Given all the digits $0,\dots,9$ and using each digit exactly once,
What is the smallest possible number you can make whose digits are all $1$'s?
The only operations that are allowed are:
- addition ($+$)
- concatenation
and you can concatenate after a sum, or practically anywhere.
So, for example, $87+24=111$ - let us call this an answer of length 3 - and then $\operatorname{concat}(111,1)$ to give $1111$, an answer of length 4.
In this example, I have only used the digits $2, 4, 7, 8$ and $1$, but in your answer you must use ALL the digits from $0,\dots,9$.
You can also concatenate during a sum, for example:
- $\operatorname{concat}(3+4,\operatorname{concat}(1,2))$
gives $712$
whereas:
- $\operatorname{concat}(\operatorname{concat}(1,2),3+4)$
gives $127$
and:
- $\operatorname{concat}(\operatorname{concat}(3,4),1+2)$
gives $343$.
Good luck!!!