Ex Parte Menendez et al

Patent Trial and Appeal Board

May 2, 2017

12650040 (P.T.A.B. May. 2, 2017)

United States Patent and Trademark Office
UNITED STATES DEPARTMENT OF COMMERCE
United States Patent and Trademark Office
Address: COMMISSIONER FOR PATENTS
P.O.Box 1450
Alexandria, Virginia 22313-1450
www.uspto.gov
APPLICATION NO. FILING DATE FIRST NAMED INVENTOR ATTORNEY DOCKET NO. CONFIRMATION NO.
12/650,040 12/30/2009 Nereida Maria Menendez 51017-84535 6586
21888 7590 05/04/2017
THOMPSON OORT TRN T T P
EXAMINER
ONE US BANK PLAZA VIG, NARESH
SUITE 3500
ST LOUIS, MO 63101 ART UNIT PAPER NUMBER
3622
NOTIFICATION DATE DELIVERY MODE
05/04/2017 ELECTRONIC
Please find below and/or attached an Office communication concerning this application or proceeding.
The time period for reply, if any, is set in the attached communication.
Notice of the Office communication was sent electronically on above-indicated "Notification Date" to the
following e-mail address(es):
IPDOCKET@THOMPSONCOBURN.COM
PTOL-90A (Rev. 04/07)
UNITED STATES PATENT AND TRADEMARK OFFICE
BEFORE THE PATENT TRIAL AND APPEAL BOARD
Ex parte NEREIDA MARIA MENENDEZ,
PAULA S. WILLIAMS,
and MICHAEL J. MANIS
Appeal 2014—008688
Application 12/650,040
Technology Center 3600
Before ANTON W. FETTING, MICHAEL W. KIM, and
NINA L. MEDLOCK, Administrative Patent Judges.
FETTING, Administrative Patent Judge.
DECISION ON APPEAL
STATEMENT OF THE CASE1
Appellants seek review under 35 U.S.C. § 134 of a non—final rejection
of claims 1—8, 13—29, 32—35, 37-41, 46—62, 65, 66, and 75—82, the only
claims pending in the application on appeal. We have jurisdiction over the
appeal pursuant to 35 U.S.C. § 6(b).
1 Our decision will make reference to the Appellants’ Appeal Brief (“Br.,”
filed April 12, 2014) and the Examiner’s Answer (“Ans.,” mailed June 10,
2014), and Non-Final Action (“Non-Final Act.,” mailed June 13, 2013).
Appeal 2014-008688
Application 12/650,040
The Appellants invented a way of completing a rental agreement for
an item or service, such as a vehicle rental service. Specification 1:23—24.
An understanding of the invention can be derived from a reading of
exemplary claim 1, which is reproduced below (bracketed matter and some
paragraphing added).
1. A method of creating and storing an electronic rental
contract for a rental vehicle from a rental car company to permit
a user to bypass a rental counter of a car rental facility when
creating the electronic rental contract, the method comprising:
[1] creating, by a server system, a rental vehicle
reservation in response to data received from a client system
through a website, the website comprising a plurality of web
pages for access over a network by the client system;
[2] storing, by the server system, a reservation
transaction, wherein the reservation transaction is representative
of the created rental vehicle reservation;
[3] accepting, by the server system, input that is
indicative of a request by the user to create an electronic rental
contract for a rental vehicle;
[4] communicating, by the server system, data for display
to the user via a screen, the communicated data configured to
solicit additional data input from the user for a potential rental
by the user of a rental vehicle based on the rental vehicle
reservation;
[5] accepting, by the server system, the additional data in
response to input by the user;
[6] determining, by the server system, whether the user
has a pre-existing customer relationship with the rental car
company, the pre-existing customer relationship with the rental
car company being at least one member of the group consisting
of a club membership with the rental car company and being a
party to a master rental agreement (MRA) with the rental car
company;
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and
[7] in response to the server system determining that the
user does not have the pre-existing customer relationship,
(1) communicating, by the server system, an
electronic rental proposal for display to the user, the
electronic rental proposal being based on the rental
vehicle reservation and the accepted additional data,
(2) creating, by the server system, the electronic
rental contract in response to an electronic acceptance by
the user of the electronic rental proposal, the electronic
rental contract permitting the user to avoid creating a
rental contract at the rental counter when arriving at the
car rental facility to pick up a rental vehicle in
accordance with the electronic rental contract,
(3) storing, by the server system, a rental
transaction, wherein the rental transaction is
representative of the created electronic rental contract,
and
(4) communicating, by the server system, a
confirmation of the created electronic rental contract for
display to the user via a screen.
The Examiner relies upon the following prior art:
Information on Hertz Corporation, archived web pages printed
through www.archive.org (1997—2000) (Hertz).
Avis Rent A Car — Rates and Reservations,
http://www.avis.com/rates_and_reservations/ (last visited March 03,
2000) (Avis).
Hertz Announces New, Elite Levels for #1 Club Gold Members in
the US, 11 July 2000, PRNewswire Association, Inc. (Hertz Gold).
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In addition, the following references are newly cited:
Burch, Rental Car Companies Check Drivers’ Records, Sun
Sentinel,
http://articles.sunsentinel.coin/19930812/business/9301290359 1 cardri
versmotorvehicles, August 12, 1993 (Burch).
Gallian, Assigning Driver’s License Numbers, Mathematics
Magazine, pp. 13—22, v. 64, n. 1, February 1991 (Gallian).
Claims 1—8, 13—29, 32—35, 37—41, 46—62, 65, 66, and 75—82 stand
rejected under 35 U.S.C. § 103(a) as unpatentable over Hertz, Avis, and
HertzGold.
ISSUES
The issues of obviousness turn primarily on whether there is a
patentable distinction between a reservation and a contract, whether it was
predictable to automate a known manual process, and whether one of
ordinary skill in the art at the time of Appellants’ invention knew it was
possible to validate a driver license using automation.
FACTS PERTINENT TO THE ISSUES
The following enumerated Findings of Fact (FF) are believed to be
supported by a preponderance of the evidence.
Facts Related to the Prior Art
Hertz
01. Hertz is a web site for Hertz, the car rental
company, which provides the contents of the legal requirements
for its agreements and provides screens for customers to enter
rental reservations. Hertz 1—61.
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02. Hertz describes its system as allowing a customer
to make, modify, or cancel a reservation. Hertz 27.
03. Hertz describes the use of a customer profile for
entering data into a reservation. Hertz 17.
04. Hertz portrays radio button selection of entry by
customers with existing profiles and general customers. Hertz 36.
05. Hertz describes an offer for a rental vehicle for
value containing the material terms of the agreement, and
requesting acceptance by the customer. Hertz 44-46.
06. Hertz shows separate screens for initially
requesting dates and locations (Hertz 18) and for auto selection
and pricing (Hertz 24) and for additional promotions. Hertz 26.
07. Hertz describes using the master agreement data
for filling in a reservation. Hertz 27.
Avis
08. Avis describes entry and storage of a vehicle rental
reservation. Avis 1—13.
Hertz Gold
09. Hertz Gold describes offering members an
automatic invitation to move up to #1 Club Gold after completing
four rentals. Hertz Gold 1.
10. “In 1972, Hertz became the first car rental
company to recognize the strategic value of maintaining a
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customer profile database, with the introduction of Hertz #1 Club.
The service created a data file for each customer, by maintaining
driver’s license information, home address, car class information
and credit card information for instant recall. For Hertz’
customers; #1 Club helped reduce time spent making reservations
and sped the process when renting a car.” Hertz Gold 1—2.
11. “After implementing #1 Club service, Hertz
recognized the additional customer benefit to not only keeping an
active profile on customers, but also allowing] customers to
bypass the counter altogether, with the keys and completed rental
agreement ready and waiting for them.” Hertz Gold 2.
Burch
12. Burch describes how rental car companies are
checking drivers’ records from their licenses. Burch 1.
13. Burch describes that the driving record check is
performed online in less than a minute, so as not to delay the
rental transaction. Burch 1.
Gallian
14. Gallian describes how driver license numbers are
assigned. Gallian 13:Title.
15. Gallian describes how driver license numbers are
encoded for possible detection of forgery or errors.
Gallian 13: Introduction.
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ANALYSIS
This is one of three applications before us with similar claims to a car
rental system and method. The other two applications are Serial
Nos. 12/650,113 and 09/698,502. The claims in all three applications
generally recite performing an online car rental reservation that results in a
rental contract. The claims in all three applications also recite doing so in a
single session, without a customer having to visit a customer service counter
and without requiring a pre-existing relationship or master rental agreement
between the customer and the car rental company.
Method claim 1 and apparatus claim 35 are the sole independent
claims. The independent claims describe the basic steps in contracting for a
rental car. First the customer provides the information for basic availability,
such as dates and location of pickup and return. The vendor then responds
with what is available, and allows the customer to refine the request within
those parameters, such as class of car and price levels. The customer then
asks for a specific quote, and then, if the customer accepts, the customer
provides license and credit card information if it is not already of record and
contracts for the rental. The screen prints of the Hertz web site of record are
evidence of this flow. FF l.2
That the prior art describes the above is not in dispute. Instead, what
is disputed is the timing and location of these steps. In particular, the claims
recite that both the reservation and contract are made in a single session, and
2 We discern that the above flow comports with the common experience of
anyone who has rented a car.
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this is done without the customer going to a customer service counter, and is
done irrespective of whether there is some pre-existing relationship or
agreement between the customer and the car rental company. Appellants
argue that the prior art does not describe these limitations. Appellants also
nominally contend the limitations regarding the reservation process are
separated by some customer data entry steps, and the reservation and
contract steps are separated by customer acceptance steps, but these
arguments appear to be related to the single session argument as, again,
whether Hertz discloses the basic flow of data is not in dispute.
Before analyzing the specific comparisons between the claims and the
prior art, we will summarize the issues that these claims raise, because of
their number and complexity. First, the claims recite data entry and little
else. Data per se are no more than arbitrary (based on arbitrary coding
conventions) strings of binary digits irrespective of the labels attached, and,
without some explicit functionality dependent on the differences between the
actual labels, the labels are afforded no patentable weight. Absent some
functional effect, there is no patentable distinction between a master rental
agreement, a reservation, and a contract, as all are printed matter or binary
data. Absent some functional effect, any legal effect attaching to a contract
is a nullity in patent law. What is left is conventional data entry. Second,
we find that it would have been predictable to consolidate data entry, even if
the labels were given patentable weight. FF 1—11. Third, we find that it
would have been predictable for a customer to perform the same data entry
that someone at a customer service counter would perform. FF 10—11.
