Multiplicative binary search

Multiplicative binary search is a way to quickly find a number in a list of numbers. Imagine you have a list of numbers like 1, 5, 10, 15, and 20. If you wanted to find 10, you could use multiplicative binary search.

First, you would imagine that the list is like a line, where the lowest number is on the left side, and the highest number is on the right side. Now, pick a number that's in between the lowest and highest numbers. In this example, you could pick a number like 8.

Next, you would ask yourself, is 10 higher or lower than 8? In this case, 10 is higher than 8. That means you can cross out the numbers that are lower than 8. That means you only have to look at the higher numbers now, like 10, 15 and 20.

Choose another number that is in between the highest and lowest numbers. In this case, you could pick 12. Then ask yourself, is 10 higher or lower than 12? In this case, 10 is lower than 12, so you can cross out the higher numbers like 15 and 20.

Now, you would pick a number that is in between the lowest number, which is 10, and the highest number, which is 12. You could pick 11. Then ask yourself, is 10 higher or lower than 11? Since 10 is lower than 11, the only number you need to look at is 10. This means you have found the number you were looking for!