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 Oblong Difference Observation (Posted on 2015-10-15)
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.)
 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\$

Form1.Visible = True

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

For addend = 2 To 2020 Step 2
DoEvents
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

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