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Still needing HELPbut should have posted this

  1. Sep 10, 2006 #1
    there is a second part to my original puzzle...sorry

    So, IF ABC plus DEF equals GHI THEN,

    ADG, plus BEH equals CFI...

    Please any takers on this...it is driving me CRAZY !!!!

    the teasers are listed across if that helps
    A B C A D G
    +D E F + B E H
    _______ ________
    G H I C F I

    Not sure if you will see it correctly ...sorry
     
  2. jcsd
  3. Sep 10, 2006 #2

    Alkatran

    User Avatar
    Science Advisor
    Homework Helper

    The usual way to solve these puzzles is to turn your two equations into many. For example, based on the small digits: (C + F) mod 10 = (G + H) mod 10 = I. However, whenever I see these puzzles I always just write a computer program to solve them by doing a case-by-case. Here is the output of the program I wrote (notice how there are TWO answers, but that they are very similar):
    Code (Text):

    718236954     718 + 236 = 954             729 + 135 = 864
    729135864     729 + 135 = 864             718 + 236 = 954
     
    and the program:

    Code (Text):

    Dim d(1 To 9) As Long

    Private Sub Main()
        Call testDigit(1) 'start the recursion on the first digit
    End Sub
    Private Sub testDigit(ByVal index As Long)
    Dim a As Long
        For a = 1 To 9
            If digitsContain(a) = False Then 'make sure the digit is unique
                d(index) = a 'try this digit in this position
                If index < 9 Then
                    Call testDigit(index + 1) 'go to next digit if we're not at the last one
                ElseIf isValid Then 'if we're at the last digit, check the answer
                    printDigits
                End If
            End If
        Next a
        d(index) = 0 'reset digit
    End Sub
    Private Function digitsContain(ByVal n As Long) As Boolean
    Dim a As Long
        'Check if the digit 'n' is already used
        For a = 1 To 9
            If d(a) = n Then
                digitsContain = True
            End If
        Next a
    End Function
    Private Function isValid() As Boolean
        'make sure the digits match the program
        isValid = CBool(CLng(d(1) & d(2) & d(3)) + CLng(d(4) & d(5) & d(6)) = CLng(d(7) & d(8) & d(9)))
        isValid = isValid And CBool(CLng(d(1) & d(4) & d(7)) + CLng(d(2) & d(5) & d(8)) = CLng(d(3) & d(6) & d(9)))
    End Function
    Private Sub printDigits()
    Dim a As Long
    Dim s As String
        For a = LBound(d) To UBound(d)
            s = s & d(a)
        Next a
        Debug.Print s, d(1) & d(2) & d(3) & " + " & d(4) & d(5) & d(6) & " = " & d(7) & d(8) & d(9), d(1) & d(4) & d(7) & " + " & d(2) & d(5) & d(8) & " = " & d(3) & d(6) & d(9)
    End Sub
     
    Originally I missed the 'unique 1-9' requirement and was finding hundreds of answers. But when I realized they had to be unique the problem space went from a billion possibilities to 362880 possibilities, so it turned out much better!
     
    Last edited: Sep 10, 2006
  4. Sep 11, 2006 #3
    omg...THANK YOU so much....I was trying to figure it out but just assumed that no number would equal more than 10..I was so focused in that respect, I never entertained any other possibilites...geez...but thank you sooo much!
     
  5. Sep 11, 2006 #4
    Hm. I wrote a program that found 4 solutions:

    Code (Text):

    ABCDEFGHI    ABC + DEF = GHI    ADG + BEH = CFI
    146583729    146 + 583 = 729    157 + 482 = 639
    157482639    157 + 482 = 639    146 + 583 = 729
    718236954    718 + 236 = 954    729 + 135 = 864
    729135864    729 + 135 = 864    718 + 236 = 954
     
    And a few more if you include 0 (I didn't catch where 0 wasn't a valid option?):

    Code (Text):

    ABCDEFGHI    ABC + DEF = GHI    ADG + BEH = CFI
    326584910    326 + 584 = 910    359 + 281 = 640
    348562910    348 + 562 = 910    359 + 461 = 820
    359281640    359 + 281 = 640    326 + 584 = 910
    359461820    359 + 461 = 820    348 + 562 = 910
     
    And even a few more if you let 0 be a leading digit (which is bad form!)

    Code (Text):

    ABCDEFGHI    ABC + DEF = GHI    ADG + BEH = CFI
    023594617    023 + 594 = 617    056 + 291 = 347
    023695718    023 + 695 = 718    067 + 291 = 358
    045876921    045 + 876 = 921    089 + 472 = 561
    056291347    056 + 291 = 347    023 + 594 = 617
    067291358    067 + 291 = 358    023 + 695 = 718
    067854921    067 + 854 = 921    089 + 652 = 741
    089472561    089 + 472 = 561    045 + 876 = 921
    089652741    089 + 652 = 741    067 + 854 = 921
     
    DaveE
     
  6. Sep 11, 2006 #5

    Alkatran

    User Avatar
    Science Advisor
    Homework Helper

    Interestingly, when I run the program again I get all four answers. I must have missed them somehow.
     
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