 Let's say we have two numbers, two three digit numbers, let's say 742 and 427. It's quite evident that in both the numbers the digits are the same, digits are two, four or seven, which are arranged differently. Usually what we do is that when we have similar digits but different numbers formed out of them, we try to compare those numbers. And this is basically what we do in shifting numbers. Our objective is to compare these numbers. So which of these numbers is larger? So let's see how we can do this. Let's read out 742. It's 742. Quite clearly this number has 700, so I can write 7 times 100 plus since it's 42 we can write 4 times 10 because it has four 10s and then 2. What about 427? It has 400s plus 2 10s and then it has a 7. Now if we want to compare between these two because 742 has 700s. We want to see how many hundreds both the numbers have. It's quite evident that 742 is larger because it has 700s and 427 has only 400s. I don't even have to look at other digits. And that's how we can find out which number is larger. But what if we use the same digits but arrange them in a way that it's like 427 and 472. Now because both the numbers have 400s, how are we going to find out which number is larger? If we look at the breakdown again, so we have 400s for 427, then we have 2 10s and 7 1s. For 472 again we have 400s, we have 7 10s and 2. Since both the numbers have 400s we have to look at 10s because 10s are greater than 1s. So we have to look at 10s and because 427 has 2 10s but 472 has 7 10s. So it's quite clear that 427 is less than 472. And this is how we can compare numbers when the digits are being shifted. Usually in shifting numbers there are problems wherein questions are asked by giving a number say like this 529 and we have to find out the smallest number that can be formed using the given digits and the largest number that can be formed using the given digits. Since this is a 3 digit number, some number will go and multiply 100. So in a given number there would be 500s because there would be some 10s and some ones. Now every combination of digits will form different numbers. So such as in this case we have been given with 529, we can also write a number 295 using the same digits or 592 or rather 259, it could be anything. Now which number should I multiply with 100 so that out of the possibility of numbers the number formed will be the smallest. So I will choose the smallest number to multiply 100 so that I can form the smallest number. The smallest digit out of the given digits is 2. So definitely I will multiply 100 with 2. But there are 2 choices now. With 2 at the start I can either write 259 or 295. Which number should I multiply by 10 or keep at the 10th place so that the number is the smallest? The answer is next smallest number because I want to minimize the number of 10s I have. So after 2, 5 is the next smallest and I will multiply the 10s with 5 then and in the unit place I will keep the largest number. So the smallest number I can get out of the given digits is 259. So this is the smallest number that I can create out of the given digits. Now my objective is to find out the largest number that I can find using the given digits. Now I want to maximize the number of 100s that I have. That's why I will choose 9 to be multiplied by 100. Then I will maximize the number of 10s I have. So I will find out the next largest number which is again 5 and the smallest number will go in the units place which is 2. So that is 952 which is the largest number. And this is how we can find the largest or the smallest numbers. Imagine if we had 0 in between say if we had 502 so in this case if we wanted to create the smallest 3 digit number with the logic that we just discussed we will be tempted to use 0 which is the smallest number and minimize the hundreds. And then write the next smallest 2 times 10s plus 5 which will just be 25 and that won't be a 3 digit number. So when you encounter 0 in the given digits you have to make sure you do not put 0 in place of the hundreds here because it will not be a 3 digit number. So what is the turn around? We don't put 0 at the hundreds place here we just want to put 0 at the tens place. So barring 0 we have 2 as the smallest number so we will minimize hundreds by putting 2 there plus 0 times 10s plus 5. That is the smallest 3 digit number that we can find which is 205. Remember smallest number that still can be made using the digits 50 and 2 is still 25. But smallest 3 digit number that we can find here is 205. I will encourage you to find out and create smallest or the greatest numbers by taking any 4 digits or 5 digits now and play around with shifting numbers.