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Some Triangles Sum 2014 (Posted on 2014-08-12) Difficulty: 3 of 5
Determine all possible sequences of consecutive triangular numbers whose sum is precisely 2014.

Extra Challenge: A non computer program based method.

No Solution Yet Submitted by K Sengupta    
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Solution computer solution | Comment 2 of 5 |
DefDbl A-Z
Dim crlf$

Private Sub Form_Load()
 ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents
 
 firstTri = 1: lastTri = 1: Sum = 1
 add4firstTri = 2: add4lastTri = 2
 
 Do
   If Sum = 2014 Then
     Text1.Text = Text1.Text & firstTri & Str(lastTri) & "     "
     Text1.Text = Text1.Text & Str(isTri(firstTri)) & Str(isTri(lastTri)) & "     "
     For i = isTri(firstTri) To isTri(lastTri)
      Text1.Text = Text1.Text & Str(triNum(i))
     Next
     Text1.Text = Text1.Text & crlf
     DoEvents
     lastTri = lastTri + add4lastTri: Sum = Sum + lastTri: add4lastTri = add4lastTri + 1
   ElseIf Sum < 2014 Then
     lastTri = lastTri + add4lastTri: Sum = Sum + lastTri: add4lastTri = add4lastTri + 1
   Else
     Sum = Sum - firstTri
     firstTri = firstTri + add4firstTri: add4firstTri = add4firstTri + 1
   End If
   
 Loop Until firstTri > 2014
 
 
 Text1.Text = Text1.Text & crlf & firstTri & Str(lastTri) & " done"
End Sub

Function isTri(t)
n = Int(Sqr(t * 2))
np = n + 1
If n * np = 2 * t Then isTri = n Else isTri = 0
End Function

Function triNum(i)
  triNum = i * (i + 1) / 2
End Function

finds only two sequences of triangular numbers that add to 2014:

First &	   Tr(#)      All the triangular numbers in the sequnce.
last nos.  first &
   last
10 253      4 22      10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253
78 276      12 23      78 91 105 120 136 153 171 190 210 231 253 276

So, the 4th through 22 triangular numbers (10 through 253) add up to 2014 as do the 12th through 23rd (78 through 276).

  Posted by Charlie on 2014-08-12 17:10:24
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