 So let's take a look at a few more examples of using the pulverizer. So say we want to find a number that leaves remainder 3 when divided by 7, and 4 when divided by 9. So the greater remainder is 4, so we'll set up our table. The difference in the remainder is 1, and we'll form our quotients. 9 divided by 7 is 1, remainder 2. 7 divided by 2 is 3, remainder 1. 2 divided by 1 is 2, remainder 0. And because our remainder is 0, we have to stop here. Again, because our last divisor is going to be 1, any number will work as our clever number, so our first clever number can be 0. The first clever remainder will be our clever number times remainder plus the summer difference, then divided by the divisor. The preceding clever number are clever number times the quotient in its column plus the clever remainder. The preceding clever remainder is the new clever number times the remainder plus the summer difference, divided by the divisor. We'll go back one more column. The preceding clever number is our clever number times the quotient in its column plus the clever remainder. And the preceding clever remainder, which incidentally we never actually use, is going to be our new clever number times the remainder in its column plus the summer difference, divided by the divisor. And since this is the last column, we can find our solution directly, the clever number times the divisor plus the remainder, which is 4 more than a multiple of 9, which is also 3 more than a multiple of 7. Now, while we can always start with the last column, sometimes we might not want to, so let's find a number that's 5 more than a multiple of 11 and 8 more than a multiple of 17. So we'll set down our table. And again, if we go all the way to the end, our last divisor is 1, so any number will work. And again, we could use 0 as our last clever number, but remember we're going to multiply the clever number times the remainder and add the summer difference. However, this would get us involved with a lot of negative numbers, so we'll go back to the preceding column. And we want a number that, when multiplied by the remainder, 1 and then added to 3 gives a number that's divisible by 5. And so we find the first clever number is 2. And our first clever remainder will be our clever number times the remainder in its column plus the summer difference divided by the divisor. And once we have our starting point, we can roll backwards. The preceding clever number, clever number times quotient plus clever remainder. The preceding clever remainder, clever number times remainder plus the summer difference, then divided by the divisor. Back again, the clever number times a quotient plus the clever remainder. The clever remainder, the clever number times the remainder plus the summer difference divided by the divisor. And since this is the last column, we'll go ahead and find our solution. That'll be our clever number times our divisor 17 plus our remainder 8. And that's 8 more than the multiple of 17 and 5 more than the multiple of 8.