This BBC podcast is supported by ads outside the UK. and a valuable community. ASR does it. So, now you can listen to your podcast. Good morning. With the new Toyota C-HR Plus you're ready for the real work. Because it's 100% electric and has an axis radius to 607 kilometers. It's a speed of 10% to 80% within a half hour. And with 416 liters of space you're ready for the weekend. Find the new C-HR Plus on Toyota.nl. the More or Less podcast, with a programme that looks at the numbers in the news, in life and in Premier League football. I'm Tim Harford. Occasionally you meet people who have minds like calculators. Prodigies, professors, Premier League footballers? 79,507. No, 500 and what? 7. 40 per year. Yeah. That was Chelsea and England under 21 striker, Liam De Lappe, figuring out that the cube root of 79,507 is 43, which sounds hard. You may remember cubes and cube roots from school. 2 cubed is 2 times 2 times 2, or 8. The cube root is just reversing the procedure. The cube root of 8 is 2. 3 cubed is 3 times 3 times 3, that's 27, and so the cube root of 27 must be 3. And yes, 43 times 43 times 43 is 79,507, or, as Liam de Lappe would put it, The cube root of 79,507 is 43. And in case you think that was a fluke, here's another from Chelsea's Instagram feed. 778,688. 92. Yeah. How? How? How you do it Just clever innit Yes Yes it is clever So how he doing it I all for mathematical geniuses and prodigies and stuff but actually, you don't have to be a maths genius to do this. You just need to have a little bit of memory. That's Rob Easterway. He's an author, friend of the programme, and he knows a lot of cool maths tricks, which might just make him as smart as Liam DeLapp. Let's have a go, see if you can do the same. give me the cube root of 140,608. Okay, I'm going to do that by a couple of amazing mathematical genius things in my head to say the answer is going to be 52. Wow, okay. So you can do it, Liam DeLapp can do it. Yes. I can't do it. Am I missing something? Tim, you can't do it yet. Okay. You're going to be able to do this very soon. Growth mindset, I love it. First of all, this trick that I'm going to explain to you only works for two-digit numbers that are cubed. So the cube root is always going to be a two-digit number. Right. So there's two digits we're going to have to work out here, the first and second digit of the answer. So let's start with the first digit. Step one, memorise the cubes of all the numbers from one to nine. So I've already told you three cubed is 27. I mean, one cubed is one, two cubed is eight and so on. Four cubed is 64. Five cubed is 125. Those five are fairly easy to remember. Six cubed is 216. Very good. Because it's dice. Excellent. I can do dice. Excellent. Seven cubed, I'm not so sure about. Eight cubed is 512. Correct. So you've only got two to learn now. Because that's numbers, right. So seven cubed is 343. Okay, seven cubed, 343. And nine cubed? 729. Okay, I will try to... Actually, I'm going to just write them down. Yeah, sure, sure. Good. Okay, right. So one of the video clips shows DeLapp finding the cube root of 274,625. Now, all you have to worry about for the first digit is the thousands. So 274. So what you do is say, OK, I know the list of cubes. What's the cube that's just below that? Right. So 216. Correct. Which was what? Which is six cubes. Right. Your first digit is going to be six. OK, alright. So to find the first digit, you look at the numbers in the thousands and compare it to the cubes of the numbers 1 to 9. Take whichever cube is just smaller and trace it back to its cube root and that gives you the first digit. We had 274 so we look only at 274 The cube just below that is 216 which is the cube of 6 So 6 is our first number. That's a bit complex, admittedly, but luckily it gets easier. Now for the second digit. Now, let's just take a little aside for a moment. Give me a number ending in 4, a big number ending in 4. OK, 560,014. Brilliant. Cube it. I'm joking. Okay. Because I don't care. I don't know the answer either. Yeah. But I do know that the last digit is four. Because when you cube any number that ends in four, it's still four. Right. When you cube any number that ends in five, guess what ends in? Five. And six ends in? Six. And seven ends in? I'm going to say not seven. Correct. Because you already told me that seven cube is 243. But is it always three? It's always three. Okay, right. And three always ends in seven. So they kind of seven and three swap round, and actually two and eight also swap round. Right. So apart from those two, naught to nine all just cube and end in themselves. So the message of this is that the last digit of a cube number is always going to be predictable. Correct. And Delap's number was 274,625. OK, right. So it ends in five. Yeah. And it starts in six, and it's a two-digit number, so it's 65. You're a genius. Oh! Or you've got a good memory, but I'm going to go with the first. Put me up front for Chelsea, that's what I'm saying. Does this tell us something deep about maths, or is it just a clever little trick? It's one of those little pathways into numbers and the beauty of numbers and the fact that we're spotting patterns. And if you're solving something really big and important like Fermat's Last Theorem, a nice little thing to work on over the weekend, the way into it, the first step on that giant Everest of a journey is a little thing like this, spotting a pattern and saying, maybe that helps. And it's rather beautiful and it's a party trick. Love it. Let us turn to something else dear to Liam de Lapp's heart which is Premier League goals. He scores a few and Rob, you made a prediction in a book that you published in 2019 about Premier League goals. Just remind us what it was. OK, so what I said was here's a prediction. The number of goals in the Premier League next season will be 1,000. Okay, it might be a few more than that, but it's probably right to within 5%. Okay so to within 5 is between 950 and 1 Were you right Well it was all going very well until the 2022 season when the total goal record was broken and it was 1 That was nothing compared to 2023 when the 1 We weren even in an outlier So what's happened? Have defences got weaker? Have attacks got stronger or is something else going on? Yeah, football has changed. And in particular, referees have changed. So the key thing is the 22-3 season is when the Qatar World Cup happened. And I think it was as a result of that, it became an international regulation that the referees should be... No one was allowed to touch Lionel Messi or what? Yeah, well, no, they just can't. Time wasting is a real problem. We must stop it. And therefore, referees, you must be really tough on adding in time for not just injuries, but also things like goal celebrations and all these other things that take up time. So suddenly games became longer. Quite a bit longer. The number of minutes that a ball is actually in play increased by about 6% from the 2022-23 to the 2023-24 season, from about 55 minutes to just over 58. This probably can't explain the whole change. Football's a complex game, and anything from changes in tactics to differences in player quality may well have had an effect. Indeed, the goals scored increased by about 15% season to season, so it does seem something else was going on. By the way, last season I checked, it was 1180 goals. And I'm curious, do you know how many of those goals were scored by Liam De Lapp? I don't. It was 12, which is approximately 1%. So pretty good going. That is very impressive. And he was playing for Ipswich at the time, so even more impressive. Our thanks to Rob Easterway, author of Maths on the Back of an Envelope. If you have any questions or comments, please get in touch at more or less at bbc.co.uk. We'll be back next time. And until then, goodbye. This intersection where the world and America meet. Listen on BBC.com or wherever you get your podcasts.
