perplexus.info :: Geometry : Only 3 lines?

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.

Prove your answer!

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

Submitted by pcbouhid

Rating: 2.3333 (3 votes)

Solution: (Hide)

Yes, it is possible !

No one can deny that wherever this problem appears, the dots are not mathematical dots (the crossing of two lines). And to avoid this discussion, I cited the PID 405, telling you explicitly TO USE THAT DRAWING.

First, we draw one line crossing the middle line of dots (it´s not necessary to be by the center of the dots).

The other line will be draw crossing the upper row of dots, but slightly inclined, almost tangencing the two extreme dots, what is possible. This line will cross the "center" line in one point, since they are not parallel.

Doing the same with the bottom row of dots, we have another line, that also will cross the "center" line, in one point, at the other side of the drawing.

Doing this, we will have only 3 straight lines.

Obviously, the sequence of drawing isn´t the above, the explanation given is to make better understanding how could it be done. The only restriction (not lifting up the pencil) can be attended, and nothing was said about how large the paper must be !!

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
solution	jess	2005-07-19 22:48:21
re(2): To all...	pcbouhid	2005-07-15 23:03:44
re: To all...	Sam	2005-07-15 22:42:34
To all...	pcbouhid	2005-07-15 18:05:06
re: Another way	Bob Smith	2005-07-15 14:10:04
re: another trick	brianjn	2005-07-15 08:19:02
re: Solution	Richard	2005-07-15 02:51:47
Solution	Brian Smith	2005-07-15 01:23:15
another trick	Larry	2005-07-15 01:22:51
Another way	Richard	2005-07-14 20:45:56
re: One way -- some numbers	Charlie	2005-07-14 19:08:24
One way	Bob Smith	2005-07-14 17:25:46

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