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Dascal triangle (Posted on 2016-02-02) Difficulty: 3 of 5
Arrange integers 1- 15 in a triangle such that the upper row consists of 5 integers, all other rows represent each the absolute values of the differences between the adjacent members of the row above so that the 5th row contains one number only.

A bad example:

4   7  15  10   2
  3  12   5   8
    9   7   * oops!  Can't use 3 again.
Just wanted to explain the build-up..
Better luck to the solvers!

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution | Comment 1 of 8
The two mirror-image solutions are:

 6 14 15 3 13
 8 1 12 10
 7 11 2
 4 9
 5

 13 3 15 14 6
 10 12 1 8
 2 11 7
 9 4
 5
 
 DefDbl A-Z
 Dim crlf$, grid(5, 5), used(15)
 
 
 Private Sub Form_Load()
  Form1.Visible = True
  
  Text1.Text = ""
  crlf = Chr$(13) + Chr$(10)
  
  addOn 1, 1
 
 
  Text1.Text = Text1.Text & crlf & " done"
   
 End Sub
 
 Sub addOn(row, col)
  If row = 1 Then
   For i = 1 To 15
     If used(i) = 0 Then
       grid(row, col) = i
       used(i) = 1
       
       r = row: c = col + 1
       If c > 5 Then r = r + 1: c = 1
       addOn r, c
       
       used(i) = 0
     End If
   Next
  Else
   diff = Abs(grid(row - 1, col) - grid(row - 1, col + 1))
   If used(diff) = 0 Then
     grid(row, col) = diff
     used(diff) = 1
       
     r = row: c = col + 1
     If c > 6 - row Then r = r + 1: c = 1
     If r < 6 Then
       addOn r, c
     Else
       For r = 1 To 5
        For c = 1 To 6 - r
          Text1.Text = Text1.Text & Str(grid(r, c))
        Next c
        Text1.Text = Text1.Text & crlf
       Next r
       Text1.Text = Text1.Text & crlf
     End If
       
     used(diff) = 0
   End If
  End If
 End Sub


  Posted by Charlie on 2016-02-02 15:37:44
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