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Maximizing the sum (Posted on 2016-11-16) Difficulty: 3 of 5
Let me provide some facts about a couple of integers m and n:

- One of them is a 3-digit number, the other is a 2-digit number
- One of them is divisible by 11
- One has all its digits distinct
- The last digit of m^3 equals the last digit of n
- The last digit of n^3 equals the last digit of m

a. Evaluate the maximum value of m+n.
b. What possible values can m*n reach?

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( Back to comment list | You must be logged in to post comments.)
the program Comment 4 of 4 |
(In reply to part b in more concise form by Charlie)

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For a = 100 To 999
 For b = 10 To 99
   If a Mod 11 = 0 Or b Mod 11 = 0 Then
     astr$ = LTrim(Str(a)): bstr$ = LTrim(Str(b))
     good = 0
     If Mid(astr, 1, 1) <> Mid(astr, 2, 1) And Mid(astr, 1, 1) <> Mid(astr, 3, 1) And Mid(astr, 3, 1) <> Mid(astr, 2, 1) Then good = 1
     If Mid(bstr, 1, 1) <> Mid(bstr, 2, 1) Then good = 1
     If good Then
       a3 = a * a * a: b3 = b * b * b
       If a3 Mod 10 = b Mod 10 And a Mod 10 = b3 Mod 10 Then
          Text1.Text = Text1.Text & a & Str(b) & "       "
          Text1.Text = Text1.Text & mform(a + b, "###0") & mform(a * b, "#####0") & "        "
          Text1.Text = Text1.Text & mform(a3, "##########0") & mform(b3, "######0") & crlf
          If a + b > maxsum Then maxsum = a + b: mxsa = a: mxsb = b
          If a * b > maxprod Then maxprod = a * b: mxpa = a: mxpb = b
       End If
     End If
   End If
   DoEvents
 Next
 Next
 
 Text1.Text = Text1.Text & maxsum & Str(mxsa) & Str(mxsb) & crlf
 Text1.Text = Text1.Text & maxprod & Str(mxpa) & Str(mxpb) & crlf
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub

Function mform$(x, t$)
  a$ = Format$(x, t$)
  If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
  mform$ = a$
End Function


  Posted by Charlie on 2016-11-16 10:22:00
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