Fourth, the above-cited prior art describes a promotional program that allows
the customer to do just that, and avoid a customer service counter. Id. Fifth,
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even if weight were afforded to the label of a master service agreement, we
find that there is nothing about the absence of such an agreement or
relationship that would present a logistical hurdle to entering the data related
to a master agreement and reservation in a single session. FF 1—11. Sixth,
even if the master rental agreement contains data necessary for a rental, we
find that it would have been predictable to enter that same data during the
reservation and contracting phases in the absence of a master rental
agreement. Id. Seventh, we find that it was predictable to have a customer
contract for the car immediately after, and in the same session, as obtaining a
reservation. Id.
The dependent claims further recite driver license data entry and
validation. We enter Gallian and Burch as new art that shows it was known
to ask for such data and validate it online at the time of the invention.
Even before comparing the claims to the prior art, we discern that
Appellants have a high hurdle in terms of claim breadth and patentable
weight. The instant claims do not recite limitations not described in the
prior art. Rather, the claims recite not requiring portions of the car rental
experience that are described in the prior art. Removing something known
from a known process, without changing the result of the process, is
invariably predictable, unless the absence of that something is a technical
barrier to the process. This is a corollary to the volition involved in
performing the process and its steps. Nothing in the claims presents a
technical barrier that is overcome by the steps recited. The claimed
procedure is entirely volitional, and is unconstrained by inhibitory structure,
physical properties, or attributes. Equally, the claims do not recite removing
such a technical barrier. Instead, Appellants posit an industry convention of
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using a customer service counter and separating the reservation and contract
in time, and it is this separation that they suggest circumventing. As a
convention, there is nothing about using a service counter that makes
avoiding it atypical. One of ordinary skill would have known that such a
modification has readily apparent costs and benefits, and using a service
counter or not using a service counter is simply based on weighing those
readily apparent costs and benefits. KSR Int’l Co. v. Teleflex Inc., 550 U.S.
398, 421 (2007) (“A person of ordinary skill is also a person of ordinary
creativity, not an automaton.”); Winner v. Wang, 202 F.3d 1340, 1349 (Fed.
Cir. 2000) (“the district court did not clearly err in finding that one of
ordinary skill in the art would not have reasonably elected trading the benefit
of security for that of convenience. Trade-offs often concern what is
feasible, not what is, on balance, desirable. Motivation to combine requires
the latter.”).
Appellants have not identified any technological hurdle in avoiding a
customer service counter. The claims do not recite any action that would
ordinarily otherwise require, as contrasted with prefer, such a counter.
Appellants have not identified any technological hurdle to performing two
sets of data entry in a single session. The claims do not recite any action that
would ordinarily otherwise require, as contrasted with prefer, plural
sessions. Appellants have not identified any technological hurdle to
performing a second set of data entry in the same session as a first,
irrespective of the existence of some relationship between the customer and
the car rental company. The claims do not recite any action that would
ordinarily otherwise require, as contrasted with prefer, premising a second
data entry on the existence or lack thereof of such a relationship.
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As to the issue of adding data, we find that data editing is a
notoriously well-known mechanism where data, that were not there prior to
the editing, are added; this is not a significant issue. More to the point, the
distinct items of data that must be in place for a rental contract, but not
necessarily for a reservation, are a credit card and driver license. FF 6, 10—
11. We find that adding such data, after seeing that a rental is available in
the form of a reservation, would not only have been predictable, but would
have been immediately envisaged by one of ordinary skill. FF 10.
Not only would have avoiding a counter been predictable, HertzGold
shows it was known to combine a reservation and contract in a single visit,
and that avoiding such a counter was preferable. FF 10-11. Appellants
counter that HertzGold requires a master agreement. But a master
agreement is just data collected prior to a rental, as is a reservation. So, the
issue devolves to the patentable weight afforded any distinction between
data gathered prior to rental and data gathered at rental time at a customer
service counter, and the predictability of combining such data gathering.
As to structural inventions, such claims must be distinguished from
the prior art in terms of structure rather than function, see, e.g., In re
Schreiber, 128 F.3d 1473, 1477—78 (Fed. Cir. 1997). In order to satisfy the
functional limitations in an apparatus claim, however, the prior art apparatus
as disclosed must be capable of performing the claimed function. Id.
at 1478. When the functional language is associated with programming, or
some other structure required to perform the function, that programming or
structure must be present in order to meet the claim limitation. Typhoon
Touch Techs., Inc. v. Dell, Inc., 659 F.3d 1376, 1380 (Fed. Cir. 2011)
(discussing Microprocessor Enhancement Corp. v. Texas Instruments, Inc.,
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520 F.3d 1367 (Fed. Cir. 2008)). In some circumstances, generic structural
disclosures may be sufficient to meet the functional requirements, see Ergo
Licensing, LLCv. CareFusion 303, Inc., 673 F.3d 1361, 1364 (Fed. Cir.
2012) (citing Telcordia Techs., Inc. v. Cisco Sys., Inc., 612 F.3d 1365, 1376—
77 (Fed. Cir. 2010)).
Also, a structural invention is not distinguished by the work product it
operates upon, such as data in a computer. “[Expressions relating the
apparatus to contents thereof during an intended operation are of no
significance in determining patentability of the apparatus claim.” Ex parte
Thibault, 164 USPQ 666, 667 (Bd. App. 1969). Furthermore, “inclusion of
material or article worked upon by a structure being claimed does not impart
patentability to the claims.” In re Otto, 312 F.2d 937, 940 (CCPA 1963).
Claim 1 recites seven steps, viz., accept data to create X, store X,
accept input to create Y, solicit data based on X, accept the data, determine
whether Z exists, and if Z does not exist then display W, create Y, store Y,
and display Y, where X is labeled as a rental vehicle reservation, Y is
labeled as an electronic rental contract, Z is labeled as a pre-existing
customer relationship, and W is labeled as a proposal. Thus, the claim is
really to accepting data and soliciting additional data, creating data and
determining whether some criterion of data existence is met, and if not,
accepting, creating, and displaying more data. Nothing in the claim depends
on or enforces the perceptual labels the claim suggests. Mental perceptions
of what data represent are non—functional and given no weight. King
Pharm., Inc. v. Eon Labs, Inc., 616 F.3d 1267, 1279 (Fed. Cir. 2010) (“[T]he
relevant question is whether ‘there exists any new and unobvious functional
relationship between the printed matter and the substrate.’”) (citations
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omitted). See also In re Lowry, 32 F.3d 1579, 1583 (Fed.Cir.1994)
(describing printed matter as “useful and intelligible only to the human
mind”) (quoting In re Bernhart, 417 F.2d 1395, 1399 (CCPA 1969)). Data
labels are just examples of such mental perceptions. Data, being a
succession of binary digits, are just those digits, not perceptual labels of
those digits. The binary digits may, at times, impose some functional
consequence, but absent some recitation of how so, such consequence is not
an issue.
To put this in terms of the test put forward in King, nothing in the
steps depends on or enforces the perception of the data labels, and the data
label perceptions do not functionally affect the steps. The Federal Circuit in
King explicitly urged against non-functional limitations allowing the
indefinite patenting of existing known processes by merely putting those
processes in the context of such non-functional limitations. King Pharm.,
616 F.3d at 1279.
We are not persuaded by Appellants’ argument that a rental
reservation is not a rental contract. App. Br. 10—15. As the Federal Circuit
held, supra, there is no patentable distinction between two non-functional
data sets. Absent some functional effect, which Appellants have not
persuasively identified here, any legal effect attaching to a contract is a
nullity in patent law. Legal status itself is a matter of mental perception and
not physical functional effect, and is relegated to the legal arts, as contrasted
with the useful or technological arts.
We are not persuaded by Appellants’ argument that
the server system creates the rental vehicle reservation
and the electronic rental contract even if it the server system
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determines that the user has no such preexisting customer
relationship with the rental car company. Such a “one touch”
method thus exhibits a stark technical improvement over the
cited art’s “two touch” system.
App. Br. 17 (emphasis omitted). Hertz describes determining whether a
preexisting customer relationship exists for promotional purposes, as well as
administrative purposes. Whether Hertz actually chooses to contract absent
such a preexisting customer relationship is not determinative, as there are
practical reasons, for deciding whether or not to require a trip to a customer
counter. For example, requiring a customer counter experience provides
marketing opportunities for upgrades and accessories, whereas not requiring
it provides simplicity for the customer. FF 6, 11. Claim 1 does not recite or
narrow how the contract is created, and the computer creates the contract,
irrespective of whether the information is entered by the customer or by an
employee at a customer service counter.
Appellants contend that omitting a known practice of having a
customer go to a counter is non-obvious. But omission of an element and its
function in a combination is an obvious expedient if the remaining elements
perform the same functions as before. In re Karlson, 311 F.2d 581, 584
(CCPA 1963). Again, Appellants have not identified sufficiently any
patentable distinction between the initial reservation and the contract, and
even if there were, it was obvious to automate a known manual procedure.
LeapfrogEnt., Inc. v. Fisher-Price, Inc., 485 F.3d 1157, 1161 (Fed. Cir.
2007). Hertz actually describes this automation in the context of a master
agreement. FF 7. There is nothing in the absence of such an agreement that
would have made this unpredictable, as a master agreement simply contains
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data that can be acquired via other methods that would have been known to
one of ordinary skill, for example, direct user input.
We are not persuaded by Appellants’ argument that
the Hertz reference describe an exemption from having to
complete a “driving record certification form” and not an
exemption from completing a rental contract at the rental
counter as recited by claim 1. Page 9 of the Hertz reference
states unequivocally that “[a]n acceptable valid driver's license,
issued from your country of residence, MUST be presented at
time of rental.” (Emphasis in original). Page 9 further states
that ”[a]t some US locations customer/authorized driver may be
subject to an electronic DMV (Division of Motor Vehicles)
check with the issuing State Department of Motor Vehicles or
asked to complete a driving record certification form which is
required prior to renting a vehicle from Hertz.” The next
paragraphs spanning pages 9-10 of the Hertz reference
elaborate on the certifications that a customer must make
through such a form. Thus, the Hertz reference describes that
in addition to presenting a driver’s license at the time of rental,
customers may also be required to complete a verification form
that makes certain certifications regarding the customers’
driving history. As such, this form represents another term and
condition that a customer may be required to agree to in the
course of completing a rental contract at the rental counter.
