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Counting Ten Segment Paths (Posted on 2016-02-19) Difficulty: 2 of 5
Multiple paths can be drawn on the grid below following along ten of the twelve segments but never using any segment twice.
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How many such paths are there?

No Solution Yet Submitted by Brian Smith    
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Solution computer solution | Comment 2 of 6 |
Below are the 200 paths that satisfy the requirements. These certainly include reflections, rotations and reversals; 200 is not divisible by 2*4*2=16, so some of these categories of duplication may overlap. Each digit pair should be considered as a pair of x-y coordinates; there are eleven such points on each route as ten segments are traversed:

01,00,10,11,01,02,12,11,21,20,10,
01,00,10,11,01,02,12,11,21,22,12,
01,00,10,11,01,02,12,22,21,11,12,
01,00,10,11,01,02,12,22,21,20,10,
01,00,10,11,12,02,01,11,21,20,10,
01,00,10,11,12,02,01,11,21,22,12,
01,00,10,11,12,22,21,11,01,02,12,
01,00,10,11,21,22,12,02,01,11,12,
01,00,10,11,21,22,12,11,01,02,12,
01,00,10,20,21,11,01,02,12,11,10,
01,00,10,20,21,11,01,02,12,22,21,
01,00,10,20,21,11,12,02,01,11,10,
01,00,10,20,21,22,12,02,01,11,10,
01,00,10,20,21,22,12,02,01,11,12,
01,00,10,20,21,22,12,02,01,11,21,
01,00,10,20,21,22,12,11,01,02,12,
01,02,12,11,01,00,10,11,21,20,10,
01,02,12,11,01,00,10,11,21,22,12,
01,02,12,11,01,00,10,20,21,11,10,
01,02,12,11,01,00,10,20,21,22,12,
01,02,12,11,10,00,01,11,21,20,10,
01,02,12,11,10,00,01,11,21,22,12,
01,02,12,11,10,20,21,11,01,00,10,
01,02,12,11,21,20,10,00,01,11,10,
01,02,12,11,21,20,10,11,01,00,10,
01,02,12,22,21,11,01,00,10,11,12,
01,02,12,22,21,11,01,00,10,20,21,
01,02,12,22,21,11,10,00,01,11,12,
01,02,12,22,21,20,10,00,01,11,10,
01,02,12,22,21,20,10,00,01,11,12,
01,02,12,22,21,20,10,00,01,11,21,
01,02,12,22,21,20,10,11,01,00,10,
01,11,10,00,01,02,12,11,21,20,10,
01,11,10,00,01,02,12,11,21,22,12,
01,11,10,00,01,02,12,22,21,11,12,
01,11,10,00,01,02,12,22,21,20,10,
01,11,10,20,21,11,12,02,01,00,10,
01,11,10,20,21,22,12,02,01,00,10,
01,11,12,02,01,00,10,11,21,20,10,
01,11,12,02,01,00,10,11,21,22,12,
01,11,12,02,01,00,10,20,21,11,10,
01,11,12,02,01,00,10,20,21,22,12,
01,11,12,22,21,11,10,00,01,02,12,
01,11,12,22,21,20,10,00,01,02,12,
01,11,21,20,10,00,01,02,12,11,10,
01,11,21,20,10,00,01,02,12,22,21,
01,11,21,20,10,11,12,02,01,00,10,
01,11,21,22,12,02,01,00,10,11,12,
01,11,21,22,12,02,01,00,10,20,21,
01,11,21,22,12,11,10,00,01,02,12,
10,00,01,02,12,11,10,20,21,11,01,
10,00,01,02,12,11,10,20,21,22,12,
10,00,01,02,12,11,21,20,10,11,01,
10,00,01,02,12,22,21,11,10,20,21,
10,00,01,02,12,22,21,20,10,11,01,
10,00,01,02,12,22,21,20,10,11,12,
10,00,01,02,12,22,21,20,10,11,21,
10,00,01,11,10,20,21,11,12,02,01,
10,00,01,11,10,20,21,11,12,22,21,
10,00,01,11,10,20,21,22,12,02,01,
10,00,01,11,10,20,21,22,12,11,21,
