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Given VI, evaluate VII (Posted on 2017-02-01) Difficulty: 2 of 5
The integers x(1), x(2), x(3), x(4), x(5), x(6), x(7)
comply with the recursive formula: x(n+3)=x(n+2)*(x(n+1)+x(n))

If x(6)=144 what is the value of x(7)?

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution (spoiler) Comment 1 of 1
DefDbl A-Z
Dim crlf$, fct(20, 1), x(7)


Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)

 For tot = 3 To 500
   For a0 = 0 To tot
   For b0 = 0 To tot
    DoEvents
    For a = -a0 To a0 Step 2 * a0
    For b = -b0 To b0 Step 2 * b0
            c = tot - a - b
            x(1) = a: x(2) = b: x(3) = c
            If a = -7 And b = -1 And c = -1 Then
              xx = xx
            End If
            For s = 4 To 7
              x(s) = x(s - 1) * (x(s - 2) + x(s - 3))
            Next
            If x(6) = 144 Then
              For i = 1 To 7
                Text1.Text = Text1.Text & Str(x(i))
              Next
              Text1.Text = Text1.Text & crlf
            End If
            If b = 0 Then Exit For
    Next
    If a = 0 Then Exit For
    Next
   Next
   Next
 Next


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

find the possible sequences

-2 4 2 4 24 144 4032
 2-4 6-12-24 144-5184
 2 1 2 6 18 144 3456
 5 3-1-8-16 144-3456
 5-4 6 6 12 144 2592
 7 1 1 8 16 144 3456

The puzzle doesn't say that only positive integers are allowed, but only with that restriction is there a unique answer: 3456.

  Posted by Charlie on 2017-02-01 10:55:25
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