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Max and Min (Posted on 2014-09-22) Difficulty: 2 of 5
Given P=(a/b+c/d)*(e/f+g/h) ,
where a,b,c.., ...h are 8 distinct positive integers, all below 25 and all fractions are proper fractions, find the highest and the lowest values of P.

Rem: P&P solution preferred.

See The Solution Submitted by Ady TZIDON    
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Solution computer solution | Comment 2 of 3 |
(In reply to Guesses by Jer)

Dim crlf$, used(25)


Private Sub Form_Load()
 ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents
 mini = 0.05: maxi = 3.25
 For a = 1 To 25
  If used(a) = 0 Then
    used(a) = 1
 For b = a + 1 To 25
  If used(b) = 0 Then
    used(b) = 1
    ab = a / b
 For c = a + 1 To 25
  If used(c) = 0 Then
    used(c) = 1
 For e = a + 1 To 25
  If used(e) = 0 Then
    used(e) = 1
 For d = c + 1 To 25
  If used(d) = 0 Then
    used(d) = 1
    abcd = ab + c / d
 For f = e + 1 To 25
  If used(f) = 0 Then
    used(f) = 1
    ef = e / f
 For g = e + 1 To 25
  If used(g) = 0 Then
    used(g) = 1
 For h = g + 1 To 25
  If used(h) = 0 Then
    used(h) = 1
    abcdefgh = abcd * (ef + g / h)
    rounded = Int(abcdefgh + 0.5)
    If abcdefgh < mini Then
      Text1.Text = Text1.Text & Str(a) & Str(b) & Str(c) & Str(d) & Str(e) & Str(f) & Str(g) & Str(h) & Str(abcdefgh) & crlf
      mini = abcdefgh
      DoEvents
    End If
    If abcdefgh > maxi Then
      Text1.Text = Text1.Text & Str(a) & Str(b) & Str(c) & Str(d) & Str(e) & Str(f) & Str(g) & Str(h) & Str(abcdefgh) & crlf
      maxi = abcdefgh
      DoEvents
    End If
    used(h) = 0
  End If
 Next
    used(g) = 0
  End If
 Next
    used(f) = 0
  End If
 Next
    used(d) = 0
  End If
 Next
    used(e) = 0
  End If
 Next
    used(c) = 0
  End If
 Next
    used(b) = 0
  End If
 Next
    used(a) = 0
  End If
 Next

 Text1.Text = Text1.Text & crlf & " done"
End Sub

finds

...
 1 22 2 25 3 23 4 24 3.72727272727273E-02
 
 so the minimum is (1/22 + 2/25) * (3/23 + 4/24) = 0.03727272...
 
...
 18 19 24 25 20 21 22 23 3.64098071265119
 
 and the maximum is (18/19 + 24/25) * (20/21 + 22/23) = 3.64098071265119.


  Posted by Charlie on 2014-09-22 12:22:25
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