2003 AMC 12B Question 8

Let $\clubsuit(x)$ denote the sum of the digits of the positive integer $x.$ For example, $\clubsuit(8) = 8$ and $\clubsuit(123) = 1 + 2 + 3 = 6.$ For how many two-digit values of $x$ is $\clubsuit(\clubsuit(x)) = 3?$