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Math Help - I guess this is a cryptorithm?

  1. #1
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    I guess this is a cryptorithm?

    ABC
    X DE
    ---------
    FGHD
    CAAC
    -------------
    IDBDD

    [picture if text example is terrible - I guess this is a cryptorithm?-itshard.png
    Im pretty far into it, but I cant put down any numbers.
    Im not sure if D is 6 or no.

    Heres some of the info Ive got so far:

    E ≠ 1 , D ≠ 1 , and C ≠ 1

    E ≠ 5 , D ≠ 5 , and C ≠ 5

    I = C + 1

    E*C = ?D, '?' stands for an unknown digit.

    D*C = ?C

    A, C, D, E, F, I cant be 0.

    Thanks in notice. Taking any skype calls: heck7er
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  2. #2
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    Opalg's Avatar
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    Re: I guess this is a cryptorithm?

    The key to this is the line CAAC. That number must be a multiple of 11 (sum of digits in even-numbered positions = sum of digits in odd-numbered positions). Since D is obviously not a multiple of 11, it follows that ABC, and hence also IDBDD, must be multiples of 11.

    Assuming that the letters A to I stand for the numbers 1 to 9 in some order, you should be able to see fairly soon that D=6. Thus the bottom line becomes I6B66, which can only be a multiple of 11 if I+B = 6 or 17. You can rule out 17 quite easily, and then you soon find the remaining values.

    Spoiler:
    Code:
      814
     x 69
    -----
     7326
    4884
    -----
    56166
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  3. #3
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    Joined
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    Re: I guess this is a cryptorithm?

    Quote Originally Posted by Opalg View Post
    The key to this is the line CAAC. That number must be a multiple of 11 (sum of digits in even-numbered positions = sum of digits in odd-numbered positions). Since D is obviously not a multiple of 11, it follows that ABC, and hence also IDBDD, must be multiples of 11.

    Assuming that the letters A to I stand for the numbers 1 to 9 in some order, you should be able to see fairly soon that D=6. Thus the bottom line becomes I6B66, which can only be a multiple of 11 if I+B = 6 or 17. You can rule out 17 quite easily, and then you soon find the remaining values.

    Spoiler:
    Code:
      814
     x 69
    -----
     7326
    4884
    -----
    56166
    Ty mate. I used your key to check, the bonus tips were very useful. Once again, thanks.
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