# Kiriti's number

Number Theory Level 4

Let $$N$$ be the smallest positive integer such that the product of $$99$$ and $$N$$ is a number with all digits $$1$$. What is the digit sum of $$N$$?

This problem is posed by Kiriti M.

Details and assumptions

The digit sum of a number is the sum of all its digits. For example the digit sum of 1123 is $$1 + 1 + 2 + 3 = 7$$.

×