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.
(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 |
two more solutions (computer solutions)
