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 Given VI, evaluate VII (Posted on 2017-02-01)
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 No Rating

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 computer solution (spoiler) Comment 1 of 1
DefDbl A-Z
Dim crlf\$, fct(20, 1), x(7)

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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