On Nov 2 nd, 2008, 11:46am, Eigenray wrote: Even if there were only 4 dots, it would still be impossible (in the plane). « Last Edit: Nov 2 nd, 2008, 1:46pm by Eigenray » The interesting thing is that the converse holds as well: a graph can be embedded in the plane if and only if it doesn't contain either the utilities graph (K 3,3) or the complete graph on 5 vertices (K 5) as a minor (that is, by removing vertices, edges, or contracting edges).Įdit: There are five dots! How many do you see now? I saw 2 rows of 3 dots and my mind jumped straight to K 3,3.Įven if there were only 5 dots, it would still be impossible (in the plane). Wikipedia, Google, Mathworld, Integer sequence DB « Last Edit: Nov 2 nd, 2008, 8:23am by towr » top and bottom, and left and right wrap together) See attachment, line-ends with the same color are connected over the torus/donut (i.e. * Actually, it seems this one can also still be done on a torus. However, it can still be solved on the surface of some object* (as long as it has enough holes in the right places), just not on the plane. If each dot has to be connected to all five other dots, then it's not quite the same problem, but even more difficult. You can do the utility problem on a torus (donut).īut in the plane (or equivalently on the surface of a sphere) it is impossible (as explained in Eigenray's link). Re: Connect the 6 dots together, is this impossibl ut.png Some people are average, some are just mean. « Last Edit: Nov 2 nd, 2008, 11:47am by Eigenray » It's known as the utilities problem, and it is in fact impossible. Re: Connect the 6 dots together, is this impossibl So you'll end up with a lot of lines, and they can also curve around the dots, they don't have to go straight.īut the thing is, you can't cross the lines, so they can't touch. So like, if you start with the top left dot and connect it to the other 5, do the same to every other dot. Okay, well you have to make each dot connect to the other 5 dots. Please, I'm like dying for the solution, like literally! And if you can't find the solution, recommend a forum which i can post this puzzle on and get some good responses.Īnd apparently it's a maths problem, so maybe you could maths to solve it, i have no idea S So there is this puzzle, a puzzle which everybody on every site which has this puzzle has claimed to be impossible, but according to my maths teacher is not. Topic: Connect the 6 dots together, is this impossible? (Read 19219 times) RIDDLES SITE WRITE MATH! Home Help Search Members Login RegisterĮasy (Moderators: SMQ, ThudnBlunder, Grimbal, Icarus, william wu, towr, Eigenray)Ĭonnect the 6 dots together, is this impossible? « wu :: forums - Connect the 6 dots together, is this impossible? » There are at least another 5 solutions I have come across - can you think of others.Wu :: forums - Connect the 6 dots together, is this impossible? 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. If we had a thick pencil, we could join the dots with just three lines. 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. 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. Imagine the pattern of dots below drawn on a sheet of paper.
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