perplexus.info :: Just Math : 2016 and Simultaneous Settlement

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.

See The Solution Submitted by K Sengupta

Rating: 4.5000 (2 votes)

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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

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

End Sub

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

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