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

Home > Just Math
Oblong Difference Observation (Posted on 2015-10-15) Difficulty: 3 of 5
Find all possible pairs (M, N) of oblong numbers that satisfy:

M - N = 2016

Prove that there are no others.

*** As an extra challenge solve this puzzle without using a computer program aided method.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution two more solutions (computer solutions) | Comment 2 of 3 |
(In reply to solution by xdog)

                    ordinal
      M       N     oblongs
    2256     240    47   15
    3422    1406    58   37
   13572   11556   116  107
   21756   19740   147  140  *
  113906  111890   337  334  *
 1017072 1015056  1008 1007
 
* these two were not in xdog's solution

These are the only ones as, beyond the 1008th oblong, the oblongs are farther apart than 2016 and farther than 2016 from any oblong before.
 
DefDbl A-Z
Dim crlf$


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

 For addend = 2 To 2020 Step 2
   DoEvents
   obl = obl + addend
   n = obl: m = n + 2016
   If isObl(m) Then
     Text1.Text = Text1.Text & mform(m, "#######0") & mform(n, "#######0") & mform(isObl(m), "#####0") & mform(isObl(n), "####0") & crlf
   End If
 Next

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

Function mform$(x, t$)
  a$ = Format$(x, t$)
  If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
  mform$ = a$
End Function

Function isObl(o)
n = Int(Sqr(o))
np = n + 1
If n * np = o Then isObl = n Else isObl = 0
End Function


 


  Posted by Charlie on 2015-10-15 13:58:20
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (10)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information