Page 10 of the Hertz reference (reproduced below) merely
states that some customers are exempt from this additional
requirement to complete a driving record certification form.
App. Br. 18—19 (emphasis omitted). Even granting the requirement for a
license, automation of a known manual activity is obvious. Leapfrog, id. It
is unnecessary to actually see a driver license to validate it, because
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automated systems provide such validation services.3 FF 12—15. We enter
Gallian and Burch as new art that shows it was known to ask for such data
and validate it online, at the time of the invention.
One of ordinary skill would have known that it was the marketing of
promotional activities that prompted Hertz to require trips to the customer
service counter, rather than having a person perform such validation, in view
of the notoriety of much more secure and certain ways of automated
validation. FF 6, 12—15. Because the Examiner did not present this finding,
we will enter the same rejection as a new ground to afford Appellants an
opportunity to respond.
We are not persuaded by Appellants’ argument that
Only the HertzGold reference describes any type of
counter bypass feature, and as explained above and below, this
counter bypass feature is limited to customers who have a
preexisting master rental agreement (MRA) through a frequent
renter club with Hertz. (See also the “Second Declaration of
David G. Smith Pursuant to 37 CFR 1.132” dated April 5,
2013; e.g., paragraph 16 et seq. thereof).
Furthermore, the inclusion of Hertz #1 Club Gold
members on a list with “U.S. Government on official business”
at page 10 of the Hertz reference to identify types of customers
who need not be subjected to a driving record certification that
may be used at some Hertz locations fails to render claim 1
obvious. The reason Hertz #1 Club Gold members are able
avoid completing a rental contract at a rental counter as per the
HertzGold reference is because the Hertz #1 Club Gold
customers have signed a pre-existing MRA. As such, at best,
3 This is known to anyone who has ever been pulled over in a car by a
policeman or seen a representation of this on television.
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page 10 of the Hertz reference in combination with HertzGold
would merely teach that US government employees on official
business might also be entitled to enjoy similar benefits if such
US government employees were also parties to a pre-existing
MRA. There is simply no teaching in any of the cited
references that counter bypass capability should be extended to
customers without pre-existing MRAs. Any interpretation of
the cited references to the contrary would require the improper
use of hindsight based on the teachings of the subject patent
application as opposed to the state of the art at the time of
invention.
App. Br. 20 (emphasis omitted). Our analysis of the prior argument applies
here as well. Again, we are unpersuaded that it is hindsight to volitionally
eliminate a known step that does not alter the function.
We are not persuaded by Appellants’ argument that
the Office Action alleges that the Hertz and Avis
references disclose the step in claim 1 that recites “accepting,
by the server system, input that is indicative of a request by the
user to create an electronic rental contract for a rental vehicle.”
The Office Action cites to pages 67—68 of Hertz to support this
statement. The Office Action fails to cite to any passage in the
Avis reference in support of this statement. However, the Hertz
reference as understood by Applicant only includes 61 pages.
As such, it is error for the Office Action to allege that pages
67-68 of Hertz disclose these features. Furthermore, the Hertz
reference only discloses a website that is capable of creating a
rental vehicle reservation in response to customer input. There
are no disclosures in the Hertz reference corresponding to the
“accepting, by the server system, input that is indicative of a
request by the user to create an electronic rental contract for a
rental vehicle” step of claim 1. For example, there is no
counterpart or equivalent in the Hertz reference to the “Rent”
button 292 shown in Figure 6D2 for an example embodiment.
This error by the Examiner with respect to determining the
scope and content of the prior art constitutes reversible error in
the obviousness rejection of claim 1.
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App. Br. 22—23 (emphasis omitted). Again, absent some functional effect,
which Appellants have not persuasively identified here, there is no
patentable distinction between a reservation and a contract, and, in any
event, customer acceptance of a contract is a known requirement of
contracts. There must be some manner of indicating such acceptance to
evidence the act. To the extent the contract may require information not in a
reservation, claim 1 does not recite this, and in any event Hertz describes
creating a contract, which involves entry of the required information. As to
the argued button in the disclosure, this is not in the claim. Again, the issue
is the predictability of automatically performing a known manual operation
of converting a reservation into a contract, which we addressed supra.
We are not persuaded by Appellants’ argument that
the Hertz and Avis systems merely disclose websites for
creating rental vehicle reservations. There is no capability
disclosed or taught by Hertz or Avis for adding an option to
convert such a rental vehicle reservation into a rental contract.
Furthermore, the HertzGold reference fails to teach or suggest
additional steps whereby the rental vehicle reservation is
converted into a rental contract. With HertzGold, the user starts
with a preexisting MRA, not a pre-existing rental vehicle
reservation. HertzGold teaches that users with pre-existing
MRAs should go to a web page customized for such customers
(this web page is shown in Exhibit 7). From the webpage of
Exhibit 7, the customer with the pre-existing MRA proceeds
directly to a rental transaction that permits the customer to
bypass the rental counter during pickup. Even if one assumed
for the sake of argument that this rental transaction could be
equated to the “electronic rental contract” of claim 1, this
means that HertzGold would lack the steps from claim 1 which
recite that a rental vehicle reservation first be created. Thus, if
HertzGold were combined with Hertz and Avis by a person
skilled in the art, the resultant combination would yield two
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separate parallel paths for customers - the Hertz/Avis general
reservation booking path for customers who do not have pre­
existing MRAs and the HertzGold path for customers who do
have pre-existing MRAs. The only source of inspiration for a
“one touch, two transaction” method is Applicant’s patent
application; not the prior art.
App. Br. 24 (emphasis omitted). Again, the issue is the predictability of
automatically performing a known manual operation of converting a
reservation into a contract, which we addressed supra.
We are not persuaded by Appellants’ argument that
the Office Action includes a conclusory statement that it
would have been obvious to modify HertzGold to expand the
ability to create electronic rental contracts to all customers in
order “to save on personnel cost”. However, the Office Action
does not articulate how this action would actually lead to
savings in personnel cost. Moreover, because the HertzGold
reference teaches the use of computer technology that
specifically prevents the result that the Examiner alleges is
obvious, Applicant respectfully submits that HertzGold actually
teaches away from the invention rather than renders it obvious.
App. Br. 24—25. Appellants appear to overlook the personnel cost savings
accrued whenever a practice previously performed by personnel, such as
those at a customer service counter, is automated. Hertz does not say that it
conditions the automated conversion of a reservation into a contract because
doing so unconditionally was unknown or would be detrimental. Such
conditioning was volitional. Again, the potential marketing reasons for the
practice in Hertz are too well-known to conclude that the inclusion of
customer interaction with the counter was because one of ordinary skill was
unaware of the potential for automation and the strengths of automation.
We are not persuaded by Appellants’ argument that there is
19
Appeal 2014-008688
Application 12/650,040
no evidence of record suggesting that a customer who is
not a #1 Club Gold member, and who has not completed an
MRA, could bypass the rental counter via the Hertz computer
systems to create an electronic rental agreement as recited in
claim 1. The only conclusion supported by the evidence is that
the Hertz #1 Club Gold system limits rental counter bypass to
only customers who have completed a master rental agreement.
Thus, HertzGold fails to teach that customers without a
completed master rental agreement may bypass the rental
counter and create an electronic rental contract.
App. Br. 27 (emphasis omitted). Again, Hertz Gold describes a volitional
conditioning of bypassing a counter on such an agreement. The issue is the
predictability of automatically performing a known manual operation of
collecting necessary information and converting a reservation into a contract
in a single session, which we addressed supra.
We are not persuaded by Appellants argument as to claim 35 that
the recitations in claim 35 regarding the configurations of
the server system must be given patentable weight during
examination. That is, no features recited in the body of
claim 35 constitute “nonfunctional descriptive material”
(NFDM). While this issue was not raised by the Examiner in
the June 13, 2013 Office Action, the issue of which claim terms
are entitled to patentable weight was raised in the Decision on
Appeal dated February 7, 2013 for the parent ‘502 patent
application as noted above. (See Decision on Appeal dated
February 7, 2013; page 11, lines 7-9).
The Court of Customs and Patent Appeals (CCPA) and
Federal Circuit have repeatedly found that for a claim element
to constitute functional descriptive material (which enjoys
patentable weight during examination), rather than NFDM, the
claim element need only provide functionality with respect to
the end use of a claimed system.
App. Br. 29 (emphasis omitted). Claim 35 recites a system performing the
steps of claim 1 and so the analysis, including that of patentable weight, is
20
Appeal 2014-008688
Application 12/650,040
similar. As to the system, the Hertz system clearly shows the capacity to
perform the recited steps of sending and receiving data, and whether
someone at a customer service counter or the user enters data is irrelevant to
such capacity.
We are not persuaded by Appellants’ argument that, as to claims 78
and 82, reciting a single session, the art fails to describe this. App. Br. 33—
34. This is addressed supra and is simply the logical implication of
automating the conversion of the reservation into a contract.
We are not persuaded by Appellants’ argument that, as to claims 8,
17, and 21, reciting validating a driver license, the art fails to describe this.
App. Br. 34—36. As we find supra, knowledge of automating driver license
validation was in the general public, let alone with those of ordinary skill,
and is supported by Gallian and Burch.
We are not persuaded by Appellants’ argument that, as to claims 18
and 51, reciting checking whether a driver license number conforms to a
valid pattern, the art fails to describe this. App. Br. 36—37. As no particular
implementation is recited, validating the license number is validating its
pattern.4 We also enter Gallian and Burch as new art that shows it was
known to ask for such data and validate it online at the time of the invention.
We are not persuaded by Appellants’ argument that, as to claims 75
and 79, reciting permitting the user to electronically modify the pre-filled
profile information without modifying the MRA, the art fails to describe
21
Appeal 2014-008688
Application 12/650,040
this. App. Br. 37—38. There is no patentable distinction between the profile
and MRA. To the extent the argument is the predictability of changing only
one of two similar datasets, the notoriety of needing to make one-off
corrections was too widely known to say this would have been
unpredictable.
We are not persuaded by Appellants’ argument that, as to claims 76
and 80, reciting automatically pre-filling at least a portion of the retrieved
profile information into at least one field of the screen for the rental
transaction, the art fails to describe this, along with the option of not having
such a profile. App. Br. 39-40. The argument is not that the art fails
absolutely to describe automatically pre-filling at least a portion of the
retrieved profile information into at least one field of the screen for the rental
transaction, as the art clearly describes this. The argument is the absence of
the choice. Hertz describes the two alternatives of having and not having a
profile, and the automation of converting the reservation into a contract in
the presence of a profile. We find supra that it would have been predictable
to extend the automation of converting a reservation into a contract, even in
the context of no profile, as the existence of the reservation itself
presupposes the entry of data that would have been contained in the profile,
regardless of the source of that data.
