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Question 117608: My problem is: 7xy (seven hundred and something) times 4z (forty something) = abcde. the variables are each a different whole number between 0 - 9 - excluding 7 and 4 which is already used. I've found a few things to narrow the problem down - such as the answer should be between 29442 (701 X 42) and 38514 (786 x 49) and that I don't thing y or z can be 0 or 1. - your help is appreciated.
Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! I tried to look for something useful to help with this problem.
I made 7xy equal to (700 + 10x + y).
I made 4z equal to (40 + z).
Then multiplied those together to get
That didn't inspire any great thoughts.
In the end I worked up a simple EXCEL spreadsheet that cycled through the available numbers until it worked.
A less than elegant solution.
I'm not sure of the benefit of the exercise.
But here's the answer.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website! I, too, could not think of a reasonable methodology, so I hammered through the list of numbers starting with 701 and 40 using a visual basic routine to simply multiply the numbers and check the results for the presence of each of the digits. If there is a logical way to approach this, I'd like someone to share.
John
Here's the Visual Basic for Applications code that finds the answer:
Option Explicit
Sub SolveIt()
Dim i As Long
Dim j As Long
Dim Ans As Long
For i = 701 To 798
For j = 40 To 49
Ans = i * j
If OneOfEach(i, j, Ans) Then
Worksheets(1).Range("A1") = i
Worksheets(1).Range("A2") = j
Worksheets(1).Range("A3") = Ans
End If
Next j
Next i
End Sub
Function OneOfEach(Big As Long, Small As Long, Product As Long) As Boolean
Dim k As Long
Dim Complete As String
Complete = Trim(Str(Big)) & Trim(Str(Small)) & Trim(Str(Product))
For k = 0 To 9
If InStr(Complete, Trim(Str(k))) = 0 Then
DISABLED_event_OneOfEach= False
Exit Function
End If
Next k
DISABLED_event_OneOfEach= True
End Function
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