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 2016 and Simultaneous Settlement (Posted on 2016-05-26)
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
 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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