Suppose a six-digit identification number is assigned to each student in a middle school. The sixth digit is a check digit, and is assigned to make the sum of the six digits divisible by 9. The digit 9 is not used as the check digit.
a. Under this scheme, how many valid identification numbers are possible?
b. Is 439713 a valid identification number? How will a number be recognized as invalid?
c. If the first five digits of an identification number are 35028, then find the check digit.
d. A student writes her identification number down to check in after arriving late to school, but the secretary cannot read the student’s handwriting. Suppose that the secretary can identify four of the digits, so the number reads 13??44. List all the possibilities for the middle two digits.
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