jmc

Looking at the values, we notice that $11-7=4$, $9-5=4$ and $6-2=4$. This means we are looking for a value that is four less than a multiple of $11$, $9$, and $6$. The least common multiple of these numbers is $11\cdot 3^2\cdot 2=198$, so the numbers that fulfill this can be written as $198k-4$, where $k$ is a positive integer. This value is only a three-digit integer when $k$ is $1,2,3,4$ or $5$, which gives $194,392,590,788,$ and $986$ respectively. Thus, we have $5$ values, so our answer is $\boxed{5}$.