Question 79
For a real number $t$, $\lfloor t \rfloor$ is the greatest integer less than or equal to $t$ and $\{ t \} = t - \lfloor t \rfloor$ is the fractional part of $t$. How many real numbers $x$ between $1$ and $23$ satisfy $\lfloor x \rfloor \{ x \} = 2 \sqrt{x}$?