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