24 Feb 08
Originally posted by anthranilateUsing the top line as a base for this explanation;
u have 6 dots..
. . .
. . .
upper dots must connect with all bottom dots and either way, with a line..
cross line is illegal...
Draw large sort of ellipses around the outside of the rest of the dots to connect the left most dot to the other 3.........
Directly connect the center dot to the other 3 using straight lines....
for the right hand dot go right around........... Aghhhhh to hard to explain.... Do it on paper.....
The other option is to do this with your lines since you never stipulated that the lines had to connect directly....
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l l l
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24 Feb 08
2 edits
Originally posted by MexicoYou cannot connect all of them as the last dot pairing will have a complete barrier (360 degrees).
Using the top line as a base for this explanation;
Draw large sort of ellipses around the outside of the rest of the dots to connect the left most dot to the other 3.........
Directly connect the center dot to the other 3 using straight lines....
for the right hand dot go right around........... Aghhhhh to hard to explain.... Do it on paper.....
The o ...[text shortened]... e you never stipulated that the lines had to connect directly....
._._.
l l l
._._.
This does work if you do not have to have 9 lines, but use one line to connect one top dot with all three bottom dots, then you only need three lines (or one line if you want to extend it further).
24 Feb 08
Yea I did this when I was a kid, remembered that I had a solution which was really clever..... Then remembered what it was....
The puzzle is impossible unless you do what I did, actually won 10 pounds for this which is quite funny because I half cheated......
Basically to connect the last one I went out around the edge of the page and used that gap to solve the puzzle.......
25 Feb 08
Originally posted by GregMNo - but they are connected. The 4-colour theorem applies to any planar graph (this is a graph - a collection of nodes (points) and vertexes (lines)). A planar graph is any graph that can be drawn on a sphere such that no lines cross.
Isn't this equivalent to map-coloring? The four-color theorem should apply. Is it possible to completely connect 5 dots to each other with non-crossing lines?
It can be shown that a graph is not planar if and only if it contains the graph described above (called k[3,3]) or the connected graph on 5 vertexes (k[5] - a pentagon with all nodes connected to all other nodes) embedded in it. This leads quite nicely onto the 5-colour problem.
I know this reads quite awfully - http://tinyurl.com/33zkwr
[wiki] describes it better.
25 Feb 08
Originally posted by anthranilateThe answer is that it can't be done. Unless you have a torus like geometry or a paper with a hole in it or otherwise, then it can be done with a trick. But on a flat surface, like a paper, it can't be done.
can u guys post the answer..............really appreciate it