# The smallest 12 digit natural number for which the sum of its digits is 80.

So everytime I heard the word smallest natural number of 5 digits for example I do this in my head:

100000...
^
|


which means that there must be a one in there:

So I type in 1000 and then add more digits to have $$1000\,9999\,9999$$

Now into my calculator I calculated that this is is not 80 rather just 73, so I'll have to add a 7 out there to have $$1007\,9999\,9999$$

But is my answer correct? If not why my method fails and what is the correct method?

-
I would say that your reasoning is valid, perfect in fact. –  Lee Yiyuan Mar 7 at 18:57