20040504, 12:42  #1 
3×13×43 Posts 
shongo Network
Ok we had this discussion on another board  nobody could figure it out. It was the draw a figure without lifting your pencil. According to euler it won't work because there are more than 2 points with odd number of vertices. Well then I did research and found out about shongo networks  and the very drawing we talked about was shown. For the life of me, I can't figure it out though.
At the bottom of this page http://educ.queensu.ca/~fmc/april2002/Shongo.htm there are 3 drawings  its the middle of the 3. Does anyone know how to do it without there being a trick (ie drawing extra line or folding paper) 
20040515, 11:27  #2  
May 2004
2^{2} Posts 
Quote:


20040515, 14:24  #3  
"William"
May 2003
New Haven
2^{3}·5·59 Posts 
Quote:
First consider the case of starting here. When you trace out, there are now an even number of untraced line segments. Every time you return to the point, there will be an odd number of untraced line segments, to you can leave again. Eventually you will leave with zero untraced segments and never return. So if you start here, you will end someplace else. Second consider the case of starting someplace else. Every time you return to the point, there will be an even number of untraced links left, and every time you depart the point there will be an odd number of untraced links left. Eventually you will reach the point with zero untraced links conected to the point so you will quit. Hence every point with an odd number of links must be eiher a starting point or an ending point. The diagram has FOUR points with an odd number of links. The only way trace it is to use TWO lines to get two starting points and two ending points. William 

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