a clinical finish past Andre Onana to double his team’s lead in the first half. Harry Kane - 8. Went through several spells without touching the ball but proved his quality by setting up the first goal thanks to some top quality hold up play and slotted home a perfect penalty when called on. Subs: Kingsley Coman - 6, Eric Maxim Choupo-Moting - 7, Mathys Tel - 8, Thomas Muller - n/a Manchester United Andre Onana – 5. Picked out a few good passes and made some nice saves but all that is overshadowed by a howler that allowed Sane’s shot to sneak under him and give Bayern the lead. Diogo Dalot – 6. Out-paced and out-classed by Musiala in the build-up to the second goal. Seemed to suffer from a lack of confidence like most of United’s defence but was willing to put his body on the line. Victor Lindelof - 6. Dealt well with the aerial balls into the box but got caught a couple of times out of position and didn’t have the legs to recover properly. Lisandro Martinez - 6. Grew frustrated as the night went on before getting into a scrap with Leon Goretzka and earning an unnecessary yellow card. Sergio Reguilon - 7. Wasn’t afraid to make sharp forward runs trying to force United into the final third whilst also relishing the battle against Sane. Looks to be settling into his role at left-back. Casemiro - 8. The more defensive of United’s two holding midfielders, sat deep to keep the shape compact and provide cover for the back line but played a couple of wonderful passes over the top for Bruno Fernandes before scoring two late goals with his first real forays up the pitch. Christian Eriksen - 5. Latched onto a loose ball early in the game but drilled a shot straight at the goalkeeper when he should have scored. Harshly judged to have handled the ball inside the box leading to the penalty. Facundo Pellestri - 5. Failed to toe United ahead early in the game and was denied any better chances for the rest of the match. Bruno Fernandes - 7. Was the playmaker for most of United’s attacks and led the press well off the ball. Misplaced a couple of difficult passes but was always looking to get the ball into the box even with his team chasing the game. Assisted Casemiro for the third goal. Marcus Rashford - 6. Pacey down the line, getting the better of Laimer on a few occasions. Set up Hojlund’s goal with a deft touch inside the penalty area but needs to be more creative in the wide areas. Rasmus Hojlund - 7. Made an impact at the top of the pitch with a well taken goal in the second half. His first for the club and signs are there that he’ll get plenty more. Subs: Scott McTominay 6, Anthony Martial - n/a, Alejandro Garnacho - n/a Read More Bizarre clash with Bayern ends in predictable outcome for Manchester United Arsenal are back in the Champions League — and they look like contenders too Bizarre clash with Bayern ends in predictable outcome for Manchester United Tottenham have Harry Kane ‘buy-back clause’ as Daniel Levy reveals option Erik ten Hag concerned by Manchester United’s mounting injury problems