US currency serial numbers have an 8-digit interior number. Fresh bills from the bank often have consecutive serial numbers, sometimes with a run of five or ten bills. We used to play dollar-bill poker in high school, which proved to be a useful exercise in combinatorics and probability. (Should 11122334 rank above or below 11223344?) (This was c. 1963. I just looked closely at a bill and notice they've moved the serial number, but it still has the 8 interior digits. The surrounding letters must also be part of the "serial number", since 10^8 bills would be inadequate to uniquely distinguish the circulating currency.) Also c. 1965, I was coding some business program for an IBM customer, and was given a check-digit algorithm that alternately added and subtracted digits. Perhaps we took the result mod 10 to get the check; I can't recall. I've made consecutive internet car reservations with Avis late at night, and the confirmation numbers they provide have some simple check digits. More scarily, I made two tax-extension phone calls to the IRS a few years ago. You call their automated system and key in various info, and promise to mail a check. They provide a confirmation number which appears to be a serious attempt at scrambling, but it's no good. Rich -----Original Message----- From: math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com on behalf of Thane Plambeck Sent: Wed 5/17/2006 11:22 PM To: math-fun Subject: [math-fun] big numbers and how they're made I bought this book, "Identification Numbers and Check Digit Schemes" in the hopes that it would describe the ID number / checksum / hashing schemes actually used in some real applications. I'd like to give a talk on the subject to a general audience. http://www.amazon.com/gp/product/0883857200/104-8328046-6239112?v=glance&n=2... However, this book left me unsatisfied. Ideally, I'd like to know, for example, how to distinguish between a valid UPS tracking number and an invalid one, or (say) a valid US twenty dollar bill serial number and an invalid one. UPS tracking#: 1Z9999999999999999 US $20 bill, Series 2004: EB 42994244 D Such schemes are presumably often proprietary / unpublished, for security reasons, although the "there is no security through obscurity" maxim would seem to apply. Googling hasn't turned up much, except in a few unsavory hacking resources (mostly how to forge a valid credit card number) Anyone know a good resource? -- Thane Plambeck http://www.plambeck.org/ehome.htm _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun