I believe that’s the furthest you can get out of the box when solving the $4\times4$ puzzle, but I know that for the $7 \times7$ square If you extend all of the lines off the page, you can see the two solutions use the same set of lines. When it comes to categorising solutions, however, these two are in the same family. Of course, you allowed yourself to go outside the box this time, but what angles did your lines go at? The majority of solvers try lines that go horizontally, vertically, or at a $45^$ approach, then most likely your solution looked like one of these two:īoth solutions are just extensions of the 9 dot solution. How did you get on? If you gave the puzzle a serious go, then you probably did find a solution. Please have a go at the puzzle before reading on… Warning: the rest of the article contains spoilers for this puzzle. It’s exactly the same idea, but this time instead of using four straight lines, you are allowed to use six straight lines.Ĭan you find a solution? And if you want a proper challenge, can you find a solution that nobody else is likely to find? I strongly encourage you at this point to have a go at the 16 dots problem, and allow yourself at least ten minutes on it before returning to this article, because there are spoilers aplenty coming up. What I find interesting, however, is that the lessons of the nine dots puzzle are often quickly forgotten when the puzzle is modified. Deliberately challenging your assumptions and allowing yourself to be ‘silly’, at least for a short period, can be a handy strategy for creative problem solving in all walks of life. The solution is a useful metaphor for the challenge of problem solving, when we often become restricted by constraints of our own making. The solution to the nine dot puzzle led to the cliche of ‘thinking outside the box’ (that’s a massive clue to the solution, but if you still can’t find the answer, you’ll find it at the bottom of the article). He called it the Columbus egg puzzle, after an apocryphal story about Christopher Columbus challenging his colleagues to get a boiled egg to stand on its end - a challenge that seemed impossible until Columbus crushed the base of the egg and rested it on its now flat bottom. The puzzle first rose to notoriety when Sam Loyd included it in his 1914 cyclopedia of puzzles. You’ll have no problem finding a solution with five lines, but in the unlikely event that you’ve never seen this puzzle before, four lines might prove to be a struggle. No tricks are needed, no folding the paper and no using an ultra-fat pen. There are nine dots arranged in a square, and your challenge is to join all the dots using only four straight line strokes of a pen, and with your pen never leaving the paper. Dog leads, mirrors and Hermann Minkowski.Significant figures: David Singmaster (1938–2023).Do the shuffle: finding π in your playlists.Penguins: the emperors of fluid dynamics.Chalkdust issue 14 – Coming 22 November.
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