Hello, everybody! Today I’m going to review this packet of mathematical tricks. Now, I bought this about a year ago in a shop called Hawkin’s Bazaar.. It’s one of my favorite shops. Now that’s probably advertising, but screw it! No one watches these things, anyway. It is one of my favorite shops. It’s full of things that flash and make a noise– and I don’t just mean a bloke in a dirty mac with a harmonica in his gob. So, it’s a great shop. Now, it cost me about £4. It’s made by a company called Tobar. Now let’s have a look at the packaging here. It’s called Mathematical Curiosities, or Curiosités Mathémathiques, or Mathmatical Wißbegierde, there. It’s got a few mathematical symbols dotted about. There’s a cross there, an equals sign, pi there– full marks for knowing that capital Sigma [Σ] is a mathematical symbol, but they could have just been going through WingDings, so we should be grateful that we don’t have a smiley face on the front. At the bottom here, it says “Have Fun With Numbers,” which is a really naff thing to say. I mean, I like maths, and I do have fun with numbers. But it’s not a sentence to use. What else do we have here? Well, it also says “Demonstrating Amazing Mathematical Anomalies,” which makes it sound like I’m going to unleash a black hole, or something, Which is further compounded by the fact that they call these tricks “Devices.” So it does sound like the Large Hadron Collider inside. Let’s take a look. OK, inside there aren’t any black holes. We have some instructions here, which are fairly clear, which is pretty good. In mine you’ll find a piece of paper with a number of proofs on it. But your copy probably won’t have that. And what else have we got? OK, let’s have a look at the first trick. So we’ve got four tricks in here. And the first one is called the “Think of a Number” card. OK, what you do is you get your volunteer to think of a number between one and sixty-four. And then they have to go through these cards, and pick which cards their number appears on. You put all their cards in a pile. You put all the cards on which the number does not appear on upside-down on another pile. And then you put them all together, you lie them on the key, and through the little window you’ll find the number your volunteer picked. Now, I really like this trick! Because this is just another way of doing Venn diagrams. You may have heard of Venn diagrams before. So Venn diagrams look like this. So, for example, if A here are “Things that are green,” so that might be grass, the Incredible Hulk, Al Gore–something like that. And if B here are things that I hate, which might be traffic, S Club 7, your face. Then in the middle here are going to be things that are common to both. So that might be something like sprouts, or something like that. Now, if I want to do a Venn diagram with three sets, it looks like this. And as you can see here, you can split up the diagram into eight regions. Now, you can uniquely define each region by which set it’s in, and which sets it’s not in. For example here, region two is in set A and set B, but it’s not in set C. Region five there is in all three sets, but on the other hand, region eight out here is in none of the sets. Now, if I could draw a Venn diagram with six sets, it would have sixty-four regions. And that’s exactly what we’re doing with these cards. So we’re just uniquely defining each number by which set it’s in, and which set it’s not in. So that’s pretty good. I like that. Now, the second trick in this pack is called Magic Number Cards. Now, for this one, what you do is you get your volunteer to think of a number under sixty. And they have to pick out the cards on which their number appears. And then you can tell them instantly what their number was, because what you do is you add up the numbers in the top left corner on the cards which they pick. And this works by using the powers of two. You see, in the top left corner all we have here are the powers of two. That’s one, two, four, eight, sixteen, thirty-two and sixty-four. And all numbers can be written as a sum of powers of two. This is called ‘binary,’ and it’s the same language that computers use. This is one you get a lot in Christmas crackers. For people in other countries who don’t know what crackers are, they’re brightly decorated cardboard tubes, and inside they have a toy, a paper hat, and a joke, usually of the quality of “What lies at the bottom of the sea and quivers?” “A nervous wreck.” They’re a bit like Kinder eggs, which are a toy, a surprise, and some chocolate. Some people complain about Kinder eggs because the toy is the surprise. So what I reckon they should do is have the toy, and the chocolate, and then they should put in a little note inside that says, “You’re adopted!” But maybe that’s just me. Anyway, you can make these yourself. All you need are six cards, and what you do is you put the powers of two in the top left corner. And then you start to fill the cards with the other numbers. So six would be written on cards two and four. And twenty-eight would be written on cards four, eight and sixteen. If you really want to impress, and do this as a magic trick, what you can do is you can make the cards different colors, and then remember which color goes with which number. And then you can predict your volunteer’s number without even looking at the cards. The third trick is called The Magic Calculator, which are these sticks here, and what you do is you put them together, and you can make four four-digit numbers, which you instantly add up. And I really like these tricks where you can instantly add up complicated numbers. This one works by using the third line. And what you do is you take away two from the third line, and you stick a two in front, and that gives you the grand total. So that’s quite easy to use. And if you’re interested in how it works, there’s the algebra for it. Total=1000(18+a)+100(18+b)+10(18+c)+(18+d)
=20,000+(1000a+100b+10c+d-2) But never mind that. And finally, we have these Addition Dice. And what you do–we have five dice here, and each face has a three-digit number on it. You roll the dice, and again, you can instantly add up the total. This one works by adding up the last digits on each dice. So, again, that’s another nice one. And if you’re–again, if you’re interested, there’s the algebra for that one. Total=100(8-a)+40+a
=100(50-(a+b+c+d+e))+(a+b+c+d+e) And that’s it! Pretty nerdy, but fun maths tricks, and I think I did have fun with numbers today. So, as usual, if you have been, thanks for watching.