Moser's trick
Moser's trick is a way to solve complex mathematical problems by using a simple tool. Imagine you have a really big problem, like figuring out the total number of apples in a huge orchard. It seems difficult because you will have to count each apple one by one. But with Moser's trick, you can make it much easier.
To start, let's imagine there are 100 apples in one row. You can easily count them by pointing at each apple and saying the number. Now, let's say you have many rows of apples, stacked one on top of the other. There could be 1000 rows or even more.
If you were to count all the apples by yourself, it would take a very long time. But instead, you use Moser's trick. It involves thinking about the problem in a different way. Instead of focusing on each individual apple, you focus on groups of apples.
Let's say you take one apple from each row and put them in a separate pile. Now you have 100 apples in that pile. But wait! You haven't counted all the apples yet. What about the apples that you didn't pick? Well, you know that every row had one apple taken, so you can just count the number of rows you have left. Let's say you have 900 rows left. That means there are 900 more apples that you haven't counted.
So, using Moser's trick, you know there are 100 apples in the pile you made and 900 apples in the remaining rows. So, the total number of apples in the orchard is 100 + 900 = 1000.
This trick works because instead of counting all the apples individually, you use a smaller number (in this case, the number of apples in the pile) and then figure out the rest based on the number of groups remaining.
Moser's trick can be used for many different types of problems, not just counting apples. It's a way to make complex problems easier by breaking them down into smaller, more manageable parts. And that's what makes it so cool!
To start, let's imagine there are 100 apples in one row. You can easily count them by pointing at each apple and saying the number. Now, let's say you have many rows of apples, stacked one on top of the other. There could be 1000 rows or even more.
If you were to count all the apples by yourself, it would take a very long time. But instead, you use Moser's trick. It involves thinking about the problem in a different way. Instead of focusing on each individual apple, you focus on groups of apples.
Let's say you take one apple from each row and put them in a separate pile. Now you have 100 apples in that pile. But wait! You haven't counted all the apples yet. What about the apples that you didn't pick? Well, you know that every row had one apple taken, so you can just count the number of rows you have left. Let's say you have 900 rows left. That means there are 900 more apples that you haven't counted.
So, using Moser's trick, you know there are 100 apples in the pile you made and 900 apples in the remaining rows. So, the total number of apples in the orchard is 100 + 900 = 1000.
This trick works because instead of counting all the apples individually, you use a smaller number (in this case, the number of apples in the pile) and then figure out the rest based on the number of groups remaining.
Moser's trick can be used for many different types of problems, not just counting apples. It's a way to make complex problems easier by breaking them down into smaller, more manageable parts. And that's what makes it so cool!