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* * * OFF TOPIC * * * Permutations of matching 7 out of 9 numbers

Posted By: leobueno
Date: Wednesday, 16 March 2016, at 10:07 p.m.

For our non-US members, a bit of introduction (from Wikipedia) is due.

In the United States, a Social Security number (SSN) is a nine-digit number issued to U.S. citizens, permanent residents and temporary (working) residents.

The number is issued to an individual by the Social Security Administration, an independent agency of the United States government.

Although its primary purpose is to track individuals for Social Security purposes, the Social Security number has become a de facto national identification number for taxation and other purposes.

The SSN is one of the principal identifies used by credit bureaus, along with a person's date of birth, and other characteristics (matching elements) to identify people in their databases.

This post concerns the use of partial matching of SSNs as a personal identifier.

For one of the credit bureaus, 7 of 9 numbers is a good enough matching element. Here is what it said in a case where two people's information was improperly commingled:

* * *

Q. You said their Social Security numbers were similar, but you agree they were different?

A. Yes. They are different. They're what we call a seven-for-nine Social Security number. And a seven-for-nine is that -- seven of the nine digits match exactly, or are in -- and are in the same place in the -- in the Social Security number. What is different is in two places in the Social Security number, there are different numbers. They differ.

* * *

Note these restrictions. Some special numbers are never allocated: Numbers with all zeros in any digit group (000-##-####, ###-00-####, ###-##-0000). Numbers with 666 or 900-999 in the first digit group.

Here is the question: How many permutations of a 7 for 9 SSN are there?

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