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2016 and Simultaneous Settlement (Posted on 2016-05-26) Difficulty: 3 of 5
Find all possible positive integer solutions to this system of simultaneous equations:

AB+CD = 2016, and:
AD - BC = 1

*** For an extra challenge, solve this puzzle without a computer program aided method.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Solution computer solution (spoiler) | Comment 1 of 2
A, B, C and D are:

14 89 11 70

respectively

from

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For tot = 2 To 2017
   For a = 1 To tot - 1
    DoEvents
     b = tot - 1
     ab = a * b
     cd = 2016 - ab
     If cd > 0 Then
       For c = 1 To cd
         If cd Mod c = 0 Then
           d = cd / c
           If a * d - b * c = 1 Then
             Text1.Text = Text1.Text & a & Str(b) & Str(c) & Str(d) & crlf
           End If
         End If
       Next
     End If
   Next
 Next
 
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


  Posted by Charlie on 2016-05-26 10:55:52
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