1. Find all such numbers $k$ for which

$$
(k / 2)!(k / 4)=2016+k^{2}
$$

The symbol $n!$ denotes the factorial of the number $n$, which is the product of all integers from 1 to $n$ inclusive (defined only for non-negative integers; $0!=1$).
Solution. Note that the left side makes sense only for even values of $k$. We directly verify that $k=2,4,6,8,10$ do not work, while $k=12$ gives a correct equality.

With each further increase of $k$ by 2, the expression $(k / 2)!$ increases by at least 7 times, i.e., the left side grows by more than 7 times. At the same time, the right side increases by less than double: $(k+1)^{2}-k^{2}<12$. Therefore, for $k>12$, the left side is greater than the right side.

Answer: $k=12$.