**Spoiler: Bad English Ahead!!**

(1a) The question I want to ask is in the topic. I am trying to find if there is some generalized way to find the minimum number that "contain" all n-digit (or below) number, as "substrings".

(1b) If there isn't, is there anyway to find out the number of digits of the number?

i.e. for n = 1, I am trying to find the number that contains all the 1-digit number i.e. "0 ~ 9" (0 is 1-digit)

which turns out to be

1023456789, with 10 digits.

As a little "Extension" to (1b), can all the subsequence substrings with "length 2" for the "n=2" case contain all 2-digit number without repeat?

for example: suppose the answer be "1295837152"

All the substrings in the answer are:

12,29,95,58,83,37,71,15,52

which do not repeat.

And in general, how about for "n = k"? (k is positive integers)

(n=1 is True, since the substrings in 1023456789 are just the 1-digit numbers, which would be distinct)