Problem

The last digit of a five-digit identification number is the check digit. The check digit...

The last digit of a five-digit identification number is the check digit. The check digit is assigned so that the sum of all the digits is divisible by 7. Only the digits 0 through 6 will be used in the identification numbers.

a. Under this scheme, how many valid identification numbers are possible?

b. Suppose a single-digit error has been made in the number 36253, but the check digit is correct. Correct the number in as many ways as possible.

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