Suppose we have a number with the following format ($9$ digits): $$\mathrm{xxxxxxxxx}$$ Now, suppose we have $100,000$ numbers using the left $5$ digits in the above format.

How many 6, 7 and 8 numbers can be generated without any overlap with 5 digits, 6 digits and 7 digits number, using the left 6, 7 and 8 digits of the format?

The remaining numbers of the format could be any thing.

I know that there is $100K$, $1M$, $10M$ and $100M$ numbers can be generated using the left digits. But I don't know about the overlaps between the generated numbers.

An example:
$5$ digit number: 101010000
$6$ digit number: 101010000

We can't recognize the difference of the numbers.


If you have $100,000$ five digit numbers you have all of them, from $00000$ through $99999$. That means you cannot generate any $6,7,8$ digit numbers without overlap. For each five digit number you delete from the list, you can add $10$ six digit numbers, or $100$ seven digit numbers, or $1000$ eight digit numbers or some mix of them.


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