Still needing HELPbut should have posted this

[strack22]

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

 

[Alkatran]

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):

718236954     718 + 236 = 954             729 + 135 = 864
729135864     729 + 135 = 864             718 + 236 = 954

and the program:

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!

 

[strack22]

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!

 

[davee123]

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):

718236954     718 + 236 = 954             729 + 135 = 864
729135864     729 + 135 = 864             718 + 236 = 954

Hm. I wrote a program that found 4 solutions:

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?):

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!)

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

 

[Alkatran]

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