# How many 6, 7 and 8 digits could be generated

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.