Could you please help me with the following problem, How many different 4-digit numbers are there that use each of the digits 7,8,9,and 0? Please list them.

Ryan ( student,grade 4)

Hi Ryan,

Imagine that you have a small pad of paper and you are going to write one 4-digit number on each page from the pad. Tear of the first page and write 7 on it.


If you now want to add a second digit you can add an 8, a 9 or a 0, so you need to take two more pages from the pad and write

7 8    
7 9    
7 0    

To add a third digit to any one of the pages you have two choices. For example the page that starts 78 you can extend to 789 or 780. So now you have

7 8 9  
7 8 0  
7 9 8  
7 9 0  
7 0 8  
7 0 9  

Finally for each of the six pages above you only have one digit that can be added. Thus the list so far is

7 8 9 0
7 8 0 9
7 9 8 0
7 9 0 8
7 0 8 9
7 0 9 8

This is the list of all 4-digit numbers that start with 7 and use each of the digits 7,8,9,and 0?

Now repeat this process but start with 8 rather than 7. Do it again, starting with 9 and finally do it starting with 0.


In October 2018 we received the following question from Pamela.

My daughter was given this question which you had answered:

However, her teacher said that any number combination beginning with "0" would not count as a four digit number.
I noticed in your response you said to complete it starting with zero.
Could you please clarify for me if in fact the numbers that start with 0 (0789, 0879, etc.) are three digit or four digit numbers and explain why?


Hi Pamela,

Your daughter's teacher is correct. My last statement should have been "Do it again, starting with 9.You can't start with zero as that would give a three digit number."

Thanks for pointing out my error.



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