A 9-bit string is a string of length 9 made of 0’s & 1’s.
There are different 9-bit strings.
If we have a collection of 513 9-bit strings then at least two are equal.
Now think of a SS#, change all the nonzero digits to 1’s.
EX: 120-90-1109 becomes 110101101 & 430-20-5402 becomes 110101101.
That is one 9-bit string. Can you finish?