DefDbl A-Z

Dim crlf$, used(30)

Private Sub Form_Load()

 Form1.Visible = True

 

 Text1.Text = ""

 crlf = Chr$(13) + Chr$(10)

 

 minimum = 100

 

 For a = 1 To 23

   used(a) = 1

 For b = a + 1 To 30

   used(b) = 1

 For c = a + 1 To 29

   If used(c) = 0 Then

     used(c) = 1

 For d = c + 1 To 30

   If used(d) = 0 Then

     used(d) = 1

 For e = a + 1 To 29

   If used(e) = 0 Then

     used(e) = 1

     DoEvents

 For f = e + 1 To 30

   If used(f) = 0 Then

     used(f) = 1

 For g = e + 1 To 29

   If used(g) = 0 Then

     used(g) = 1

 For h = g + 1 To 30

   If used(h) = 0 Then

     used(h) = 1

       If a * b + c * d = e * f + g * h Then

        If a * b + c * d <= minimum Then

         Text1.Text = Text1.Text & Str(a) & Str(b) & Str(c) & Str(d) & Str(e) & Str(f) & Str(g) & Str(h) & "  " & a * b + c * d & crlf

         minimum = a * b + c * d

        End If

       End If

     used(h) = 0

   End If

 Next

     used(g) = 0

   End If

 Next

     used(f) = 0

   End If

 Next

     used(e) = 0

   End If

 Next

     used(d) = 0

   End If

 Next

     used(c) = 0

   End If

 Next

  used(b) = 0

 Next

  used(a) = 0

 Next

   

 Text1.Text = Text1.Text & minimum & crlf & " done"

  

End Sub

finds the minimum is 31, per:

 1 2 3 19 4 6 5 7  59

 1 2 4 13 3 8 5 6  54

 1 2 5 10 3 8 4 7  52

 1 2 6 7 3 8 4 5  44

 1 4 5 7 2 6 3 9  39

 1 5 3 11 2 7 4 6  38

 1 6 3 10 2 8 4 5  36

 1 6 4 7 2 5 3 8  34

 1 7 3 9 2 5 4 6  34

 1 7 4 6 2 8 3 5  31

 

where the last, best, line represents

1*7 + 4*6 = 2*8 + 3*5 = 31

where a had to be the smallest number of all 8

b had to be larger than a (of course)

same with c larger than a 

d larger than c

e larger than a

f larger than e

g larger than e

h larger than g

wlog. The rules merely eliminate trivial variations.