Let's consider all 4 digits sequences:
0000 0001 0002 ... 9999
Obviously there is a large sequence containing all of them as substrings (the concatenation of all of them).
My question is, what is the length of the smallest possible such sequence (since the minimum is attained)?
For 1 digit, the answer is clearly :
(or any permutation).
For 2 digits numbers, it it can be shortened, since "001" contains both "00" and "01".
But I have no clue on how to get to a definitive answer.
I spotted this similar question, but I'm not interested in the permutations of the alphabet, but 4-sequences.