Question 104
A positive integer $n$ is magical if
$$
\lfloor\sqrt{\lceil\sqrt{n}\rceil}\rfloor=\lceil\sqrt{\lfloor\sqrt{n}\rfloor}\rceil,
$$
where $\lfloor\cdot\rfloor$ and $\lceil\cdot\rceil$ represent the floor and ceiling function respectively. Find the number of magical integers between 1 and 10,000, inclusive.
$$
\lfloor\sqrt{\lceil\sqrt{n}\rceil}\rfloor=\lceil\sqrt{\lfloor\sqrt{n}\rfloor}\rceil,
$$
where $\lfloor\cdot\rfloor$ and $\lceil\cdot\rceil$ represent the floor and ceiling function respectively. Find the number of magical integers between 1 and 10,000, inclusive.