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Modular Arithmetic- Finding missing ISBN-10 entry..I'm stuck halfway?
Suppose that an ISBN-10 has a smudged entry where the question mark appears in the number 0-716?-2841-9. Determine missing digit.
I think that the missing digit is 7 and I was able to come up with the following equation.
(178+6x) mod 11=0
I need help finding x, (178+6x) mod 11=0. Detailed steps. The more detailed the better!!
Thank you!
[10(0) + 9(7) + 8(1) + 7(6) + 6x + 5(2) + 4(8) + 3(4) + 2(1) + 1(9)] mod 11 = 0
(0+ 63 + 8 + 42 + 6x + 10 + 32 + 12 + 2+ 9) mod 11 = 0
(113 + 6x + 65) = 0
(178 + 6x) mod 11 = 0
So far, we agree.
Now, 178 / 11 = 16 R 2, so we have:
(2 + 6x) mod 11 = 0
Quick table of values:
x 6x 2+6x (2+6x)mod 11
0 0 2 2
1 6 8 8
2 12 14 3
3 18 20 9
4 24 26 4
5 30 32 10
6 36 38 5
7 42 44 0
Found it.
x=7
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