 Hey bro, we need to discuss something with you. What is this? Magic. Magic. Magic? What kind of a magic? Then let me show it to you. But before I do it on you, I will turn away from the board so that later you should not say that I have done some trick on you. Okay, are you ready? Yes, I am ready. Okay, so step number one. Take a three digit number such that the unit's place and the hundred's place should not be the same. Okay, so let me repeat. The hundred's position and the unit's position should have different numbers, right? Perfect. Okay, so let me take a number. Don't tell me that number otherwise you will say that I have you know done some trick. Okay, I have taken the number. Okay, now step number two is reverse the digits and get another three digit number. You subtract the smaller one from the larger one. Are you done with that? Let me do that. This is step number three. Step number three, you have subtracted the smaller one from the larger one. I still don't know what digits you have taken, what number it was. Now, what you need to do is reverse the three digits once again and get another number, fourth number. Wonderful. Now it will be very simple step for you, my mathematics champion. You just need to add the third and the fourth number. Don't tell me the result. And abracadabra, I know the number. Ready? Yes. The number is one, zero, eight, nine. That's a magic. How do you do that? So now guys, we are going to see how this trick works. It's not any magic. There is always a mathematics behind it. So let's find out what real mathematics is behind this calculation. Let us say abc is a three digit number such that a is not equal to c. We'll see the relevance of this condition later. Now if abc is a three digit number, I have purposely put these brackets such that it denotes it is a concatenation and it's not a times b times c. It's not a times b times c. It's abc as in three digits concatenated together. What does it mean? It means this number's value is 100 times a plus 10 times b plus c. Isn't it? So this is the number. Then this was the first step. We had taken one three digit number with three different digits, making sure that the units place and the hundreds place digits are not same. Now what was the second step? We had to reverse this number. So the reverse number would be c, b, a. Reverse as in when we reverse the order of the digits. Then the number is 100 c plus 10 b plus a. Isn't it? Now what did we do next? The third step was to take the difference. Assuming this number was larger, so we take the difference. What will we get? We will get 100 times a minus c. This 10 b and 10 b obviously will get cancelled and then it will be c minus a. Isn't it guys? Now after this what did we do? We had to reverse the digits order once again. But in this particular expression it's not very clear what other digits are. Hence we have to express this as another three digit number let's say p, q, r. Where we have to now identify what is p, what is q and what is r in this particular expression. So what do I do guys? So p, q, r if you see will be something like 100 times p plus 10 times q plus r. Now in this case we can see there is a factor of 100 here and there is one something similar to r here but there is no term containing a 10. So what do I do? I do some borrowing. So what I am doing is from here let us say we write this expression as 100 a minus c minus 1. Why did I do that? Because I borrowed 100 from it and this I can write it as plus 100. So if you see for this first term I have written 100 times a minus c minus 1 plus 100. So total is this term only. Now the rest of it is c minus a. Isn't it? I hope there is no problem so far. Then what I can write it as once again c carefully a minus c minus 1 plus my dear friends. I can write this 100 as 9 into 10 plus 10 plus c minus a. So I have purposefully broken down this 100 as 9 times 10 plus 10. Why? Because somewhere I want this 10 times some digit. Now I am getting 1 c here. So this number becomes 100 a minus c minus 1 plus 10 times 9 plus c minus a plus 10. Now if you look carefully don't you think we have got our PQ and R? What are PQ and R guys? So if you see P in this case will be a minus c minus 1. Isn't it? a minus c minus 1. Whatever was associated with the factor 100 is P. So this entire thing is P. Now obviously what's Q? Q is 9. And what's R? If you see R will be equal to c minus a plus 10. Correct? Now this was our third number. If you remember the first number was the original number. Then we reversed the digits. Then we took the difference. Now this 100 a minus c plus c minus a was our third number. Isn't it? And for that we have got the digits of that number which is P equals a minus c minus 1. Q equals 9 and R is c minus a plus 10. And that number was this one. This number. This is the third number guys. Which is same as this difference. So this difference is same as this number. Now what was the fourth step? Fourth step was again to reverse the order of the digits. So hence if you see this is P. Let me write it as P. This is Q and this is R. If I have to reverse the order of the digits the new number will be. Let me write. Let me rewrite the third number. So this is number 3. Third number is 100 times this one a minus c minus 1 plus 10 times 9 plus c minus a plus 10. Isn't it? Fantastic. Now reverse the digits for number 4. Fourth number is 100 times the R. So this is my R. This is R. So 100 times that R which is c minus a plus 10. Then this same number because Q remains as it is. And the unit's place will be my P now. So this is P. This is Q. And so this is P. This is Q. This was R, right? So hence last unit's place will be a minus c minus 1 folks. So hence if you see this is number 3, number 4 in R magic. And now what was the last step to add the number 3 and the number 4? Isn't it? Let us add. So if you see 100 common here. So what will you get? A minus c minus 1 plus c minus a plus 10. Isn't it? First this column sum is this one. This one is nothing but 90 plus 90, 180. And this one if you add you will get c minus a plus 10. Then plus a minus c minus 1. Now the mathematics, the algebra is very simple here. A and a gets cancelled, c and c gets cancelled. Minus 1 plus 10 is 9. 9 times 100. Let me write it here. 900. Isn't it? Then plus 180 and this c. This c goes a for a goes 10 minus 1 is 9. So my dear friends as you see we are getting a constant number 1089. So what is it? So you take any a b c such that a is not equal to c. And you do this entire process. Let me recap it quick fast. What is it? Take the number, reverse the order of the digits. Take the difference. Whatever is the result? So result was this number, third number. You again reverse the order of the digits and take the sum. You will get a constant 1089. I hope you understood the proof. Hey guys I hope you all enjoyed this video. And I think you can try this trick on your friends and relatives. And do let us know whether this trick is going to work for a four digit number. What do you think Tushar sir? Yeah, so that could be a good question for generalization. So guys please try if it is true only for a three digit number. Or you can try similarly for any four digit, five digit or n digit number. That would be a good question to engage with. So for such magic tricks with mathematics, we'll be coming up with more such videos. I hope you enjoyed the video. So please do like, subscribe and then keep rocking. Thank you. Bye bye take care.