We are not persuaded by Appellants’ argument that, as to claims 25
and 58, reciting a user-selectable link that is effective upon user selection to
4 Beyond that, we discern that the notoriety of hashing as an additional
check on validity was too notorious at the time of filing to consider this
22
Appeal 2014-008688
Application 12/650,040
link the user to the first web page, the art fails to describe this, but instead
describes the conventional link in a reservation confirmation email that
would merely take the user back to a reservation page of the website so the
user can cancel or modify the reservation; not convert such a reservation into
a rental contract as claimed. App. Br. 41 42. As set forth above, we find
that the cited art discloses “accepting . . . input that is indicative of a request
by the user to create an electronic rental contract for a rental vehicle,” as
recited in independent claim 1, from which claim 25 depends ultimately.
FF 5, 7, 10, 11. Independent claim 1, however, does not indicate the manner
in which such acceptance is required. Appellants admit that “conventional
link in a reservation confirmation email would . . . take the user back to a
reservation page of the website.” App. Br. 41. One of ordinary skill would
have known that any particular link is not limited to any purportedly
“conventional” uses, but would be configured to perform any action desired,
in this case, the “accepting . . . input” function disclosed in the prior art..
We are not persuaded by Appellants’ argument that, as to claim 2,
reciting determining that the user does not have a pre-existing MRA with the
rental car company, the art fails to describe this. App. Br. 41 42. This is
simply making explicit what claim 1 implies.
We have reviewed the Declarations by Mr. Smith and find them
unpersuasive.
The Board has broad discretion as to the weight to give to
declarations offered in the course of prosecution. See Velander
v. Garner, 348 F.3d 1359, 1371 (Fed. Cir. 2003)
unpredictable
23
Appeal 2014-008688
Application 12/650,040
(“[A]ccord[ing] little weight to broad conclusory statements [in
expert testimony before the Board] that it determined were
unsupported by corroborating references [was] within the
discretion of the trier of fact to give each item of evidence such
weight as it feels appropriate.”); cf. Ashland Oil, Inc. v. Delta
Resins & Refractories, Inc., 776 F.2d 281, 294 (Fed. Cir. 1985)
(“Opinion testimony rendered by experts must be given
consideration, and while not controlling, generally is entitled to
some weight. Lack of factual support for expert opinion going
to factual determinations, however, may render the testimony of
little probative value in a validity determination.” (citations
omitted)). Although there is “no reason why opinion evidence
relating to a fact issue should not be considered by an
examiner,” In re Alton, 76 F.3d 1168, 1175 n.10 (Fed. Cir.
1996), the Board is entitled to weigh the declarations and
conclude that the lack of factual corroboration warrants
discounting the opinions expressed in the declarations, see
Velander, 348 F.3d at 1371; Ashland Oil, 776 F.2d at 294.
In re American Academy of Science 367 F.3d 1359, 1368 (Fed. Cir. 2004).
We find that Mr. Smith’s Declarations describe conventional practices in the
rental industry, and not technical hurdles that were difficult to overcome.
Choosing whether to allow a computer or a human to interact in converting a
reservation to a contract is no more than a decision weighing (i) the
marketing opportunity and adaptability of human intervention against (ii) the
speed and efficiency of automation. One of ordinary skill would have
known to weigh either more heavily than the other based on various factors,
such as corporate strategy in demonstrating handholding and tactics in
reducing time a customer has to spend in administration. Simply because a
practice is conventional does not mean a different practice was unknown,
unpredictable, or disparaged.
24
Appeal 2014-008688
Application 12/650,040
CONCLUSIONS OF LAW
The rejection of claims 1—8, 13—29, 32—35, 37-41, 46—62, 65, 66, and
75—82 under 35 U.S.C. § 103(a) as unpatentable over Hertz, Avis, and
HertzGold is proper in view of additional evidence presented herein.
Because of the additional evidence, we denominate the rejection over art as a
new ground.
NEW GROUND OF REJECTION
The following new ground of rejection is entered pursuant to
37 C.F.R. § 41.50(b). Claims 1-8, 13-29, 32-35, 37-41, 46-62, 65, 66, and
75—82 are rejected under 35 U.S.C. § 101 as directed to non-statutory subject
matter.
The Supreme Court
set forth a framework for distinguishing patents that
claim laws of nature, natural phenomena, and abstract ideas
from those that claim patent-eligible applications of those
concepts. First, [ ] determine whether the claims at issue are
directed to one of those patent-ineligible concepts. ... If so, we
then ask, “[wjhat else is there in the claims before us? ... To
answer that question, [ ] consider the elements of each claim
both individually and “as an ordered combination” to determine
whether the additional elements “transform the nature of the
claim” into a patent-eligible application. [The Court] described
step two of this analysis as a search for an “‘inventive
concept’”—i.e., an element or combination of elements that is
“sufficient to ensure that the patent in practice amounts to
significantly more than a patent upon the [ineligible concept]
itself.”
25
Appeal 2014-008688
Application 12/650,040
Alice Corp., Pty. Ltd. v CLSBankInt’l, 134 S. Ct. 2347, 2355 (2014) (citing
Mayo Collaborative Services v. Prometheus Laboratories, Inc., 132 S. Ct.
1289 (2012)).
To perform this test, we must first determine whether the claims at
issue are directed to a patent-ineligible concept.
Although the Court in Alice made a direct finding as to what the
claims were directed to, we find that this case’s claims themselves, and the
Specification, provide enough information to inform one as to what they are
directed to.
The preamble to claim 1 recites that it is a method of creating and
storing an electronic rental contract for a rental vehicle. The steps in claim 1
result in creating an electronic rental contract from a reservation transaction.
We do not discern any functional language in claim 1, for example, any verb
that would only have been relevant to the realm of vehicle reservations. The
Specification at 1:23 recites that the invention relates to completing and
storing an electronic rental agreement. Thus, all this evidence shows that
claim 1 is directed to completing and storing an electronic rental agreement
from a reservation transaction. Further, although the words “electronic” and
“rental” are used, again, we do not discern that removing the “electronic”
and “rental” terminology appreciably affects the functional language of
independent claim 1. The “electronic” limitations, such as “server system,”
are generic, and the “rental” limitations are merely descriptive, and do not
affect how any of the steps are performed. For example, the “creating . . .”
step would function in the same way, whether the data created are “a rental
vehicle reservation,” as recited, or some other form of data. Additionally,
we discern that, after removing “rental” limitations, a “reservation
26
Appeal 2014-008688
Application 12/650,040
transaction” is merely previously gathered data. We find that all contracts,
at some level, must be based on previously gathered data. Accordingly, we
find that independent claim 1 is directed to entering into an agreement or
contract.
It follows from prior Supreme Court cases, and Bilski in particular,
that the claims at issue here are directed to an abstract idea. Like the risk
hedging in Bilski, we find that the concept of entering into a contract (based
on previously gathered information) is a fundamental business practice long
prevalent in our system of commerce. We find also that the creation and use
of contracts is also a building block of our legal system. Thus, entering into
a contract, like hedging, is an “abstract idea” beyond the scope of § 101. See
Alice Corp. Pty. Ltd., 134 S. Ct. at 2356.
As in Alice Corp. Pty. Ltd., we need not labor to delimit the precise
contours of the “abstract ideas” category in this case. It is enough to
recognize that there is no meaningful distinction in the level of abstraction
between the concept of risk hedging in Bilski and the concept of entering
into a contract at issue here. Both are squarely within the realm of “abstract
ideas” as the Court has used that term. See Alice Corp. Pty. Ltd., 134 S. Ct.
at 2357. We conclude that the claims at issue are directed to a patent-
ineligible concept.
The introduction of a computer into the claims does not alter the
analysis at Mayo step two.
[T]he mere recitation of a generic computer cannot
transform a patent-ineligible abstract idea into a patent-eligible
invention. Stating an abstract idea “while adding the words
‘apply if” is not enough for patent eligibility. Nor is limiting
the use of an abstract idea “‘to a particular technological
27
Appeal 2014-008688
Application 12/650,040
environment.’” Stating an abstract idea while adding the words
“apply it with a computer” simply combines those two steps,
with the same deficient result. Thus, if a patent’s recitation of a
computer amounts to a mere instruction to “implement [t]” an
abstract idea “on ... a computer,” that addition cannot impart
patent eligibility. This conclusion accords with the preemption
concern that undergirds our §101 jurisprudence. Given the
ubiquity of computers, wholly generic computer
implementation is not generally the sort of “additional
feature[e]” that provides any “practical assurance that the
process is more than a drafting effort designed to monopolize
the [abstract idea] itself.”
Alice Corp. Pty. Ltd., 134 S. Ct. at 2358 (citations omitted). “[T]he relevant
question is whether the claims here do more than simply instruct the
practitioner to implement the abstract idea ... on a generic computer.” Id. at
2359. They do not.
Taking the claim elements separately, the function performed by the
computer at each step of the process is purely conventional. Using a
computer to accept and store data, and make simple “yes” or “no”
determinations, to create a digital file amounts to electronic data query and
retrieval—one of the most basic functions of a computer. All of these
computer functions are well-understood, routine, conventional activities
previously known to the industry. In short, each step does no more than
require a generic computer to perform generic computer functions.
Considered as an ordered combination, the computer components of
Appellants’ method add nothing that is not already present when the steps
are considered separately. Viewed as a whole, Appellants’ method claims
simply recite the concept of entering into a contract, as performed by a
generic computer. The method claims do not, for example, purport to
28
Appeal 2014-008688
Application 12/650,040
improve the functioning of the computer itself. Nor do they effect an
improvement in any other technology or technical field. Instead, the claims
at issue amount to nothing significantly more than an instruction to apply the
abstract idea of entering into a contract using some unspecified, generic
computer. Under our precedents, that is not “‘enough’ to transform an
abstract idea into a patent-eligible invention. See Alice Corp. Pty. Ltd.,
134 S. Ct, at 2360.
As to system claim 35, it is
no different from the method claims in substance. The
method claims recite the abstract idea implemented on a generic
computer; the system claims recite a handful of generic
computer components configured to implement the same idea.
This Court has long “wam[ed] . . . against” interpreting § 101 in
ways that make patent eligibility ‘depend simply on the
draftsman’s art.’”
Alice Corp. Pty. Ltd., 134 S. Ct. at 2360.