10,00,01,11,12,22,21,11,10,20,21,
10,00,01,11,12,22,21,20,10,11,21,
10,00,01,11,21,20,10,11,12,02,01,
10,00,01,11,21,20,10,11,12,22,21,
10,00,01,11,21,22,12,11,10,20,21,
10,11,01,00,10,20,21,11,12,02,01,
10,11,01,00,10,20,21,11,12,22,21,
10,11,01,00,10,20,21,22,12,02,01,
10,11,01,00,10,20,21,22,12,11,21,
10,11,01,02,12,11,21,20,10,00,01,
10,11,01,02,12,22,21,20,10,00,01,
10,11,12,02,01,00,10,20,21,11,01,
10,11,12,02,01,00,10,20,21,22,12,
10,11,12,02,01,11,21,20,10,00,01,
10,11,12,22,21,11,01,00,10,20,21,
10,11,12,22,21,20,10,00,01,02,12,
10,11,12,22,21,20,10,00,01,11,21,
10,11,21,20,10,00,01,02,12,11,01,
10,11,21,20,10,00,01,02,12,22,21,
10,11,21,20,10,00,01,11,12,02,01,
10,11,21,20,10,00,01,11,12,22,21,
10,11,21,22,12,02,01,00,10,20,21,
10,11,21,22,12,11,01,00,10,20,21,
10,20,21,11,01,00,10,11,12,02,01,
10,20,21,11,01,00,10,11,12,22,21,
10,20,21,11,01,02,12,11,10,00,01,
10,20,21,11,10,00,01,02,12,11,01,
10,20,21,11,10,00,01,02,12,22,21,
10,20,21,11,10,00,01,11,12,02,01,
10,20,21,11,10,00,01,11,12,22,21,
10,20,21,11,12,02,01,00,10,11,01,
10,20,21,11,12,02,01,11,10,00,01,
10,20,21,22,12,02,01,00,10,11,01,
10,20,21,22,12,02,01,00,10,11,12,
10,20,21,22,12,02,01,00,10,11,21,
10,20,21,22,12,02,01,11,10,00,01,
10,20,21,22,12,11,01,00,10,11,21,
10,20,21,22,12,11,10,00,01,02,12,
10,20,21,22,12,11,10,00,01,11,21,
12,02,01,00,10,11,12,22,21,11,01,
12,02,01,00,10,11,12,22,21,20,10,
12,02,01,00,10,11,21,22,12,11,01,
12,02,01,00,10,20,21,11,12,22,21,
12,02,01,00,10,20,21,22,12,11,01,
12,02,01,00,10,20,21,22,12,11,10,
12,02,01,00,10,20,21,22,12,11,21,
12,02,01,11,10,20,21,11,12,22,21,
12,02,01,11,10,20,21,22,12,11,21,
12,02,01,11,12,22,21,11,10,00,01,
12,02,01,11,12,22,21,11,10,20,21,
12,02,01,11,12,22,21,20,10,00,01,
12,02,01,11,12,22,21,20,10,11,21,
12,02,01,11,21,20,10,11,12,22,21,
12,02,01,11,21,22,12,11,10,00,01,
12,02,01,11,21,22,12,11,10,20,21,
12,11,01,00,10,11,21,22,12,02,01,
12,11,01,00,10,20,21,22,12,02,01,
12,11,01,02,12,22,21,11,10,00,01,
12,11,01,02,12,22,21,11,10,20,21,
12,11,01,02,12,22,21,20,10,00,01,
12,11,01,02,12,22,21,20,10,11,21,
12,11,10,00,01,02,12,22,21,11,01,
12,11,10,00,01,02,12,22,21,20,10,
12,11,10,00,01,11,21,22,12,02,01,
12,11,10,20,21,11,01,02,12,22,21,
12,11,10,20,21,22,12,02,01,00,10,
12,11,10,20,21,22,12,02,01,11,21,
12,11,21,20,10,00,01,02,12,22,21,
12,11,21,20,10,11,01,02,12,22,21,
12,11,21,22,12,02,01,00,10,11,01,
12,11,21,22,12,02,01,00,10,20,21,
12,11,21,22,12,02,01,11,10,00,01,
12,11,21,22,12,02,01,11,10,20,21,
12,22,21,11,01,00,10,11,12,02,01,
12,22,21,11,01,02,12,11,10,00,01,
12,22,21,11,01,02,12,11,10,20,21,
12,22,21,11,10,00,01,02,12,11,01,
12,22,21,11,10,00,01,11,12,02,01,
12,22,21,11,12,02,01,00,10,11,01,
12,22,21,11,12,02,01,00,10,20,21,
12,22,21,11,12,02,01,11,10,00,01,
12,22,21,11,12,02,01,11,10,20,21,
12,22,21,20,10,00,01,02,12,11,01,
12,22,21,20,10,00,01,02,12,11,10,
12,22,21,20,10,00,01,02,12,11,21,
12,22,21,20,10,00,01,11,12,02,01,
