# Thread: Out of Box thinking

1. ## Out of Box thinking

There is a relatively common "Out of the Box Puzzle" where one is given a 9 -dots set up in a 3x3 pattern and asked to connect the dots by drawing four straight, continuous lines, without ever lifting the pencil from the paper. The pattern and one of the common solutions is attached.

But the further out of the box puzzle is to connect the dots by drawing only THREE straight, continuous lines, without ever lifting the pencil from the paper.

Steve

2. ## Re: Out of Box thinking

I can do it with one line <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">if I am allowed to fold the paper as many times as I want!</span hide>

StuartR

3. ## Re: Out of Box thinking

Given that the dots have <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">a non-zero diameter</span hide>, the picture in the attached zip file shows a way.

4. ## Re: Out of Box thinking

<img src=/S/thumbup.gif border=0 alt=thumbup width=15 height=15> <img src=/S/clapping.gif border=0 alt=clapping width=19 height=23> Nice out of box thinking. The key to the puzzle is that very point you mention: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">It is 9-dot puzzle, not a nine-point puzzle. The dots have 2 dimensions on paper and thus the line does not have to go through the center of all of them...</span hide>

Steve

5. ## Re: Out of Box thinking

Presumably there must be a restriction on the width of the pencil too, otherwise you could probably do it with one very thick line!

6. ## Re: Out of Box thinking

So just adding a little bit of discussion...

I was able to do this with one straight line but did some "out of the box thinking" and used <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> a non-Euclidean plane in the form of a cylinder and having points with non zero diameter (dots) and drew a spiral around it</span hide>

It may not have been in the spirit of the puzzle but I did it 'cos I could <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

7. ## Re: Out of Box thinking

Jezza,

I think that your solution and mine are topologically equivalent. It's just a matter of whether you <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">fold the space as well as the paper</span hide>.

StuartR

8. ## Re: Out of Box thinking

Yes that is the real out of box thinking<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">small points and a thick line</span hide>

But the question comes, if you at a seminar and given a sheet of paper with the 9 points and pencil, how many could do the 4 lines and how many could do the 3 lines?

Steve

9. ## Re: Out of Box thinking

I like this solution to the puzzle as well. The original will have to be modified to indicate tha the paper stays flat on the table... <img src=/S/smile.gif border=0 alt=smile width=15 height=15>

Steve

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