Finding the Missing Digit of a 5-Digit Number

[BobG]

I have a five digit number - no, it's not that easy
I rearrange the digits and subtract the smaller number from the larger.

The difference is also a five digit number. I jumble up the digits of the difference. Four of the digits of the difference are 2172.

What's the missing digit of the difference?

 

[TenaliRaman]

brute force , hapahazard hand waving and abra cadabras are giving me the missing digit as ::6::

Let me see if i can see through some technique here ...
interesting problem btw.

-- AI

 

[Tide]

The missing digit would have to be 6 since the difference must be a multiple of 9.

 

[TenaliRaman]

duh! ofcourse!

-- AI
**i should sincerely stop playing notpron, i am losing sight of the obvious**

 

[eddo]

i'm missing something, why does it have to be a multiple of 9?

 

[Rogerio]

i'm missing something, why does it have to be a multiple of 9?

Remember (10^k - 1) is always multiple of 9.
So, for each digit A , you have:
A*10^n - A*10^m = A*(10^n - 10^m) which is multiple of 9 .