The dependent claims recite conventional data entry operations and
user interface features or recite the automotive rental context features, which
add nothing to overcome the abstract nature of the claims.
DECISION
The rejection of claims 1—8, 13—29, 32—35, 37—41, 46—62, 65, 66, and
75—82 under 35 U.S.C. § 103 is affirmed, but denominated as a new ground.
The following new ground of rejection is entered pursuant to
37 C.F.R. § 41.50(b): claims 1-8, 13-29, 32-35, 37-A1, 46-62, 65, 66, and
75—82 are rejected under 35 U.S.C. § 101 as directed to non-statutory
subject matter.
29
Appeal 2014-008688
Application 12/650,040
Our decision is not a final agency action.
This decision contains a new ground of rejection pursuant to
37 C.F.R. § 41.50(b). Section 41.50(b) provides “[a] new ground of
rejection pursuant to this paragraph shall not be considered final for judicial
review.” Section 41.50(b) also provides:
When the Board enters such a non-final decision, the
appellant, within two months from the date of the decision,
must exercise one of the following two options with respect to
the new ground of rejection to avoid termination of the appeal
as to the rejected claims:
(1) Reopen prosecution. Submit an appropriate
amendment of the claims so rejected or new Evidence relating
to the claims so rejected, or both, and have the matter
reconsidered by the examiner, in which event the prosecution
will be remanded to the examiner. The new ground of rejection
is binding upon the examiner unless an amendment or new
Evidence not previously of Record is made which, in the
opinion of the examiner, overcomes the new ground of rejection
designated in the decision. Should the examiner reject the
claims, appellant may again appeal to the Board pursuant to this
subpart.
(2) Request rehearing. Request that the proceeding be
reheard under § 41.52 by the Board upon the same Record. The
request for rehearing must address any new ground of rejection
and state with particularity the points believed to have been
misapprehended or overlooked in entering the new ground of
rejection and also state all other grounds upon which rehearing
is sought.
Further guidance on responding to a new ground of rejection can
be found in the Manual of Patent Examining Procedure § 1214.01.
30
Appeal 2014-008688
Application 12/650,040
No time period for taking any subsequent action in connection with
this appeal may be extended under 37 C.F.R. § 1.136(a).
See 37 C.F.R. § 1.136(a)(l)(iv) (2011).
AFFIRMED; 37 C.F.R, $ 41.50(b)
31
2/25/2017 Rental Car Companies Check Drivers' Records - tribunedigital-sunsentinel
Homs ---> Collections Motor Vehicies
[
Rental Car Companies Check Drivers'
Records
August 12.1993 j ByA.D. BURCH, Staff Writer
Your driving record affects more than your pride or pocketbook under policies adopted recently by the
nation's largest car rente! agencies.
Budget, Avis, Hertz and National are refusing to rent vehicles in some states to drivers with poor or
tainted records, a move to lower the cost of soaring liability costs.
The leasing agencies are now checking state motor vehicle records by computer before consumers
can get the keys. The driving record check is supposed to take less than a minute, so it is not expected
to delay getting a car rental.
Related Articles
Fort Lauderdale-based Alamo Rent A Car, is also considering a policy involving drivers' checks, but the
details are being worked out, said Liz Clark, director of public affairs.
Check Safety Recalls On Cars, Boats, Medicine
July 27, 2009
Law Bans Open Containers Of Alcohol In Motor
Vehicles
April 2, 1986
Failure To Pay Child Support Could Mean Losing
License
May 4 1998
Drivers May Catch A Break On Auto Tags
January 5, 2000
Leasing officials point to this multimillion-dollar phrase: "vicarious liability," as the reason for the new
policies. Vicarious liability is a law in New York and Florida allowing the owners of the vehicle to be held
liable even if the customer caused the accident.
"The cost of injuries is skyrocketing," said The Hertz Corporation spokesman Joe Russo, although he
did not have specific figures. "Just by virtue of us owning the car, we have to take the hit. So we are
now trying to identify the high-risk drivers and (say) they are no longer entitled to the privilege of renting
a car."
The program is limited to drivers in states where the program is operating, including Florida, New York,
Maryland and Ohio. For example, a New York- registered driver would be screened when attempting to
rent a car in Florida but not Utah, where the program is not being used.
Unlicensed Driver Dies In Accident On 1-95
j ,,6 lgg? Hertz, National and Budget report a denial rate that peaked at 10 percent of the drivers whose licenses
were checked. That rate has stabilized at 6 percent. The companies declined to release total leasing
numbers.
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Hertz, based in Park Ridge, N.J., began its program in July 1992 in New York. It brought Florida on-line
in April and the greater Washington, D.C., area in June. The company has made preliminary plans to
add California later this year. Avis launched its program for Florida and New York drivers about a month
ago. Likewise, National and Budget adopted their policies late last year.
"The (Division of Motor Vehicles) is a tool to help us overcome difficulties in doing business," said
Michael Olsen, spokesman for the Minneapolis-based National Car Rental System Inc. "It also helps
with the safety issue."
Companies do not have access to motor vehicle records so they contract with TML Informational
Services, of Forest Hills, N.Y., which had direct access to the DMV databases. Rental agents enter the
driver's license number into the computer system. A TML representative runs the number and kicks
back a computer answer to the rental agent within 30 seconds, based on a series of criteria.
Although the rules vary among the companies, the red flag or denial usually bleeps across the
computer screen if a driver has a suspended, expired or revoked licenses, a history of driving under the
influence, driving without insurance or a license, or posssession of a stolen car.
In beginning the safe-driving program, the companies also launched a consumer awareness campaign.
http://articles.sun-sentinel.com/1993-08-12/business/9301290359_1_car-drivers-motor-vehicles 1/3
2/25/2017 Rental Car Companies Check Drivers' Records - tribunedigital-sunsentinel
"We have posted signs at the rental counters and our reservation sales agents (headquartered) in
Tulsa (Okla.) will tell Florida and New York consumers they are likely to run a check on their licenses so
they are not surprised when it pops up," said Ray Noble, spokesman for the Garden City, N.Y.-based
Avis Inc.
BAD DRIVERS BEWARE
The criteria for vehicle leasing vary by company. Here are the basic criteria used by Hertz and Avis:
1. Driver's license suspended, revoked, invalid, surrendered or expired, if not cleared.
2. Eight or more points on driving record within the past 24 months (48 months for reckless disregard
for life and property). Department of Motor Vehicle Accident Prevention credits are taken into
consideration.
3. Conviction for DWI/DWAI/DUI within past 72 months.
4. Three or more convictions for moving violations within past 36 months.
5. Two or more accidents within past 36 months.
6. One or more accidents resulting in fatality or bodily injury within past 48 months. (This applies only to
rentals in New York area; Avis does not use this criterion.)
7. Failure to report an accident or leaving the scene of an accident within the past 48 months.
8. Operating a motor vehicle without insurance or a valid driver's license within the past 48 months.
9. Permitting operation of a motor vehicle without insurance or unlicensed operation of a motor vehicle
within past 48 months.
10. Possession of stolen vehicle or use of a vehicle in a crime within 48 hours.
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http://articles.sun-sentinel.com/1993-08-12/business/9301290359_1_car-drivers-motor-vehicles 2/3
VOL. 64, NO. 1, FEBRUARY 1991 13
Assigning Driver's License Numbers
JOSEPH A. GALLIAN
University of Minnesota
Duluth, MN 5S812
"You know my name
look up the number”
John Lennon and Paul McCartney, You know my name,
single, B-side of Let it be, March 1970.
Introduction
.Among the individual states, a wide variety of methods are used to assign driver’s
license numbers. The three most common methods, a sequential number, the social
security number, and a computer-generated number, are uninteresting mathemati­
cally. On the other hand, many states encode data such as month and date of birth,
year of birth, and sex in ways that involve elementary mathematics. Seven states go so
far as to employ a check digit for possible detection of forgery or errors. Several states
assign driver’s license numbers by applying complicated hashing functions to the first,
middle, and last names and formulas or tables for the month and date of birth.
Surprisingly, the assignment of numbers is not always injective. In Michigan, for
instance, there are 56 numbers whose inverse image has two or more members. New
Jersey incorporates eye color into the number. Some states keep their method
confidential. In a few instances, administrators of the license bureaus do not know the
method used to assign numbers in their state! In this paper we discuss some of the
methods we have uncovered.
Check Digit Schemes in General Use
Schemes for the assignment of identification numbers are extremely varied in
methodology' and in the information encoded. Most interesting to mathematicians are
those that incorporate an extra digit for the detection of errors or fraud. Although the
purpose of this paper is to analyze the methods used for driver’s license numbers, it is
worthwhile to begin with a brief survey of the methods employed to assign check
digits to the most ubiquitous numbers in use and to provide a theoretical result that
delineates their limitations.
The simplest and least effective method for assigning a check digit is to use the
remainder or inverse of the remainder of the identification number modulo some .
number. For airline tickets, UPS packages, and Federal Express mail the check digit
is the identification number modulo 7. At the bottom of Figure 1 we see the airline
ticket number 17000459570 (the airline code 012 is not used in the calculation) is
assigned a check digit 3 since 17000459570 * 3 mod 7.
U.S. postal money orders use the remainder modulo 9 while VISA travelers checks
use the inverse of the number modulo 9. Thus, the check digit for the VISA number
1002044679091 is 2 since 1002044679091 * 7 mod 9.
14 MATHEMATICS MAGAZINE
■ ’ZBnT£ZX2X‘aXlTtX.t2X£Tn^rrr?’rrr’rjYTrriTTTn'T7TriTt
I 1KMTMUFST *lt» IMPS \RFFT/f5-7t 7000:459:570
DULUTHTVU AOCr'
CAMPUS-'W S
fi fset
FIGURE 1
Airline ticket with number 17000459570 and check digit 3.
The modulo 7 schemes detect all errors involving a single digit except those where
b is substituted for a and \a-b\ —1. Likewise, an error of the sort at - a
... _* ■ ■ ■ Qj • ■ ■ a. • • • will go undetected if 'a,: - dj =7 or if 6 divides j - i.
The modulo 9 schemes are slightly better at detecting single-digit errors: Only a
substitution of a 9 for a 0 or vice versa goes undetected. On the other hand, the only
errors of the form • ■ • a, ■ ■ ■ a. • • • ■ * • Oj * * • a, • • * that are undetected are
those involving the check digit itself. (A quick proof of this is to observe that the
residue of a number modulo 9 is the residue of the sum of its digits modulo 9.)
