# Solved Problem 1: Largest 3 Digit Number

What is the largest number 3-digit number that can be formed between 300 and than 800 using the digits 2, 5, 8 and 6 if the digits cannot be repeated?

**Solution**

In this problem, we need to find a 3 digit number that is more than 300 and less than 800.

*Selecting the Hundreds Digit*

There are only two possible number that can be placed in the hundred’s digit. Since the number that we are looking for is more than 300, we cannot place 2 in the hundred’s digit. Also, we cannot place 8 in the hundred’s digit since it will be more than 800. Therefore, we can only choose between 5 and 6. Since we want the largest number, we have to choose 6. So our number is 6AB where A and B are the tens and the ones digit respectively.

*Selecting the Tens Digit*

The digits cannot be repeated, so we cannot choose 6 anymore. We are only left with 2, 5, and 8. We want the largest number, so we place the largest digit in the highest place value. Therefore, we choose 8.

So, our number is 68B where B is the ones digit.

*Selecting the Ones Digit*

The digits cannot be repeated, so we cannot choose 6 and 8 anymore. We are only left with 2 and 5. Since we want the largest number, we choose 5 since 5 is greater than 2.

Therefore, the 3-digit that we are looking for is 685.

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