All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Arithmetic Product Puzzle (Posted on 2015-08-13)
Determine the smallest positive integer that is expressible as the product of three distinct positive integers in arithmetic sequence in precisely two ways.

What are the next two smallest positive integers with this property?

**** As an example, 105 is expressible as the product of three positive integers (3, 5 and 7) in arithmetic sequence in only one way as no other positive integer triplet in arithmetic sequence multiplies to 105.

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution Comment 1 of 1

The first 7 (under 2000) are:

`  n  ways 231 2 440 2 504 2 840 21560 21680 21848 2`

The first three's details are:

` n  sequence231 1 11 21231 3 7 11440 2 11 20440 5 8 11504 4 9 14504 7 8 9`

By rearranging the output of:

DefDbl A-Z
Dim crlf\$

Form1.Visible = True

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

high = 2000
ReDim ways(high)
For a = 1 To high
For d = 1 To high - a
s = a * (a + d) * (a + 2 * d)
If s <= high Then ways(s) = ways(s) + 1 Else Exit For
If s = 231 Or s = 440 Or s = 504 Then
Text1.Text = Text1.Text & s & Str(a) & Str(a + d) & Str(a + 2 * d) & crlf
End If
Next
Next

For i = 1 To high
If ways(i) = 2 Then Text1.Text = Text1.Text & i & Str(ways(i)) & crlf: DoEvents
Next

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

End Sub

The lines

If s = 231 Or s = 440 Or s = 504 Then
Text1.Text = Text1.Text & s & Str(a) & Str(a + d) & Str(a + 2 * d) & crlf
End If

were obviously added after the first run determined the first three solutions.

 Posted by Charlie on 2015-08-13 14:52:35

 Search: Search body:
Forums (0)