I was trying to formulate some problem. I want to find a relation between a floor and ceiling function. Suppose the Property 1 satisfies that it has $\lfloor \frac{n}{2} \rfloor$ number of $X$. Then the Property 2 satisfies that it has $k = \lceil \frac{d}{2} \rceil$ where $d = \lfloor \frac{n}{2} \rfloor$. I tried to put $k = \lceil \frac{n}{4} \rceil$ but it is contradicting for some values of $n$. Like if I take $n = 9$, then
$d = \lfloor \frac{9}{2} \rfloor$ $\Rightarrow d = 4$ and thus $k = 2$.
But if I take $k = \lceil \frac{n}{4} \rceil$ then $k = \lceil \frac{9}{4} \rceil$ $\Rightarrow k = 3$
which contradicts. Is there any way to find the relation between $n$ and $k$ directly. Kindly help. My data is given below for different values of $n$.