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 Arithmetic Product Puzzle 2 (Posted on 2016-06-14)
The product of precisely N (N > 2) integers in arithmetic sequence is 1575.

Find the possible values of N.

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution Comment 2 of 2 |
N can be 7 or 3, based on

(i) Sequence starting at -7, increments of 2, through 5.
It has 4 negative elements, making the product positive 1575:
-7, -5, -3, -1,  1,  3,  5   (7 elements)

(ii) Sequence starting at -25, increments of 16, through 7.
It has 2 negative elements, making the product positive 1575:
-25, -9,  7     (3 elements)

The computer output:

-7 2 5   7
-7 -5 -3 -1  1  3  5
-25 16 7   3
-25 -9  7

from

DefDbl A-Z
Dim crlf\$

Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

For st0 = 1 To 1575
For st = -st0 To st0 Step st0 + st0
For diff = 1 To 1575
DoEvents
prod = 1
k = st: terms = 0
Do
terms = terms + 1
prod = prod * k
If Abs(prod) > 1575 Then Exit Do
If prod = 1575 And terms > 2 Then
Text1.Text = Text1.Text & st & Str(diff) & Str(k) & "   " & terms & crlf
For i = st To k Step diff
Text1.Text = Text1.Text & " " & Str(i)
Next
Text1.Text = Text1.Text & crlf
End If
k = k + diff
Loop Until k = 0
Next diff
Next
Next

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

End Sub

 Posted by Charlie on 2016-06-14 09:55:53

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