Nearly all methods for assigning a check digit to a string of digits involve a scalar
product of two vectors and modular arithmetic. For a string axa2 ••• ak_x and a
modulus n, many schemes assign a check digit ak so that
(aj, a2,..., ak) • (wk, w2, ■.,, wk) = Omod n.
We call such schemes linear and we call the vector (tf w2__ _ wk) the weighting
vector. The Universal Product Code (UPC) used on grocery items employs the
weighting vector (3,1,3,1,3,1,3,1,3,1,3,1) with n =* 10: the International Standard
Book Number (ISBN) utilizes (10,9,8,7,6,5,4,3,2,1) and n = 11; banks in the U S.
use (7,3,9,7,3,9,7,3,9) with n = 10; many Western countries use (7,3,1,7,3.1___)
with n = 10 to assign check digits to numbers on passports. Notice that the division
schemes mentioned at the outset of this section are also linear with weighting vectors
of the form (10*-2,10t-3,.... 10°, ± 1).
The error-detecting capability of linear schemes is given by the following theorem.
Theorem. Suppose a number ata.2 • • ■ ak satisfies the condition (ax,a2>..., at) ■
(t£j. w2, • • •, wk) = Omod n. Then the single error occasioned by substituting a\ for a,
is undetectable if and only if (a| — ai)wi is divisible by n and a sole error of the form
• • ■ a( ■ ■ ■ Oj ■ ■ ■ -* aj ■■■ a, ■ is undetectable if and only if (ai — aj)(wi —
wf is divisible by n.
Proof If a\ is substituted for at, then the dot product of the correct number and
the incorrect number differ by ^ — aJtVf. Thus, the error is undetected if and only if
(o' — afw, = Omod n.
Now consider an error of the form * * * at ■ * • aj • • • • • • a, * * • at • * * . Here
the dot product of the correct number and the incorrect number differ by
VOL. 64, NO, 1, FEBRUARY 1991 15
(a,u.-, + OjWj) - (OjtCf + a,Wj) = (ai-aJ)(wi- Wj)
The conclusion now follows as before.
Since the most common moduli are 10 and 11, the following corollary is worth
mention.
Corollary. Suppose an identification number axaz • • • ak satisfies
(Gj. a2...... dj.) â–  (wx,w2,...,wk) = Omodn
where 0 < at < n for each i. Then all single-digit errors occurring in the ith position
are detectable if and only if ic, is relatively prime to n and all errors of the form
■ • ■ at • ■ ■ Qj ■ • ■ aj ai - • ■ are detectable if and only if w( — u>j is rela­
tively prime to n.
The above theorem verifies our claims about the error-detection capability of the
schemes used on money orders and airline tickets. It also explains why the bank and
passport schemes will detect some errors of the form • • • abc • • * -* • * • cba • • •
while the UPC code will detect no such errors. Observe that because 11 is prime the
ISBN code detects 100% of all single-digit errors and 100% of all errors invoking
the interchange of two digits. But there is a price to pay for using the modulus 11:
The number at needed to satisfy the condition may be 10, which is two digits. In this
case, an alphabetic character such as X or A is used or such numbers are not issued.
As we will see below there are schemes that use the modulus 11 that do not resort to
an alphabetic character, but there is a price to pay for this too: Not all transposition
errors are detectable. More information about check digits schemes in use can be
found in [1], [21 [3]. [4], [6], [7], [8],
Check Digits on Driver's License Numbers
The state of Utah assigns an eight-digit driver’s license number in sequential order,
say {jjfl, * * • a8, then appends a check digit a9 using a linear scheme with weighting
vector (9,8,7,6,5,4,3,2,1) and modulus 10. This method is identical to that used by
the American Chemical Society for its chemical registry numbers. Assuming that all
errors are equally likely,1 this method detects 73/81 or 90.1% of all single-digit errors
and 100% of all transposition errors (i.e., errors of the form • * • ab • * • -♦ ■ • ■ ba
â–  â–  â–  ).2
To verify the single-error detection rate, observe from our theorem that in positions
2, 4, 6, and 8 substitution of b for a will go undetected when |a — i| * 5; in position
5, a substitution of b for a will go undetected when a and b have the same parity.
Thus in each of positions 2, 4, 6, and 8 there are 10 undetected errors among 90
possible errors while in the fifth position, 40 of the 90 possible errors are undetected.
1 In practice all errors are not equally likely. One study [7, p. 15] revealed that a substitution of a "5” for
a “3” was 17 times as likely as a substitution of a “9” for a “1.” However, available data are insufficient to
assign reliable probabilities to the various error possibilities,
2A highly publicized error of this kind recently occurred when Lt. Col. Oliver North gave U.S. Assistant
Secretary of State EUiot Abrams an incorrect Swiss bank account number for depositing $10 million for the
contras. The correct number begins with “386”; the number North gave to Abrams begins with ‘‘368.“
16 MATHEMATICS MAGAZINE
So, in all, 80 of 810 errors are undetected.
Someone working for the Canadian province of Quebec, probably having seen a
scheme like the one used by Utah somewhere, came up with the laughable weighting
vector (12,11,10,9,... ,2,1) with modulus 10 to assip a check digit. Of course, any
error in the third position is undetectable and weights of 12 and 11 have the same
effect as the weights 2 and 1.
Newfoundland uses the weighting vector (1,2,3,4,5,6,7,8,1) with modulus 10.
This is nearly identical to the Utah scheme except that it will not detect the event
that the first and last digit are interchanged.
Three states use a modified linear scheme with modulus 11. New Mexico and
Tennessee append a check digit aH to ala2 ■ • • a7 as follows: First calculate
x = -(aj.tij. ... ,a-) • (2,7,6,5,4,3,2)modll.
If .v = 0. aH is 1; if x = 10, as = 0; otherwise as = .r. This method catches 100% of all
single-digit errors. Furthermore, the only errors of the form a, Oj ■■ ■ -* * - •
aJ - â–  â–  a. â–  â–  â–  that go undetected are those where i = 1 and j = 7 (an unlikely error
indeed) and some involving the check digits 0 and 1. Assuming that all transposition
errors are equally likely,3 this method detects 98.2% of such errors. The Vermont
scheme is the same as the one used by New Mexico except that when x = 0, the
letter ‘A" is the check. This method, like the ISBN method, yields a 100% detection
rate for both single-digit and transposition errors, but utilizes two formats for
numbers. Notice that there would be nothing lost if the weighting vector began with
8 instead of 2 and there would be a slight gain since errors of the form axat • • • a7as
—*■ a7a.i ■ ■ ■ a,as would be detectable.
The state of Washington and the province of Manitoba use a check digit scheme
devised by IBM in 1964 to assip a check digit. The license number is a blend of 12
alphabetic and numeric characters. To compute the Washington check digit, alpha­
betic characters are assigned numeric values as follows: * -»pr, A -*■ 1. B -»2......./ ->
9, / -* 1. K -*2,..., R -* 9. S -» 2, T -» 3.......Z ->9. (Notice the aberration at S.) The
12-character license number, after an alphabetic to numeric conversion, then corre­
sponds to a string of digits ala1 ■ ■ • av2 with a10 as the check digit calculated as
; ■■■ ha • • •, suppose
such an error is undetected. We consider four cases. For simplicity, assume a in the
correct number is in position 2, 4 or 6. The alternative case gives the same result.
Case 1. a, b < 5
Then 2a + b = 2b 4* a mod 10.
Thus a - b =* 0 and a = b.
Case 2. a < 5, b 3> 5
Then 2a + b**2b — 9 + a mod 10.
It follows that b — a = 9 so that b = 9 and a = 0.
Case 3. a > 5, b < 5
Then 2a — 9 + b & 2b + a mod 10.
So, a — b = 9 and a = 9 and b = 0.
Case 4. a > 5, b > 5
Then 2a — 9 + b = 2b-9+a mod 10.
Thus o - b = 0 and a = b.
So all transposition errors except 09 <-» 90 are detected. Since there are 90 possible
transposition errors, the error detection rate is 88/90 or 97.8%.
It is worth noting that Gumm [4] has shown that it is not possible to improve upon
these rates with any system that uses addition modulo 10 to compute the check digit
without utilizing an extra character, as was the case for the New Mexico scheme.
Wisconsin appends a check digit to a 13-digit string. Unfortunately, I have not
been able to figure out how this scheme works. I know it isn’t linear; for if so, the
weighting vector (tOj,tv2,wm, wu) could be determined by gathering up a large
number of valid license numbers to produce a system of linear equations with the
m/s as the unknowns. I have done this for modulo 10 and 11 to no avail. To
circumvent any peculiarity that might arise involving a check digit of 10 in a modulo
11 scheme (e.g„ New Mexico), I avoided numbers with a check digit of 0 or 1.
Encoding Personal Data
Here is the driver’s license number of a Wisconsin resident: E 425-7276-9176-07.
What information about the holder can you deduce from this number: year of birth,
day and month of birth, sex, name? None of these is obvious. Let’s go the other
direction. I am a resident of Minnesota. I was bom on January 5, 1942, and my
middle name is Anthony. From this can you deduce my driver’s license number?
Eleven states assign their driver s license numbers with hashing functions applied
solely to personal data. A good hash function should be fast and minimize collisions
(see [5, pp. 506-544] for a detailed discussion of this topic). Of course, there will be
occasions when two or more individuals have enough personal data in common that
collisions will occur. Most states have a tie-breaking mechanism to handle this
situation. Coding license numbers only from personal data enables automobile
insurers, government entities, and law enforcement agencies to determine the num­
bers when necessary.
Washington uses a complicated blend of name, check digit, and codes for the
month and date of birth to assign its numbers. This 12-digit identifier consists of the
18 MATHEMATICS MAGAZINE
first five letters of the surname; the first and middle initials (* is used when a name
has less than five characters, or there is no middle initial); the year of birth subtracted
from 100 (we suspect this is done to disguise the year of birth); a check digit; a code
for the month of birth; and a code for the day of birth. For instance, Fielding Mellish
(no middle name) bom on 10/29/42 receives the identifier MELLI F* 587P9. When
checked against a file of 1.6 million items, this scheme yielded duplicates at the rate
of 0.03% and only one number appeared as many as four times. (Most of the
duplications represented twins.) To ensure that the correspondence between individ­
uals and numbers is injective, 17 alternate codes for month and year of birth are
available. For example, an S can be used instead of a B for January or a Z instead of
a 9 for the year of birth. Interestingly, the check digit is invariant under all alternate
coding. The primary code and one alternate for months is given in Table 1 and the
code for the days is given in Table 2. Notice the absence of completely predictable
patterns.
