Question 13
Ben has 16 balls labeled $1$, $2$, $3$, $\ldots$, $16$, as well as 4 indistinguishable boxes. Two balls are neighbors if their labels differ by $1$. Compute the number of ways for him to put 4 balls in each box such that each ball is in the same box as at least one of its neighbors. (The order in which the balls are placed does not matter.)