Example 1:
Find the check digit: 0-11168-03004-?

With the 3-1-3-1 pattern:

Writing everything out separately:
0*3+1+1*3+1+6*3+8+0*3+3+0*3+0+4*3+N≡0 (mod 10)
1+3+1+18+8+3+12+N≡0 (mod 10)
46+N≡0 (mod 10)
6 +N≡0 (mod 10)
So N=4 because 6+4=10≡0 (mod 10)

 Collecting numbers in odd places and numbers in even places:
(1+6+4)*3+(1+1+8+3)+N≡0 (mod 10)
11*3+13+N≡0 (mod 10)
33+13+N≡0 (mod 10)
6 +N≡0 (mod 10)
So N=4 because 6+4=10≡0 (mod 10)

With the 7-9-7-9 pattern:

Writing everything out separately:
0*7+1*9+1*7+1*9+6*7+8*9+0*7+3*9+0*7+0*9+4*7≡
9+7+9+42+72+27+48≡
9+7+9+2+2+7+8≡
16+9+4+15≡
6+13+5≡
9+5≡ 4 (mod 10)

Collecting numbers in odd places and numbers in even places:
(1+6+4)*7+(1+1+8+3)*9 ≡
11*7+13*9≡
1*7+3*9≡
7+27≡
34≡4 (mod 10)
So the check digit is 4


Example 2:

Find the check digit: 0-18008-01167-? I'm just going to write out the version where you collect numbers in odd and even places before you multiply this time--I make fewer mistakes that way.

With the 3-1-3-1 pattern:
(8+1+7)*3+(1+8+1+6)+N≡0
16*3+16+N≡0
6*3+6+N≡0
18+6+N≡0
4+N≡0 (mod 10)
N=6 (beause 6+6=10≡0 (mod 10))

With the 7-9-7-9 pattern
(8+1+7)*7+(1+8+1+6)*9≡
16*7+16*9≡
6*7+6*9≡
42+54≡6 (mod 10)

Printable answers:

 

check digit

08748611661?

?=0

01116803004?

?=4

04878941860?

?=9

61266806369?

?=5

01258778013?

?=8

01800801167?

?=6

07166204012?

?=3

If you think any of my answers are wrong (sometimes I make a mistake too), you should check them with the check digit calculator

Please send me an e-mail if you find an error so I can fix it.

2. Do a check digit calculation mod 10 to decide which of these UPC codes is correct, and which has an error:
When you're doing these, one good way is to use the first 11 digits to figure out the check digit, and if the check digits match, then the code is correct; if the check digits don't match, then the code has an error. Another way to do it is to write out the calculations with either the 3-1-3-1 pattern or the 7-9-7-9- pattern, but this time add in the check digit (and multiply that check digit by 1 or 9 respectively): if you get 0, the code was valid, if you don't get 0, then the code had an error.

A. 0-72512-06868-7 Correct

B. 0-09252-45310-1 Has an error

C. 1-24431-65100-2 Has an error

D. 0-11676-10881-5 Correct

3. Example 1. 0-?0735-00458-1

Using the 3-1-3-1 rule:

Writing it all out
0*3 + N + 0*3 + 7 + 3*3 + 5 + 0x3 + 0 + 4*3 + 5 + 8*3+1 ≡0 (mod 10)
N+7+9+5+12+5+24+1≡0 (mod 10)
N+63≡0 (mod 10)
N+3≡0 (mod 10)
N=7

Collecting evens and odds
(3+4+8)*3+N+7+5+5+1≡0 (mod 10)
15*3+N+18≡0 (mod 10)
5*3+N+8≡0 (mod 10)
N+23≡0 (mod 10)
N+3≡0 (mod 10)
N=7

Using the 7-9-7-9 rule (slightly more difficult)

Writing it all out
0*7 + N*9 + 0*7 + 7*9 + 3*7 + 5*9 + 0*7 + 0*9 + 4*7 + 5*9 + 8*7 ≡1
9N+63+21+45+28+45+56≡1 (mod 10)
9N+3+1+5+8+5+6≡1 (mod 10)
9N+28≡1 (mod 10)
9N+8≡1
9N ≡1-8≡3(mod 10)
9N≡3 (what *9 has a 3 as its ones digit? 7*9=63≡3(mod 10)
N=7

Collecting evens and odds
(3+4+8)*7+(N+7+5+5)*9≡1 (mod 10)
15*73+9N+17*9≡1 (mod 10)
5*3+9N+7*9≡1 (mod 10)
15+9N+63≡1 (mod 10)
9N+5+3≡1 (mod 10)
9N+8≡1
9N ≡1-8≡3(mod 10)
9N≡3 (what *9 has a 3 as its ones digit? 7*9=63≡3(mod 10)
N=7

Example 2. 1-?0584-17613-9

Using the 3-1-3-1 rule:

Writing it all out
1*3 + N + 0*3 + 5 + 8*3 + 4 + 1*3 + 7 + 6*3 + 1 + 3*3 +9≡0 (mod 10)
3+N+5+24+4+3+7+18+1+9+9≡0 (mod 10)
N+ 83≡0 (mod 10)
N+3≡0 (mod 10)
N=7 (because 7+3=10≡0 (mod 10))

 Collecting evens and odds
(1+8+1+6+3)*3+N+5+4+7+1+9≡0 (mod 10)
19*3+N+26≡0 (mod 10)
9*3+N+6≡0 (mod 10)
N+27+6≡0 (mod 10)
N+33≡0 (mod 10)
N+3≡0 (mod 10)
N=7


Using the 7-9-7-9 rule

Writing it all out
1*7 + N*9 + 0*7 + 5*9 + 8*7 + 4*9 + 1*7 + 7*9 + 6*7 + 1*9 + 3*7 ≡9
7+9N+45+56+36+7+63+42+9+21≡9 (mod 10)
9N+ 7+5+6+6+7+3+2+9+1≡9 (mod 10)
9N+46≡9 (mod 10)
9N+6≡9 (mod 10)
9N≡9-6 (mod 10)
9N≡3 (mod 10) (what times 9 has a ones digit of 3? 7*9=63≡3 (mod 10))
N=7

Collecting evens and odds
(1+8+1+6+3)*7+(N+5+4+7+1)*+9≡9 (mod 10)
19*7+N+17*9≡9 (mod 10)
9*7+N+7*9≡9 (mod 10)
N+63+63≡9 (mod 10))
N+3+3≡9 (mod 10)
N+6≡9 (mod 10)
9N≡9-6 (mod 10)
9N≡3 (mod 10) (what times 9 has a ones digit of 3? 7*9=63≡3 (mod 10))
N=7

 

Printable answers to other #3 problems:

Code

missing digit

0-?0735-00458-1

7
1-?0584-17613-9 7

0-41?40-56400-3

5

0-4154?-33111-7

0

0-41540-5?401-0

6

0-21200-665?2-6

2