In a flat plane there are the same distance between 1 and 2, as between 5 and 8, right? It's easy to see that there are 12 pairs that have the same distance between them. or do we mean "arranged in a *perfect* 3x3 square."? 'twas probably the first genuinely neat/beautiful solution I ever saw.ĭraw nine dots so that they are arranged in a 3x3 square. Good job on thinking outside the box! However, I came across this problem when I was in school, and there is a very neat solution which is also "outside the box". But the question was how to connect the spot wi have to keep in mind that the problem is translated in 3D.ĭoes that have any sense to you ?Curiously, you use the phrase "project your problem onto a sphere" - but the thing is, the reason your problem works is because there is no decent projection from a flat plane onto a sphere! (and everyone is busy thinking in flat space.)Īnyway, your solution is certainly correct, especially since we live on a sphere. I got the task from my teacher in high school. They are perfectly straight, you just have to keep in mind that the problem is translated in 3D. So three lines are : north pole-south pole, south pole-north pole and again north pole-south pole. And connect them with 3 straight lines (you change the directions of your pen on north and south pole). Look, it seems pretty natural to plant your 9 spots here. When I presented my anwser to my teacher in high school, he told me that's wrong and other students made fun of me □ So you pick 3 evenly distant meridianes and place your dots. sphere meridianes are perfectly straight if you look at them from the right angle. I had an idea of doing it with three straight lines (i projected my problem on a sphere). But the question was how to connect the spot with 4 lines. But what about three.ĭraw nine dots so that they are arranged in a 3x3 square.Ĭan you connect all nine dots with 3 STRAIGHT lines without taking pen (or pencil or chalk or other marking-tool) from paper? Ok, we know how to do it with 4 straight lines.
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