Number Trick - Numberphile

DR. JAMES GRIME: So we're going to do a little mathematical trick that I'm hoping that people will like and they'll try out on their friends and family. So let's do it. We're going to write out four-digit numbers. So like this, right? Now, you've got 3,485, but we'll take it in turns. So give me a four-digit number. You could just shout out four digits if you want. Go on. BRADY HARAN: You want one from me? DR. JAMES GRIME: Yeah. BRADY HARAN: 7,721. DR. JAMES GRIME: 7,721. And now I'll come up with a different one, like 2,278. Give me another. BRADY HARAN: 1,891. DR. JAMES GRIME: 1,891. And I'll come up with another one, like 8, 1-- something-- 8. And we're going to add these together. 3,485, 7,721, 8, 1-- and 8, there you go. So we see what that is. Let's see what the answer is. OK, so the final answer is 23,483. Now, before I started the trick, I made a prediction on that strip of brown paper. Let's have a look. Let's have a look at my prediction. If I open up my prediction, it says, I predict 23,483. And then I think what you're meant to say here is tra-da! Do you want to see how to do it? Shall we learn how to do it? All right, and then people can do it to their friends, as well. Did you notice I started it off? So I picked a number to begin with. Then you picked a number. Then the number I picked after you-- and we took it in turns-- remember, I picked the digits column by column add up to 9. So 7 and 2, 7 and 2, 2 and 7, 1 and 8. So these two together are equal to 9,999. The next two rows, I did the same thing. Can you see? They add up to 9. I had the 0 there when you picked the 9. And that's 9,999. So the last four rows together are going to be just shy-- well, this is just shy of 10,000. Add them together. It's just shy of 20,000. It's 2 short. It's 19,998. So I knew that the last four numbers were 19,998. So what I did to make the prediction-- I had thought of this in advance. And then I added 20,000 to it, which is quite easy to do, because you put the digit 2 at the beginning. And then because it's 2 less than 20,000, I subtract the number 2. So you put the digit 2 at the start. And then you subtract 2 from the end. And you can make your prediction. And you can look like a mathematical genius. MATT PARKER: Back to the chosen card. You're just not going to get far enough. But what you will do is you'll take off, well, let's say 12. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. And then obviously you're going to do the thing with, oh, no, that's not it, it didn't work, boo hoo. The trick now is, instead of putting these back on top, put them underneath.