Cardinal of the quotient set

Question

Let $X = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$. In $X \times X$ define the equivalence $(a,b)\:\mathcal{R}\:(c,d)$ if $a+b=c+d$. Then what is the cardinal of the quotient set?

I know that $|X| = 9$, so $| X \times X | = |X| |X| = 81$. But how use the relation for the cardinal of the quotient set?

Thank you.

Answer 1

Hint

Let $r = a+b$ with $a,b\in X$

How many different values can $r$ have?