For $1 \le n \le 100$, how many integers are there such that $\frac{n}{n+1}$ is a repeating decimal?

This question has already been answered on StackExchange. It's a pretty neat solution imo. 

Link: https://math.stackexchange.com/questions/1463896/for-1-leq-n-leq-100-how-many-integers-are-there-such-that-fracnn1-is-a