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Special number

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There are random numbers generators. It's a well known fact. But a less known fact is that every random number generator has its inventory imp. Its job is to supervisor the generated numbers so that all numbers are generated equally.
 
Our imp's name is Igor and he is working for such a number generator that can generate up to ten digit numbers, while no such number with all same digits can be generated (they don't look random enough).
 
His job is to write down every generated number (right aligned) and its inventory number. The inventory number says, how many digits of each were used in the random number. In the example you can see the generated random number 7970123 as well as its inventory number.
 
Yesterday, a strange situation happened. After Igor wrote down another inventory number that day, he found out, it was completely same as the random number it belongs to!
 
What number was it?
 
 

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6210001000



I can explain the process that I used in more depth if needed...but it's really not too difficult if you begin by choosing the first number in the randomly generated number and start filling in the inventory number step by step based on that...I started this process with the number starting with 9 and worked my way backwards, but you could do it starting at 1 and work your way up.

As you do that, you'll find that the generated number can't start with a 9, 8, or 7...you eventually get to numbers that start with 6:
6 ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? 1 ? ? ?

6 ? ? ? ? ? 1 ? ? ?
? 1 ? ? ? ? 1 ? ? ?

6 1 ? ? ? ? 1 ? ? ?
? 2 ? ? ? ? 1 ? ? ?

 

Have to change our generated number to match the inventory number...

6 2 ? ? ? ? 1 ? ? ?
? 2 1 ? ? ? ? ? ? ?

6 2 1 ? ? ? 1 ? ? ?
? 2 1 ? ? ? 1 ? ? ?

6 2 1 ? ? ? 1 ? ? ?
6 2 1 ? ? ? 1 ? ? ?

6210001000

Edited by Pickett
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