(A Vehicle Identification Number (VIN) is a unique code (e.g.: 1G6AF5SX6D0125409
ID: 3888219 • Letter: #
Question
(A Vehicle Identification Number (VIN) is a unique code (e.g.: 1G6AF5SX6D0125409) used by the automotive industry to identify individual vehicles. Since 1981, each on-road vehicle built and sold in the United States typically (exceptional cases disregarded for the purpose of this exercise) is required to contain a 17-character VIN structured and constrained as follows: A three-character (alpha-numeric) world manufacturer identifier (WMI). The letters 'I', 'O' and 'Q' are to be excluded. A five-character (alpha-numeric) vehicle descriptor (VD). The letters 'I', 'O' and 'Q' are to be excluded. A single (numeric or 'X') check digit (CD). The digit is calculated from the other 16 letters/digits (and is used for detection of invalid VIN). A one-character (alpha-numeric) model year (MY). The letters 'I', 'O', 'Q', 'U' and 'Z', and the digit '0', are to be excluded. A one-character (alpha-numeric) plant code (PC). The letters 'I', 'O' and 'Q' are to be excluded. A six-character (alpha-numeric) serial number (SN). The letters 'I', 'O' and 'Q' are to be excluded. Auxiliary notes:- only UPPERCASE letters (alphabets) allowed
- the usual 10 decimal numeral digits ('0' through '9') are allowed except for model year for which '0' is not allowed.
- none of the letters 'I', 'O' and 'Q' is allowed for any part of the VIN
- 'U' and 'Z' (in addition to the 'I', 'O', 'Q' and '0' noted above) are also not allowed for model year
- serial number is alpha-numeric in general (i.e., not necessarily numeric although it is most commonly so) From the above, compute the theoretical maximum number of (distinct) VINs the underlying structure would be able to support.
Explanation / Answer
Step 1: Please apply these rules to the example and for every position write available possible characters.
1G6AF5SX6D0125409
1G6 Manufacturer identification 33
AF5SX Vehicle descriptor 33
6 Check Digit 1
D Model Year 30
0 Plant code 33
125409 33
Note that there are 26 uppercase alphabets and 10 digits. So total 36 different characters are there. Exclude the characters and then come up with 33 or 30 as above for each position.
Step 2: The character in every position is independant of all other positions except for the check digit. So muptiply all the possibilities for every position that gives the theoritical number of VIN
e.g.
1G6 Manufacture identification can have
33 * 33 * 33 combinations like 000, 001, ...00A..1G6,.,A00,...AAA,....ABC,....ZZZ
Similarly for each of there.
As these are all independant of other values, multiplying all of them together gives the solution.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.