Re: Interesting puzzle
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I have no idea how you did that.
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PMed. Just because this thread has somewhat tickled my fancy, I'm going to explain how I did it. Basically for my own amusement. If anyone is actually interested in discussing this, though, I am really interested in hearing what you math (graph theory) gurus have to say about this.
My logic is as follows:
1. The problem has a solution.
2. Therefore, if we had no choices as to where we put the dots, we would solve the problem.
3. Therefore, we should limit our choices as much as possible and we are thereby forced to solve the problem.
4. Therefore:
a. move all dots to the bottom
b. take one dot, preferably with only a few connections, to the top
c. move the dots which connect to the initial dot to the top in such a way that their lines do not cross
d. pick the newest dot with the fewest connections
e. if there is only one connection, move it to the top
f. if there is more than one connection, if there is a connection which connects to two or more dots on the top, move it to the top such that the lines do not overlap
NB: There is only ONE way to do this. As long as a bottom dot connects to MULTIPLE top dots there is NO CHOICE. There is only ONE way to move it to the top such that the lines among the top dots do not overlap (ignore lines going back to bottom dots). THIS IS THE KEY.
g. Continue on selecting top dots with as few connections as possible and bottom dots which connect to multiple top dots until all dots are on the top and no lines overlap.
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