Question 117608
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
                OneOfEach = False
                Exit Function
            End If
        Next k
        OneOfEach = True
End Function