The identification number for a bank printed on a check consists of
eight digits x1 . . . x8, followed by a ninth check digit x9, with
x9 ≡ 7x1 +3x2 + 9x3 + 7x4 + 3x5 + 9x6 + 7x7 + 3x8 (mod 10).
(a) What is the check digit following the eight-digit identification number
00185403 for a bank?
(b) Will this scheme detect a change in one of the digits? Prove your
(c) Will this scheme detect a change the transposition of two consecutive,
but distinct digits? Prove your answer.
(a) Just substitute the values into the formula and calculate:
x9 ≡ 7*0 +3*0 + 9*1 + 7*8 + 3*5 + 9*4 + 7*0 + 3*3 (mod 10) =
= 125(mod 10) = 5
(b) The change in only one digit will always change the id number.
The change will be a*b(mod ...