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 Only 3 lines? (Posted on 2005-07-14)
It is well-known the solution to the problem of connecting nine dots, arranged in three rows of 3 dots, with four straight lines, without lifting up the pencil from the paper where they are drawn, and without any tricks at all, like folding the paper, etc...
```           o        o        o

o        o        o

o        o        o```
The question is: given the nine dots above, is it possible to connect them with only 3 straight lines ? The restrictions are the same, that is, without lifting up the pencil from the paper where they are drawn, no tricks allowed, and if you retrace a line, you must count one more line.

Note: this is a revisit to the problem Nine Dots already posted in this site and you can use that drawing for reference.

 See The Solution Submitted by pcbouhid Rating: 2.3333 (3 votes)

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 another trick | Comment 4 of 12 |
Since the problem states "no tricks allowed" I'm assuming that the points must all be of zero radius, and that it's impossible, but I can't figure out how to do a proof of that.

Another thought, which is probably trick and thus not allowed, is to consider the paper to be on the surface of a sphere, which means the straight lines could be like lines of longitude on the earth.  So if the lines go 1/4 the circumference of the sphere in each direction, then it could be done in 3 lines.

 Posted by Larry on 2005-07-15 01:22:51

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