Question 114
For positive integer $n$, $a_n = n\sqrt{5} - \lfloor n\sqrt{5} \rfloor$. Compute the maximum value and the minimum value of $a_1, a_2, \dots, a_{2009}$. (For real number $x$, $\lfloor x \rfloor$ denotes the greatest integer less than or equal to $x$.) (Posed by Wang Zhixiong)