Question 11
For any positive integer $x$, define $\operatorname{Accident}(x)$ to be the set of ordered pairs $(s, t)$ with $s \in \{0,2,4,5,7,9,11\}$ and $t \in \{1,3,6,8,10\}$ such that $x+s-t$ is divisible by $12$. For any nonnegative integer $i$, let $a_{i}$ denote the number of $x \in \{0,1, \ldots, 11\}$ for which $|\operatorname{Accident}(x)|=i$. Find
$$
a_{0}^{2}+a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+a_{5}^{2}
$$
$$
a_{0}^{2}+a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+a_{5}^{2}
$$