The Nine Dot Puzzle

1. someguy
   June 5th, 2008 at 5:12 pm

   There are two more solutions.
   A) using only one line
   B) using one line of zero length (i.e. using a degenerate line which is a point)

   Regarding A) The problem can be solved with a single line if:

   - the dots are not infinitely small (as in the 3 line solution)
   - you have enough paper to cover the planet (Or at least enough of a strip to go once around the earth)

   Just draw a line which goes almost - but not quite - through the three dots at the bottom. The line will go around the planet twice and ‘corkscrew’ through the remaining points.

   If you feel like using less paper just bend a small piece of paper with the puzzle on it into a cylinder.

   Reagrding B)

   Fold the paper so that all dots touch. Punch a line thrugh the paper. If it is ‘ideal’ paper (zero thickness) then the line will have zero length. If it is not ideal paper then the folding is a bit more tricky, but you can still do it if you fold it like a crown (a dort at each apex) and have the dots touch.

2. Alex
   June 5th, 2008 at 5:15 pm

   Maybe all you have to do is look at it cross-eyed, then you can solve it with one dot!

3. Ishmael
   June 5th, 2008 at 5:34 pm

   Unfortunately, the RSS feed reveals the answer without having to click first… Thankfully, I already knew the answer to this one.

4. Ashley
   June 5th, 2008 at 5:36 pm

   Yay! I played with this in middle school. A hint for someone wanting a challenge without looking at the solution: You can do it in three lines if you expand the size of your imaginary paper a bit.

5. The Other Parker
   June 5th, 2008 at 5:51 pm

   Of course, someguy, a line drawn on a strip of paper wrapped around the earth isn’t truly a straight line…

6. Miss Cellania
   June 5th, 2008 at 5:57 pm

   I figured it out. You have to think outside the box.

7. sterlinm
   June 5th, 2008 at 6:00 pm

   This puzzle is actually the origin of “think outside the box,” with the idea being that you have to realize that the line’s aren’t restricted to the grid but can extend beyond the ‘box.’ While I suppose the solution with three is reasonable, it seems a bit dumb to me. It seems a reasonable assumption that the dots are supposed to represent abstract points. That is to say, that you wouldn’t be able to hit 3 horizontal points with an angled line. I suppose you might say that it’s reasonable to assume you can’t go outside the box either, but they seem different to me.

8. DOJ
   June 5th, 2008 at 6:04 pm

   got the 4 liner
   but i fell into the trap of thinking of the “dots” as “points”

9. sparge
   June 5th, 2008 at 8:23 pm

   You can also do it in one line if you just use a very thick line. Hey, if your points have actual width, why can’t your line?

10. BikerRay
    June 6th, 2008 at 5:31 am

    Dots, by definition, should have zero size, just as a line should have zero width. Anything else is a cheat.
    I remember this puzzle from about 50 years ago.

11. DrTom
    June 7th, 2008 at 11:40 am

    This puzzle has been around for quite a while and I’ve used it in the classroom. One day a student told me he could connect all 9 dots without using ANY lines. His solution? Print the 9-dot box on a piece of paper - set fire to the paper - and then crumble the ashes up into one straight line. The beauty of the 9-dot box is that it encourages creativity while making the point that it is O.K. to think “outside the box.”

12. Thomas
    June 7th, 2008 at 12:02 pm

    The three line solution kinda feels like cheating.

13. paul Rohrer
    June 10th, 2008 at 12:43 pm

    Is there an author / creator name to the nine dot puzzle that should be credited in a publication? I have used it for years and plan to publish it as an example of thinking outside the box.
    Thanks,
    Paul.

    PS I will gladly mention your website for more puzzles if appropriate.

14. Barbara Whitehead
    November 18th, 2008 at 9:29 pm

    As an IBMer, I presented this problem multiple times for 3 separate years 2002-2005 at Disney World for engineering week. I presented all of the solutions stated in prior comments. The intent of the different solutions is not just to think outside the box, but also show that there is more than one right answer, as well as to show that different people have different boxes. Math people think dots and lines with width is “cheating”. However, scientists working with a physical world have a box where this is “normal”. Moms with small kids have no problem imagining a fat crayon like pencil which is fatter than the picture of all 9 dots… ditto for painters Computer scientists have no problem with regular pencils, but microdots… becoming increasingly smaller until the dots seem to converge. Other engineers do a variation of the “around the world” solution. The pencil is stationary and the paper is rolled onto a cylinder, with the cylinder rolling. The pencil’s straight line indeed can cover the entire paper.

    The 4 and 3 line solutions were documented in books. I had not found the other solutions documented elsewhere prior to using them in the presentation. I’m glad to see these other solutions now being written and used.

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