Name: Valerie
Level: Secondary
From: Student

Question:

How many social security numbers are possible?

the answer is 10^9

why isn't the answer 9^9?

Hi Valerie,
I am no expert on this but I will attempt an answer. Math Central is in Canada and we don't have social security numbers but I asked a friend who is from the US and he showed me his social security number. It looks like xxx-xx-xxxx where the x's are digits. My guess is that the difference between the 9^9 that you got and the 10^9 that was expected is in whether zero is allowed as one of the digits. Is 076-50-0090 a valid social security number? I expect that it is. If so then the number has 9 digits, each of which is from 0,1,2,...,9, and hence there are 10^9 possibilities.

Cheers,
Harley