# 2021 April MIMC 10 Problems/Problem 21

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

How many solutions are there for the equation $\left \lfloor{x}\right \rfloor^{2}-\left \lceil{x}\right \rceil=0$. (Recall that $\left \lfloor{x}\right \rfloor$ is the largest integer less than $x$, and $\left \lceil{x}\right \rceil$ is the smallest integer larger than $x$.)

$\textbf{(A)} ~0 \qquad\textbf{(B)} ~1 \qquad\textbf{(C)} ~2 \qquad\textbf{(D)} ~3 \qquad\textbf{(E)} ~4 \qquad$