TABLE 1. Washington code for months.
Months Codes Alternate Codes
January B S
February C T
March D U
April } 1
May K 2
June L 3
July M 4
August N 5
September O 6
October P 7
November Q 8
December R 9
TABLE 2. Washington code for days.
I - A 7 - G 13 -L 19-R 25-5
2 - B 8-H 14 -M 20-0 26-6
3 - C 9 - Z 15 -N 21-1 27 - 7
4- D 10 -S 16 -W 22-2 28-8
5 - E ii 17-F 23-3 29-9
6 - F 12 -K 18 -Q 24-4 30 - T
Illinois, Florida, and Wisconsin encode the surname, first name, middle initial, date
of birth, and sex by a quite sophisticated scheme. The first character of the license
number is the first character of the name. The next three characters are obtained by
applying the “Soundex Coding System" to the surname as follows:
1. Delete all occurrences of h and to.
2. Assign numbers to the remaining letters as follows:
b, f,p,v~* 1 4
c, g, j, k,q, s, x,s -* 2 m,n~* 5
d, t —* 3 r —* 6
(No values are assigned to a, e, i, o, u, and y.)
3. If two or more letters with the same numeric value are adjacent, omit all but the
first. (Here a, e, t, o, u, and y act as separators.) For example, Schworer becomes
Sorer and Hugh gill becomes Ugil.
VOL. 64, NO. t, FEBRUARY 1991 19
4. Delete the first character of the original name if still present.
5. Delete all occurrences of a, e, i, o, u, and y.
6. Use the first three digits corresponding to the remaining letters; append trailing
zeros if less than three letters remain.
Here are some examples: Schworer -» S-660; Hughgill -* H-240; Skow -» S-000;
Sachs -* S-200; Lennon —» L-550; McCartney —*M-263.
We parenthetically remark that the Soundex System was designed so that likely
misspellings of a name would nevertheless result in the correct coding of the name.
For example, frequent misspellings of my name are: Gallion, Gillian, Galian, Galion,
Gilliam, Gallahan, and Galliam. Observe that all of these yield the same coding as
Gallian. We also mention that the above method differs somewhat from the system
called Soundex by Knuth in [5, p. 392],
The next three digits are determined by summing numbers that correspond to the
first name and middle initial. The scheme for doing this begins with the block 000 for
the letter A and makes jumps of 20 for especially common names and each
subsequent letter of the alphabet. A small portion of this scheme is. given in Table 3.
The values assigned to the middle initial are given in Table 4.
So Aaron G. Schlecker would be coded as S426-007 (S426 from Schlecker; 000 for
Aaron +7 for “G"), while Anne P. Schlecker would be coded as S426-053.
The last five digits of Illinois and Florida numbers capture the year and date of
birth as well as the sex. In Illinois, each day of the year is assigned a three-digit
number in sequence beginning with 001 for January 1. However, each month is
assumed to have 31 days. Thus, March 1 is given 063. These numbers are then used
to identify the month and day of birth of male drivers. For females, the scheme is
identical except January 1 begins with 601. The last two digits of the year of birth,
separated by a dash (probably for camouflage), are listed in the 5th and 4th positions
from the end of the driver’s license number. Thus, a male bom on July 18, 1942.
would have the last five digits 4-2204 while a female bom on the same day would
have 4-2804. When necessary, Illinois adds an extra character to avoid duplications.
TABLE 3. Illinois. Florida, Wisconsin given name or first initial code.
000 — A
020 - Albert, Alice
040 - Ann, Anna, Anne, .Annie. Arthur
060 B
080 _ Bernard, Bette, Bettie, Bettv
100 — C
TABLE 4. Illinois, Florida, Wisconsin middle initial code.
0 - none 10-]
1 - A 11 -K
2 - B 12-L
3 - C 13 -M
4 - D 14-N.O
5-E 15- P,Q
6 - F 16-JR
7-G 17 -S
8-H 18 - T, U. V
9-1 19 - w, x, y, z
20 MATHEMATICS MAGAZINE
Among the 9,397,518 licenses on file on January 1, 1987, this occurred in 14,856
instances. Of these, 55 numbers corresponded to three individuals (excluding the
extra digit). No number corresponded to more than three people.
The scheme to identify birthdate and sex in Florida is the same as Illinois except
each month is assumed to have 40 days and 500 is added for women. For example,
the five digits 49583 belong to a woman bom on March 3, 1949.
Wisconsin employs the same scheme as Florida to generate the first 12 of their 14
characters. The thirteenth character is an integer issued sequentially beginning with 0
to people who share the same first 12 characters. The fourteenth character is a check
digit.
A Missouri driver’s license number has 16 characters. The first 13 characters are
obtained by applying a hashing function to the first five letters of the surname, the
first three letters of the first name and the middle initial. (The method of encoding is
similar to that used by Florida.) The final three characters are a function of the month
and day of birth and sex. For a male bom in month m and day d the three digits are
63m + 2d. For a female, the corresponding formula is 63m + 2d + l. Thus the
number of a woman bom on March 4 has the final three characters 198. To avoid
duplications, Missouri assigns a 17th character. Among the first 3,921,922 numbers
issued, 31,719 have a 17th character.
Last, we discuss the scheme employed by Minnesota, Michigan, and Maryland.
The number is a function of last name, first name, middle name, month and date of
birth. The first four characters are determined by the Soundex System, as was the
case for Illinois, Florida, and Wisconsin. The first and middle names account for the
next six characters and the same algorithm is applied to both names. In the majority
of cases the first two characters of the name determine the desired three digits for
each name (see Table 5 for a sample); for common pairs of leading letters such as Al
or Ja, the third letter is invoked (see Table 6); 11 three-digit numbers are uniquely
assigned to the 11 most popular names (e.g., 189 *•* Edward; 210 «-* Elizabeth).
TABLE 5. Minnesota, Michigan, Maryland code for first and middle names
beginning with A except Al.
A 027
Aa 028 Aj 037 As 072
Ah 029 Ak 038 At 073
Ac 030 Al — Am 074
Ad 031 Am 066 Ae 075
Ae 032 An 067 Au.’ 076
Af 033 Aa 068 Ax 077
Ag 034 Ap 069 Ay 078
Ah 035 Aq 070 Ax 079
Ai 036 At 071
The final three digits are based on month and date of birth (but not year). Each day
of the year is assigned a three-digit number in a monotonicallv increasing fashion.
Although the usual pattern is to alternate increments of 3 and 2, there are numerous
seemingly random increments at unpredictable dates. The month of March illustrates
this behavior well. Notice from Table 7 that March 1 is assigned 159. Subsequent
days are assigned values by increments of 3 and 2 in alternating fashion until March
8. Then there is mi increment of 5. Notice the jump of 20 between March 19 and
March 20.
These gaps serve a practical purpose. In the event that there are two or more
individuals bom on the same month and date and with names so similar that the
VOL. 64, NO. 1 . FEBRUARY 1991 21
TABLE 6. Minnesota, Michigan, Maryland code for first and middle names
beginning with Al.
Al 039
Ala 040 Mi 049 Als 058
Aft 041 Aik 050 Alt 059
Ale 042 All 051 Alu 060
AW 043 Aim 052 Ale 061
Ale 044 Ain 053 Alw 062
Alf 045 Alo 054 Mx 063
Alg 046 Alp 055 Altj 064
Alh 047 Alq 056 Alz 065
Alt 048 Air 057
TABLE 7. Minnesota, .Michigan. Maryland code for dates in March.
1 -159
March - 158
11 - 187 21 - 229
2 - 162 12 - 189 22 - 232
3 -164 13 - 192 23 - 234
4 -167 14-194 24 - 237
5 -169 15 - 197 25 - 239
6 -172 16 - 199 26 - 242
7 - 174 17 - 202 27-244
8 -177 18-204 28 - 247
9 -182 19 - 207 29 - 249
10-184 20 - 227 30 - 252
31-254
hashing function does not distinguish between them (e.g„ Jill Paula Smith and Jimmy
Paul Smythe), the first person who applies for a license is assigned the number given
by the algorithm while the second person is assigned the next higher number thereby
using one of the numbers in the gap for birthdays. For example, if Jill Paula Smith is
bom on March 2 and is the first to receive the combination S530-441-675-162 as
determined by the algorithm, then the next person who yields the same number is
assigned S530-441-675-163 instead. Once all of the higher numbers in a gap have
been assigned, lower numbers are used. Thus the third applicant with a name
yielding the combination S530-441-675 bom on March 2 would be assigned the last
three digits 161. As of 1984, this scheme had not yielded any duplications among
4,468,080 people in Maryland while of Michigan’s 6,332,878 drivers by 1987 there are
56 that have a number not uniquely their own. In fact, Michigan has two numbers
that are each shared by four individuals and three that are each shared by three
individuals. A common cause of duplication is the custom of naming a son after the
father. When both share the same birthday a duplication occurs.
Summary
Table 8 summarizes the information the author has discovered about the coding of
driver’s license numbers. Unfortunately our knowledge is incomplete. Several states
(e.g., Florida, New York, Minnesota, Missouri, Wisconsin) keep their methods confi­
dential. In some of these cases we were able to determine the coding scheme by
examining data. A question mark after the letter X indicates the corresponding item
is used in the coding, but we do not know the method involved. The expression (A)
after an X indicates that the corresponding item is part of a scheme that is an
alternative to the social security number.
O. 1, FEBRUARY 1991 21
.E 6. Minnesota, Michigan, Maryland code for first and middle names
ining with Al.
Al 039
la 040 Alj 049 Als 058
lb 041 Aik 050 Alt 059
1c 042 All 051 Alu 060
Id 043 Aim 052 Ale 061
le 044 Ain 053 Alw 062
If 045 Alo 054 Alx 063
ig 046 Alp 055 Aly 064
Ih 047 Afo 056 Alz 065
li 048 Air 057
TABLE 7, Minnesota, Michigan. Maryland code for dates in March.
