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Math Help - hi new puzzle for u guys

  1. #1
    ggw
    ggw is offline
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    hi new puzzle for u guys

    Starting with the two two-digit numbers
    ab and cd, where ab > cd,
    concatenate them to obtain the
    four-digit number abcd.
    (note: each of the numbers: a,b,c,d are digits)

    If you subtract the difference between
    ab and cd from abcd, you obtain 5689.

    Determine the number cd.

    Last puzzle that I posted. There is no one solve it. I will post solution up this weekend...any suggestions ? and here is a little bit easier puzzle
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  2. #2
    Senior Member ecMathGeek's Avatar
    Joined
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    Posts
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    Quote Originally Posted by ggw View Post
    Starting with the two two-digit numbers
    ab and cd, where ab > cd,
    concatenate them to obtain the
    four-digit number abcd.
    (note: each of the numbers: a,b,c,d are digits)

    If you subtract the difference between
    ab and cd from abcd, you obtain 5689.

    Determine the number cd.

    Last puzzle that I posted. There is no one solve it. I will post solution up this weekend...any suggestions ? and here is a little bit easier puzzle
    We have a number: a*10^3 + b*10^2 + c*10 + d

    If we add: c*10 + d, we get:
    a*10^3 + b*10^2 + 2c*10 + 2d

    If we subract: a*10 + b, we get:
    a*10^3 + b*10^2 + (2c - a)*10 + (2d - b) = 5689

    b >= 1 --> a = 5
    b - 1 = 6 --> b = 7
    2d + 10 - b = 9 --> d = 3
    2c + 10 - a - 1 = 8 --> c = 2

    10c + d = 23
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  3. #3
    Newbie
    Joined
    May 2007
    Posts
    4
    ab > cd
    abcd-(ab-cd)=5689
    cd=?

    solution:

    let a=5, b=7 or 6
    let cd=X

    (1) for a=5, b=7

    (5700+X)-(57-X)=5689
    X=cd=23

    (2) for a=5, b=6
    (5600+X)-(56-X)=5689
    X=cd=72.5 which is trivial answer


    therfore the solution is :

    a=5
    b=7
    c=2
    c=3
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