Australian AMC 2015 - Senior Question 27

A $100\times 100\times 100$ cube $PQRSTUVW$ is made of $1\times 1\times 1$ non-overlapping cubes. $Z$ is a point on $PS$ such that $PZ=33$. Through how many of these $1\times 1\times 1$ cubes does $VZ$ pass?