â–  March - 158
1 - 159 11 - 187 21 - 229
2 -162 12- 189 22 - 232
3 -164 13- 192 23 - 234
4 -167 14- 194 24 - 237
5 - 169 15 - 197 25 - 239
6 -172 16- 199 26 - 242
7 -174 17- 202 27 - 244
8 -177. 18- 204 28 - 247
9 - 182 19- 207 29 - 249
10 - 184 20- 227 30 - 232
31 - 254
motion does not distinguish between them (e.g., Jill Paula Smith and Jimmy
the), the first person who applies for a license is assigned the number given
iorithm while the second person is assigned the next higher number thereby
of the numbers in the gap for birthdays. For example, if Jill Paula Smith is
March 2 and is the first to receive the combination S530-441-675-162 as
:d by the algorithm, then the next person who yields the same number is
S530-441-675-163 instead. Once all of the higher numbers in a gap have
gned, lower numbers are used. Thus the third applicant with a name
he combination S530-441-675 bom on March 2 would be assigned the last
its 161. As of 1984, this scheme had not yielded any duplications among
people in Maryland while of Michigan’s 6,332,878 drivers by 1987 there are
ave a number not uniquely their own. In fact, Michigan has two numbers
;aeh shared by four individuals and three that are each shared by three
s. A common cause of duplication is the custom of naming a son after the
hen both share the same birthday a duplication occurs.
y
ummarizes the information the author has discovered about the coding of
cense numbers. Unfortunately our knowledge is incomplete. Several states
ida. New York, Minnesota, Missouri, Wisconsin) keep their methods confi-
i some of these cases we were able to determine the coding scheme by
; data. A question mark after the letter X indicates the corresponding item
the coding, but we do not know the method involved. The expression (A)
X indicates that the corresponding item is part of a scheme that is an
5 to the social security number,
O
O
M
O
JC
n *â– 
M
»
f
22 MATHEMATICS MAGAZINE
TABLE 8. Summary of Schemes for Assigning Driver's License Numbers.
Stale
Socud
Security
.Vernier
Computer or
Sequential
Number
Cheek
Dipt
Last
Verne
Coded
First
iVa me
CM
THuT
Usm
CM
Ytar of
Birth
CM
Month of
Birth
Coded
Birth
Coded
Sex
Coded
Alabama X
Alula. X
Ariwoi X
Arkansas X Xf AI
California X
Colorado X
Connecticut X X
Deiaware X X
Florida X X X X X X X
Georgia X XiA.
Hawaii X
Idaho X X..., at) â– 
(t£j. w2, • • •, wk) = Omod n. Then the single error occasioned by substituting a\ for a,
is undetectable if and only if (a| — ai)wi is divisible by n and a sole error of the form
• • ■ a( ■ ■ ■ Oj ■ ■ ■ -* aj ■■■ a, ■ is undetectable if and only if (ai — aj)(wi —
wf is divisible by n.
Proof If a\ is substituted for at, then the dot product of the correct number and
the incorrect number differ by ^ — aJtVf. Thus, the error is undetected if and only if
(o' — afw, = Omod n.
Now consider an error of the form * * * at ■ * • aj • • • • • • a, * * • at • * * . Here
the dot product of the correct number and the incorrect number differ by
VOL. 64, NO, 1, FEBRUARY 1991 15
(a,u.-, + OjWj) - (OjtCf + a,Wj) = (ai-aJ)(wi- Wj)
The conclusion now follows as before.
Since the most common moduli are 10 and 11, the following corollary is worth
mention.
Corollary. Suppose an identification number axaz • • • ak satisfies
(Gj. a2...... dj.) â–  (wx,w2,...,wk) = Omodn
where 0 < at < n for each i. Then all single-digit errors occurring in the ith position
are detectable if and only if ic, is relatively prime to n and all errors of the form
■ • ■ at • ■ ■ Qj ■ • ■ aj ai - • ■ are detectable if and only if w( — u>j is rela­
tively prime to n.
The above theorem verifies our claims about the error-detection capability of the
schemes used on money orders and airline tickets. It also explains why the bank and
passport schemes will detect some errors of the form • • • abc • • * -* • * • cba • • •
while the UPC code will detect no such errors. Observe that because 11 is prime the
ISBN code detects 100% of all single-digit errors and 100% of all errors invoking
the interchange of two digits. But there is a price to pay for using the modulus 11:
The number at needed to satisfy the condition may be 10, which is two digits. In this
case, an alphabetic character such as X or A is used or such numbers are not issued.
As we will see below there are schemes that use the modulus 11 that do not resort to
an alphabetic character, but there is a price to pay for this too: Not all transposition
errors are detectable. More information about check digits schemes in use can be
found in [1], [21 [3]. [4], [6], [7], [8],
Check Digits on Driver's License Numbers
The state of Utah assigns an eight-digit driver’s license number in sequential order,
say {jjfl, * * • a8, then appends a check digit a9 using a linear scheme with weighting
vector (9,8,7,6,5,4,3,2,1) and modulus 10. This method is identical to that used by
the American Chemical Society for its chemical registry numbers. Assuming that all
errors are equally likely,1 this method detects 73/81 or 90.1% of all single-digit errors
and 100% of all transposition errors (i.e., errors of the form • * • ab • * • -♦ ■ • ■ ba
â–  â–  â–  ).2
To verify the single-error detection rate, observe from our theorem that in positions
2, 4, 6, and 8 substitution of b for a will go undetected when |a — i| * 5; in position
5, a substitution of b for a will go undetected when a and b have the same parity.
Thus in each of positions 2, 4, 6, and 8 there are 10 undetected errors among 90
possible errors while in the fifth position, 40 of the 90 possible errors are undetected.
1 In practice all errors are not equally likely. One study [7, p. 15] revealed that a substitution of a "5” for
a “3” was 17 times as likely as a substitution of a “9” for a “1.” However, available data are insufficient to
assign reliable probabilities to the various error possibilities,
2A highly publicized error of this kind recently occurred when Lt. Col. Oliver North gave U.S. Assistant
Secretary of State EUiot Abrams an incorrect Swiss bank account number for depositing $10 million for the
contras. The correct number begins with “386”; the number North gave to Abrams begins with ‘‘368.“
16 MATHEMATICS MAGAZINE
So, in all, 80 of 810 errors are undetected.
Someone working for the Canadian province of Quebec, probably having seen a
scheme like the one used by Utah somewhere, came up with the laughable weighting
vector (12,11,10,9,... ,2,1) with modulus 10 to assip a check digit. Of course, any
error in the third position is undetectable and weights of 12 and 11 have the same
effect as the weights 2 and 1.
Newfoundland uses the weighting vector (1,2,3,4,5,6,7,8,1) with modulus 10.
This is nearly identical to the Utah scheme except that it will not detect the event
that the first and last digit are interchanged.
Three states use a modified linear scheme with modulus 11. New Mexico and
Tennessee append a check digit aH to ala2 ■ • • a7 as follows: First calculate
x = -(aj.tij. ... ,a-) • (2,7,6,5,4,3,2)modll.
If .v = 0. aH is 1; if x = 10, as = 0; otherwise as = .r. This method catches 100% of all
single-digit errors. Furthermore, the only errors of the form a, Oj ■■ ■ -* * - •
aJ - â–  â–  a. â–  â–  â–  that go undetected are those where i = 1 and j = 7 (an unlikely error
indeed) and some involving the check digits 0 and 1. Assuming that all transposition
errors are equally likely,3 this method detects 98.2% of such errors. The Vermont
scheme is the same as the one used by New Mexico except that when x = 0, the
letter ‘A" is the check. This method, like the ISBN method, yields a 100% detection
rate for both single-digit and transposition errors, but utilizes two formats for
numbers. Notice that there would be nothing lost if the weighting vector began with
8 instead of 2 and there would be a slight gain since errors of the form axat • • • a7as
—*■ a7a.i ■ ■ ■ a,as would be detectable.
The state of Washington and the province of Manitoba use a check digit scheme
devised by IBM in 1964 to assip a check digit. The license number is a blend of 12
alphabetic and numeric characters. To compute the Washington check digit, alpha­
betic characters are assigned numeric values as follows: * -»pr, A -*■ 1. B -»2......./ ->
9, / -* 1. K -*2,..., R -* 9. S -» 2, T -» 3.......Z ->9. (Notice the aberration at S.) The
12-character license number, after an alphabetic to numeric conversion, then corre­
sponds to a string of digits ala1 ■ ■ • av2 with a10 as the check digit calculated as
; ■■■ ha • • •, suppose
such an error is undetected. We consider four cases. For simplicity, assume a in the
correct number is in position 2, 4 or 6. The alternative case gives the same result.
Case 1. a, b < 5
Then 2a + b = 2b 4* a mod 10.
Thus a - b =* 0 and a = b.
Case 2. a < 5, b 3> 5
Then 2a + b**2b — 9 + a mod 10.
It follows that b — a = 9 so that b = 9 and a = 0.
Case 3. a > 5, b < 5
Then 2a — 9 + b & 2b + a mod 10.
So, a — b = 9 and a = 9 and b = 0.
Case 4. a > 5, b > 5
Then 2a — 9 + b = 2b-9+a mod 10.
Thus o - b = 0 and a = b.
So all transposition errors except 09 <-» 90 are detected. Since there are 90 possible
transposition errors, the error detection rate is 88/90 or 97.8%.
It is worth noting that Gumm [4] has shown that it is not possible to improve upon
these rates with any system that uses addition modulo 10 to compute the check digit
without utilizing an extra character, as was the case for the New Mexico scheme.
Wisconsin appends a check digit to a 13-digit string. Unfortunately, I have not
been able to figure out how this scheme works. I know it isn’t linear; for if so, the
weighting vector (tOj,tv2,wm, wu) could be determined by gathering up a large
number of valid license numbers to produce a system of linear equations with the
m/s as the unknowns. I have done this for modulo 10 and 11 to no avail. To
circumvent any peculiarity that might arise involving a check digit of 10 in a modulo
11 scheme (e.g„ New Mexico), I avoided numbers with a check digit of 0 or 1.
Encoding Personal Data
Here is the driver’s license number of a Wisconsin resident: E 425-7276-9176-07.
What information about the holder can you deduce from this number: year of birth,
day and month of birth, sex, name? None of these is obvious. Let’s go the other
direction. I am a resident of Minnesota. I was bom on January 5, 1942, and my
middle name is Anthony. From this can you deduce my driver’s license number?
Eleven states assign their driver s license numbers with hashing functions applied
solely to personal data. A good hash function should be fast and minimize collisions
(see [5, pp. 506-544] for a detailed discussion of this topic). Of course, there will be
occasions when two or more individuals have enough personal data in common that
collisions will occur. Most states have a tie-breaking mechanism to handle this
situation. Coding license numbers only from personal data enables automobile
insurers, government entities, and law enforcement agencies to determine the num­
bers when necessary.
Washington uses a complicated blend of name, check digit, and codes for the
month and date of birth to assign its numbers. This 12-digit identifier consists of the