Make the Smallest and Largest Three-Digit Numbers

In this activity, we are going to make the largest and smallest three-digit numbers from five given digits.

 

Let's pretend we can only use the digits 2, 3, 4, 5 and 6.

 

To make the largest number:

Start with the largest digit in the hundreds column.

This is 6.

 

Then comes the next largest digit down in the tens column.

This is 5.

 

Lastly, comes the next largest digit in the ones column.

This is 4.

 

The largest number is  654

Did you notice that we didn't need to use the two smallest numbers, 2 and 3, to make this number?

 

To make the smallest number:

Start with the smallest digit in the hundreds column.

This is 2.

 

Then comes the next largest digit in the tens column.

This is 3.

 

Lastly, comes the next largest digit  in the ones column.

This is 4.

 

The smallest number is  234.

Did you notice that we didn't need to use the two largest numbers, 5 and 6 this time, to make this number?

 

Let's try an example question together using the same method. 

 

Example

Using any three of the digits from:

68671

make the smallest and largest three-digit numbers that you can make.

Answer

First, we should put the digits in order:

1, 6, 6, 7, 8

 

To find the smallest three-digit number we do the following:

1 is the smallest digit.

6 is the next largest digit.

6 is the next largest digit, even though it is the same as the last one.

 

So, the smallest number will be 166.

 

Now to find the largest possible three-digit number:

8 is the largest digit.

7 is the next digit down.

6 is the next digit down.

 

So, the largest number will be 876.

 

Now that you've seen a good method, it's time to try some questions on your own. 

 

Are you ready to start?