![]() ![]() ![]() There are at least another 5 solutions I have come across - can you think of others. Of course, we could question the assumption that we have to follow the rules! This solution uses five lines ) In mathematical terms, parallel lines are sometimes considered to "join" at infinity, so here's a solution that uses just three lines! Yet another solution is to fold the paper in three, so the rows of dots all line up, and fold it again and poke the pencil through! If we laid the paper on the ground, we could draw one very long line which encircles the Earth three times, joining one row of dots each timeĪnd if that sounds a bit far-fetched, we could do the same thing by rolling the paper into a cylinder. Why stop at three lines? Why not take a very thick pencil and do the job with just one line?Įven with a thinner pencil, we could still make do with three lines by folding the paper so that the dots were closer to each other. and if I could demonstrate that joining the dots with four lines is. If we had a thick pencil, we could join the dots with just three lines. On the beach in Italy my dad challenged me to connect nine dots arranged in a square. Here are some other ways you could have solved the Join the Dots problem: There is always more than one right answer to many problems. But this was never stated in the original problem! Many people who try to solve this problem start with the assumption that the lines must be inside the square formed by the dots. A solution is displayed below (spoiler alert): In the Wikipedia page linked above, the solution is labeled as 'One of many solutions to the puzzle. Your task is to join all nine dots using only four (or less) straight lines, without lifting your pencil from the paper and without retracing the lines. The aim of the Nine Dots Puzzle is to draw a path connecting 9 dots arranged in a 3 × 3 3 × 3 grid using 4 continuous straight lines, never lifting the pen/pencil from the piece of paper. ![]() Imagine the pattern of dots below drawn on a sheet of paper. ![]()
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