To do so, one goes outside the confines of the square area defined by the nine dots themselves. Wish I thought of it.It is possible to mark off the nine dots in four lines. On Dec 6 th, 2008, 12:57pm, Grimbal wrote: It does. Re: Connect the 6 dots together, is this impossibl connect7.gif If memory serves, K 7 can also be done on a torus, though not K 8 « Last Edit: Nov 2 nd, 2008, 1:52pm by Eigenray » Well, looks like I've embarrassed myself enough for one thread. « Last Edit: Nov 2 nd, 2008, 1:28pm by Hippo » Sorry for magnifying that, but until now, I felt everyone expect you Eigenray can be cought as beeing mistaken occasionaly so please take it more like a compliment Kuratowski theorem talks about divisions of K 3,3 or K 5.Īnd tetrahedron can be projected on sphere easily. 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 4 vertices (K 4) as a minor (that is, by removing vertices, edges, or contracting edges).
I saw 2 rows of 3 dots and my mind jumped straight to K 3,3.Įven if there were only 4 dots, it would still be impossible (in the plane). On Nov 2 nd, 2008, 11:46am, Eigenray wrote: Whoops, you're right. 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?
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