12,22,21,20,10,11,01,02,12,11,21,
12,22,21,20,10,11,12,02,01,00,10,
12,22,21,20,10,11,12,02,01,11,21,
21,11,01,00,10,11,12,22,21,20,10,
21,11,01,00,10,20,21,22,12,02,01,
21,11,01,00,10,20,21,22,12,11,10,
21,11,01,02,12,11,10,20,21,22,12,
21,11,01,02,12,22,21,20,10,00,01,
21,11,01,02,12,22,21,20,10,11,12,
21,11,10,00,01,02,12,22,21,20,10,
21,11,10,00,01,11,12,22,21,20,10,
21,11,10,20,21,22,12,02,01,00,10,
21,11,10,20,21,22,12,02,01,11,12,
21,11,10,20,21,22,12,11,01,00,10,
21,11,10,20,21,22,12,11,01,02,12,
21,11,12,02,01,00,10,20,21,22,12,
21,11,12,02,01,11,10,20,21,22,12,
21,11,12,22,21,20,10,00,01,02,12,
21,11,12,22,21,20,10,00,01,11,10,
21,11,12,22,21,20,10,11,01,00,10,
21,11,12,22,21,20,10,11,01,02,12,
21,20,10,00,01,02,12,11,21,22,12,
21,20,10,00,01,02,12,22,21,11,01,
21,20,10,00,01,02,12,22,21,11,10,
21,20,10,00,01,02,12,22,21,11,12,
21,20,10,00,01,11,12,22,21,11,10,
21,20,10,00,01,11,21,22,12,02,01,
21,20,10,00,01,11,21,22,12,11,10,
21,20,10,11,01,02,12,11,21,22,12,
21,20,10,11,01,02,12,22,21,11,12,
21,20,10,11,12,02,01,11,21,22,12,
21,20,10,11,12,22,21,11,01,00,10,
21,20,10,11,12,22,21,11,01,02,12,
21,20,10,11,21,22,12,02,01,00,10,
21,20,10,11,21,22,12,02,01,11,12,
21,20,10,11,21,22,12,11,01,00,10,
21,20,10,11,21,22,12,11,01,02,12,
21,22,12,02,01,00,10,11,21,20,10,
21,22,12,02,01,00,10,20,21,11,01,
21,22,12,02,01,00,10,20,21,11,10,
21,22,12,02,01,00,10,20,21,11,12,
21,22,12,02,01,11,10,20,21,11,12,
21,22,12,02,01,11,21,20,10,00,01,
21,22,12,02,01,11,21,20,10,11,12,
21,22,12,11,01,00,10,11,21,20,10,
21,22,12,11,01,00,10,20,21,11,10,
21,22,12,11,10,00,01,11,21,20,10,
21,22,12,11,10,20,21,11,01,00,10,
21,22,12,11,10,20,21,11,01,02,12,
21,22,12,11,21,20,10,00,01,02,12,
21,22,12,11,21,20,10,00,01,11,10,
21,22,12,11,21,20,10,11,01,00,10,
21,22,12,11,21,20,10,11,01,02,12,

DefDbl A-Z
Dim crlf$, h As String, x, y, ct


Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For x0 = 0 To 2
 For y0 = 0 To 2
   x = x0: y = y0
   placeIt
 Next
 Next


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

Sub placeIt()
  s$ = LTrim(Str(x)) + LTrim(Str(y))
  h = h + s + ","
  moved = 0
  For dx = -1 To 1
  For dy = -1 To 1
   If dx * dy = 0 And dx + dy <> 0 Then
     newx = x + dx: newy = y + dy
     If newx >= 0 And newx <= 2 And newy >= 0 And newy <= 2 Then
       x = newx: y = newy
       
       news$ = LTrim(Str(x)) + LTrim(Str(y))
       a$ = s + "," + news: b$ = news + "," + s
       If InStr(h, a) = 0 Then
         If InStr(h, b) = 0 Then
             placeIt
             moved = 1
         End If
       End If
       
       x = x - dx: y = y - dy
     End If
   End If
  Next
  Next
  
  If moved = 0 Then
    If Len(h) >= 33 Then
      ct = ct + 1
      Text1.Text = Text1.Text & h & crlf
    End If
  End If
  
  h = Left(h, Len(h) - 3)
End Sub


  Posted by Charlie on 2016-02-19 13:29:41
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