It's easy to make the assumption that we must use thin lines to solve the puzzle because, frankly, the puzzle is too easy if we allow a giant, thick line.īut in making this assumption, we lose out on the simplest solution! Perhaps this is not a solution intended by the original author of the 9-dots puzzle, but it definitely meets the original criteria of 'connect all 9 dots with 4 connected strokes'. Why constrain ourselves to a particular tool? Do we need to use a pencil? What if we use a paintbrush instead. We're not done yet though! Is there at least one more assumption we can tackle? Wait, you mean this puzzle can be solved with just one line? Indeed! We just needed to think beyond two dimensions.

However, does the paper need to be flat? What if we curl the paper up and use the third dimension to our advantage? We can curl the paper into a spiral tube and draw a single line that wraps around the tube, intersecting all nine dots: Usually this problem is given on a piece of paper.

Without lifting my pencil from the paper.

Are there any more assumptions we can challenge? Maybe there's more than one solution.

We just needed to think outside the box.Ĭool, the puzzle is solved! We're done now, right? Perhaps, but we made an awful lot of assumptions early on. However, do our lines need to stay inside of this box? What if we allow the lines to go a little outside the confines of the grid.Īh ha! And just like that, we can connect 9 dots with 4 connected lines. Let's pick apart our assumptions one bit at a time. Hmm, the official instructions seem quite a bit different from the rules I just enumerated above. What were the original instructions again?Ĭonnect all 9 dots with 4 connected strokes! Except something feels a little wrong here. Which connect all nine dots in a 3x3 box.Well, let's think carefully about the rules of our little game first: No matter what we do, it feels like we need five lines, not four. If you've never seen this 9-dots puzzle before, it can be frustrating at first.ĭarn! None of these patterns work.

Connect 4 dots with 4 lines