Suppose you create a seven-digit identification number so that the seventh digit is the...

Suppose you create a seven-digit identification number so that the seventh digit is the check digit. The check digit is the remainder when a weighted sum of the first six digits is divided by 7. The weighted sum is formed by multiplying each of the first six digits by the digit’s position. Thus, the weighted sum For example, if the first six digits of an identification number are 208455, then the weighted sum is1(2) + 2(0) + 3(8) +4(4) + 5(5) + 6(5) = 2 + 0 + 24 + 16 + 25 + 30 = 97. When the weighted sum is divided by 7, the remainder is 6. The complete identification number is 2084556.

Use the check-digit scheme defined above to create an example of a valid identification number with the given requirement(s).

a. The check digit is 6.

b. No digits are repeated, and the check digit is 1.

c. The first six digits are the same.