Kids who love maths

Recently I published a post on squaring numbers ending with five, but in this post, I'm going to take it a step further, and teach all the divisibility rules up to 13. Divisibility rules are the guidelines for working out if a larger number is divisible by your smaller one. They never make an error. Sadly, as there are infinite prime numbers, and therefore infinite divisibility rules, I can neither learn all of them, or teach you all of them. But chances are that you will ever need to know any above thirteen, so 'fire away!'. 1: All whole numbers are divisible by 1. 2, 4, 8, etc: To find out whether a number is divisible by 2^n, all you need to do is take the last n digits of the larger number is divisible by 2^n, or zero. e.g. 31242345840 is divisible by 8 (2^3), because the last 3 (n) digits, 840, is a multiple of 8. This is because any power of 2 (2^n) is a factor of the same power of ten (10^n). e.g. 16 (2^4) = 10000 (10^4) ÷ 625 (5^4). As you have just seen, yo...

In one of my earlier posts, I talked about the Maths Olympiad, a worldwide mathematics competition. I finished it off with an example Maths Olympiad problem from excellent.org. Here it is in its full glory. If x and y are real numbers satisfying             x 2 + xy = 20 and y 2 + xy = 30 what is the value of xy? Today I’m back to answer this problem. x² + xy = 20 y ² + xy = 30 ( x²  + xy) + ( y ² + xy) = 50 ( x²  + xy) x ( y ² + xy) = 600 ( ( x²  + xy) x ( y ² + xy)) ÷ ( ( x²  + xy) + ( y ² + xy)) = xy  ∴ 600 ÷ 50 = xy              = 12 Yours in numbers,  Lachlan

You might remember me mentioning Adam Spencer in an earlier post, and know by now that I definitely admire him. He is an excellent mathematician, and is extremely passionate, but he is also extremely modest. This is shown in his ' monster prime ' ted talk, Adam proves his modesty by admitting his own ability. "Put simply, in a room full of randomly selected people, I'm a maths genius. In a room full of maths Ph.Ds, I'm as dumb as a box of hammers." But to him, maths is more than a hobby. He might not do maths for a living, but he's as close as it gets to doing just that. He has already written several books on maths, all of which I have loved, and I'm sure that there will be more in the future.  Books by Adam Spencer: -Adam Spencer's Big Book of Numbers -A World of Numbers -Time Machine But for the second part of this post, I'll be focusing on his second book, 'A World of Numbers', which is the source of the heat facts below. T...

If you come across a number ending with five and you really need to square it, don't worry, there's an easy way. First, just think of the number as n5 (this does not mean n x 5), where n is every number before the five. To get the square, write 25 and in front of that write n x (n + 1). As an example: Say your number is 65 squared.  6 x 7 = 42 42      >42 25 25  Your answer is 4225. Your's in numbers, Lachlan

I'm back and here to celebrate the school holidays! Today I'm going to give you a series of fun activities based around STEM to work on throughout the holidays. During the holidays I might not keep up my posts, but I may post the occasional tip for the technology task. Remember, you don't have to try and do all  the tasks, just have fun.   Science: Invent a product that will revolutionise cooking. You don't have to make anything, you just have to come up with the idea and complete a scientific diagram on your creation, explaining how it works. Technology: Make a working calculator uses code. You can use block coding or line coding, I don't mind which. As long as it can do addition, subtraction, multiplication, and division.  Engineering: Build a suspension bridge using whatever material you like (I used LEGO) that can hold at least 1 kilogram of weight on its centre. Try your best to make your bridge as long as possible. Mathematics: Some might arg...

The Maths Olympiad is a world-wide competition, held at hundreds of locations around the globe. There are many Maths Olympiad competitions but some of the largest are the APSMO (Australasian Problem Solving Maths Olympiad) and of course the IMO (International Maths Olympiad). Not only is the Maths Olympiad a great competition to participate in, as I have three times so far, you can still learn from it even if you can’t participate. As an example, brilliant.org is an amazing website where you can practise Maths Olympiad questions without having to do the test. Here is one of their questions. Hopefully you’re up for the challenge.   If x  and y  are real numbers satisfying            x 2 + xy  = 20 and y 2 + xy  = 30   what is the value of xy ?   I’ll be back next with the answer in case you get stuck. Yours in numbers, Lachlan

Prime numbers are one of the fundamental areas of mathematics, and we all need to know about them. Most likely similar to a lot of you, I simply didn’t care about primes. That was until I watched the Ted Talk ‘Monster Primes’ by Adam Spencer, a mathematician who seems more suited to the role of a comedian, or ‘mathecomedian’ as I sometimes like to call it. In the video, he discusses not only many of the largest primes, he discusses how to find them, and some of the history behind the search for monster primes. Click Here to watch ‘Monster Primes’ A prime number means a number that only has two factors, one and itself. This may be all you’ve ever learnt, but there is far more to it than that, especially when it comes to finding primes in the first place. In the ted talk, Adam Spencer explains that a large prime can be found by taking 2 to the power of a prime, and subtracting one, resulting in and even larger one. However, there are many exceptions. While 2 13 – 1 = 8191, whic...

Hi, my name is Lachlan and I created this blog because I know that many of you out there are like me and just love maths. Many of you are probably parents thinking "My child loves maths, what should I do with them?!". Here you will be challenged and tested with a series of fun quizzes and tasks, and have your mind blown by astonishing facts and articles. You will also be introduced to a series of websites, videos and more, that will expand your knowledge of the vast world of math that we live in. However, in this blog we will also be diving into the depths of STEM, exploring not only pure math, but also the other areas of STEM, science, technology and engineering, which are all in turn related to math. My goal is that everybody reading my blog will take something out of it, whether it is a formula, or an idea of their own. I hope you enjoy. Yours in numbers, Lachlan P.S. I've kept all my old posts. See below. You can find our new bl...