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الرياضيات : الرياضيات التطبيقية :

Driver,s Licenses

المؤلف:  W.D. Wallis

المصدر:  Mathematics in the Real World

الجزء والصفحة:  137-139

11-2-2016

1648

The soundex is used in constructing driver’s licenses in a number of states. We shall go through the Illinois and Florida license number constructions.

The Illinois license number consists of one letter followed by 11 digits. We shall work through the construction of the number for Carl D. Springer, born on May 4,  1977.

The first four symbols are the soundex of the license-holder’s last name. As we saw above, Springer has soundex S165.

The next three characters are formed as follows: an arbitrary 3-digit number is assigned for your first name—for example,

140 for Charles, Clara

120 for Carl, Catherine

100 for all other names beginning with C

and another number (from 1 to 19) is added for your middle initial, if any (1 for A, 6 for F, 18 for T, U or V, and so on). A list of name encodings is shown in the table below. Carl is 120 and D is 4, so Mr Springer’s 5th, 6th and 7th digits are 124.

The last five are formed from your sex and date of birth:

ABCDE means the driver was born in the year 19AB; the CDE is derived from his or her birthday. First you calculate the day of the year in which the applicant was born—approximately. For some reason, the calculation is performed as though every month had 31 days. For example, if the birthday was April 2nd, you work as though January, February and March each had 31 days, so April 2nd would be the 95th day of the year (95 = 3×31+2), even though it is actually the 92nd or 93rd,  depending on whether it is a leap year. So, if the driver is a man, you would put CDE = 095. For a woman, increase the total by 600; a woman born on April 2nd has CDE = 695. For Mr Springer, May 4 is 128, so his last five digits are 77128,  and his license number is S165-1247-7128.

Sample Problem 1.1 What would be the Illinois license number for Catherine A. Churchill, born May 2, 1976?

Solution. Churchill: C624

Catherine: 120

Middle initial A: add 1, gives 121

Birth year: 76

Birth date: 4.31 + 2 = 126

Woman: add 600, gives 726

C624-1217-6726.

Illinois Driver’s License Tables

Here are the standard numbers for some common first names.

020 Albert, Alice                                              040 Ann, Anna, Anne, Annie, Arthur

080 Bernard, Bette, Bettie, Betty                120 Carl, Catherine

140 Charles, Clara                                          180 Dorothy, Donald

220 Edward, Elizabeth                                   260 Florence, Frank

300 George, Grace                                           340 Harold, Harriet

360 Harry, Hazel                                              380 Helen, Henry

440 James, Jane, Jayne                                    460 Jean, John

480 Joan, Joseph                                                560 Margaret, Martin

580 Marvin, Mary                                              600 Melvin, Mildred

680 Patricia, Paul                                               740 Richard, Ruby

760 Robert, Ruth                                                 820 Thelma, Thomas

Some minor variants may be given numbers from this list—for example, I would guess Will would be classified as 920. However, if your name is not listed, it will usually be given a code corresponding to its first letter:

900 Walter, Wanda 920 William, Wilma

For example, Eric should be 200. If you use only the first initial of your first name,  this table is used. If your license just says J. Smith you get 420. Even if your name is John Smith, it is 420, not 460—they go by the name as printed on the license.

For your middle initial, use

It is quite possible for two people to get the same number. In that case an overflow number is appended. In Illinois these are not printed on the license, but the police have access to it.

Illinois also issues a state ID. It is often used as a proof of age or identity by people who do not drive, and is also a good idea to have one when you are traveling,  in case your license is misplaced or stolen. The ID has a number derived in the same way, except that the letter is put at the end. Mr Springer’s ID number would be 1651-2477-128S, and Ms Churchill would get ID number 6241-2176-726C.

 The Florida driver’s license is very similar to the Illinois one, with three differences. First, the day-of-birth calculation is done as if there are 40 days in each month. Second, the amount added to a woman’s day of birth is 500, not 600. And finally, the overflow number is printed on the license, a single digit at the end of the number. (If there were no duplicates when the license was issued, the number is 0.)  The spacing is a little different: assuming Mr Springer applied for a Florida license and two other people had already come up with the same number, so that his overflow number was 2, his license number would be S165-124-77-128-2.

Sample Problem 1.2 What would be the Florida license number for Catherine A. Churchill, born May 2, 1976, assuming there is no overflow?

Solution. C624-121-76-662-0.

 

 

EN

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