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Arithmetic Product Puzzle 2 (Posted on 2016-06-14) Difficulty: 3 of 5
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    
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Solution 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$


Private Sub Form_Load()
 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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