Exactly what the title says: What is the shortest (fewest digits) number you can find such that somewhere in it, you can find each number 1- 100?
My thinking for this puzzle is you have an electric numeric lock that can have any code from 1-100 and you want to try all possibilities in the shortest time. (Assuming you don't have to push enter or whatever).
1-10 can be 1023456789
1-11 can be 11023456789
1-12 can be 110123456789
Also, is there some sort of formula that can extend this to other numbers (1-1000, 1-50, ...)