nine-dots-puzzleStarting from any point and without lifting your pen from the page, can you draw 4 straight lines, such that each of the nine dots has at least one line running through it?

Yes, it’s the old ‘nine dot’ problem, first popularized by Sam Loyd around the turn of the last century, and used in pretty much every creativity training session since.

The answer is well-known. However, there are several other lesser known variants of the puzzle. For example, how about….

Starting from any point and without lifting your pen from the page, can you draw 3 straight lines, such that each of the nine dots has at least one line running through it?

and how about….

Starting from any point and without lifting your pen from the page, can you draw 1 straight line, such that each of the nine dots has the line running through it?

The answer to this puzzle, and 100 others,  can be found in a new kindle ebook called PUZZLED, and is available in the UK here and USA here.

29 comments

  1. I do have an answer for the 3 line puzzle but I’m not sure if it’s fair. The lines probably don’t go through the exact centre of the dots.

    And my 1 line solution is ludicrous.

  2. I’m not sure of the solution for the three line puzzle that you had in mind but either of my solutions to the single line puzzle can be used by drawing over the single line twice.

  3. There’s nothing in the problem statement that says your line has to go through the exact center of the dot. It’s not cheating (or even against the spirit of the problem) to exploit that when solving the three-line request.

    If I can choose my pen, I can probably accommodate the one-line request as well.

  4. I heard a very funny alternative to this puzzle. Wad the paper up and stab your pen through it, eventually you will it all nine dots.

  5. this is pretty tricky but i am goofy .

    For 4 straight lines – yup it took me quite long by just using 1 pen
    For 3 straight lines – its all about the pen and positioning i think.. and i do have a solution.
    For 1 straight lines – no answer

    this puzzle reminded me of ‘hitting 3 birds in one stone’ more like 9 birds..

  6. The three-line puzzle hinges on how we interpret the diagram, isn’t it? Fairly straightforward unless we make the leap to thinking this is a representation of a Euclidian plane; that the dots are points, and the lines are one dimensional.

    I suspect a similar issue is at the heart of the one-line puzzle, if your solution is what I think it is. I guess that might have to wait

  7. 4 lines, yeah i’ve seen this before.
    3 lines, depends on the thickness of the dots.
    1 line, actually for me easier than the 3 line solution, and doesn’t require any special pen.

  8. I hadn’t seen this puzzle before, but I’ve managed to work out the 4 lines solution.

    For the other two, am I allowed non-euclidean geometry?

  9. Ok I thought about it straight after posting and do have an answer which would use the same technique for both questions but I’m not sure if I have it right because if the answer for 3 lines is correct then it’s redundant to ask about one line. So I’m not sure and am keen to see the answer.

  10. I have an idea for the 1 line puzzle, and a similar one for the 3 line one…took me about 3 seconds. I’ve already been told how to get it with four lines.

  11. I know the 3 line answer from “Your Money or Your Life” by Joe Dominguez. I think I have an answer for the 1 line. Don’t have the 4 line answer, although, I guess I don’t NEED to, since I can do it in3!

  12. My 1-line answer: Tape the paper into a cylinder and draw a line at a slight angle to what would be a line connecting adjacent dots. Eventually you should hit all of them…

  13. Ug. I can, but I suspect I am cheating! The traditional version actually had me stuck for a good ten minutes till a cliche I loathe sprang to mind and solved it for me. The others require as I said what I think constitutes cheating!

    cj x

  14. Start from corner, mark line from there to last point of same row. Then extend same line thereafter. Line will pass through 3 points. Then from extension draw inclined line through another 2 points n carry it up to the same level of column. Then join that extended line to tje point where we have started. Again from starting point draw 45degree line which will join remaining points… The shape will be like kite

  15. For the three line problem, the only solution I can think of is to start in one corner, on the outside edge of the dot. Draw a line at a slight angle such that the line goes through all three dots and extend it up until you get to a point where another line at a slight angle can be drawn to catch the three dots in the middle, extending downwards until a point is reached below the third column, then draw a straight line through the final three.

    For the one line problem, I wonder if it would work to make the paper into a moebius strip. I’m sure if it would be possible to find an angle of the line such that it eventually went through all the dots

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