HMMT 2014 U2

Let $x_{1}, \ldots, x_{100}$ be defined so that for each $i, x_{i}$ is a (uniformly) random integer between 1 and 6 inclusive. Find the expected number of integers in the set $\left\{x_{1}, x_{1}+x_{2}, \ldots, x_{1}+x_{2}+\ldots+x_{100}\right\}$ that are multiples of 6 .