What is the smallest 3-digit number of the form $aaa$ such that it is divisible by 9? (Here, $a$ represents a digit.)
I know that a number is divisible by 9 if and only if the sum of its digits is divisible by 9. So, I want to find the smallest value of $a$ such that $3a$ is divisible by 9. I can try different values of $a$ starting from 1 and see when I get a multiple of 9. If $a = 1$, then $3a = 3$, which is not divisible by 9. If $a = 2$, then $3a = 6$, which is not divisible by 9. If $s = 3$, then $3a = 9$, which is divisible by 9. So, the smallest value of $a$ that works is 3. Therefore, the smallest 3-digit number of the form $aaa$ that is divisible by 9 is $333$. 