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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?

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

1 Answer 1

up vote 2 down vote accepted

This seems correct. Any other 12-digit number with a digit sum of 80 has to be larger than this one, because one of the digits in the first, second, third or fourth spots would have to increase.

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