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    #1
    Use the UPC scheme to determine the check digit for the number $07312400508$.

    here is the example from the book

    ok so going with dot product with 07312400508
    \begin{align*}\displaystyle
    &\quad (0731 2 4 0 0 5 0 8)\cdot(3,1,3,1,3,1,3,1,3)\\
    &= 0\cdot3+7\cdot1
    +3\cdot3+1\cdot1
    +2\cdot3+4\cdot1
    +0\cdot3+0\cdot1
    +5\cdot3+0\cdot1
    +8\cdot3 \\
    &=7+9+1+6+4+15+24\\
    &=66\\
    66mod10&=6
    \end{align*}

    so far?? but the number only has 11 digits
    Last edited by karush; August 24th, 2018 at 19:57.

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    #2
    Quote Originally Posted by karush View Post
    ok so going with dot product with 07312400508
    \begin{align*}\displaystyle
    &\quad (0731 2 4 0 0 5 0 8)\cdot(3,1,3,1,3,1,3,1,3)\\
    &= 0\cdot3+7\cdot1
    +3\cdot3+1\cdot1
    +2\cdot3+4\cdot1
    +0\cdot3+0\cdot1
    +5\cdot3+0\cdot1
    +8\cdot3 \\
    &=7+9+1+6+4+15+24\\
    &=66\\
    66\pmod{10}&=6
    \end{align*}

    so far?? but the number only has 11 digits
    That is correct so far. You now have to add a twelfth digit so as to make the checksum zero$\pmod{10}$.

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    Quote Originally Posted by Opalg View Post
    That is correct so far. You now have to add a twelfth digit so as to make the checksum zero$\pmod{10}$.

    What would be the 12th digit????

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    #4
    Quote Originally Posted by karush View Post
    What would be the 12th digit????
    What do you have to add to 66 to get a multiple of 10?

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