Timeline for Why is it impossible to connect 3 black dots to 3 red dots?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 28, 2019 at 4:00 | comment | added | ppgdev | @Moo-Juice, you cannot solve this puzzle on the surface of a sphere. If you were able to do it, you could then select a point on the sphere not covered by your drawing, use the point to make a hole in the sphere and then continuously transform the sphere into a plane. Now you sphere solution would turn into a plane solution. But we already know that plane solution does not exist. Contradiction. Q.E.D. | |
| May 27, 2019 at 11:40 | comment | added | Moo-Juice | @Gnudiff this puzzle is entirely solveable when drawn on, say, an orange :) | |
| May 27, 2019 at 6:13 | vote | accept | Navid2132 | ||
| May 26, 2019 at 14:56 | comment | added | Roman Odaisky | All of the above is well summarized in this 3Blue1Brown video: youtube.com/watch?v=VvCytJvd4H0 | |
| May 25, 2019 at 23:01 | comment | added | Euro Micelli | @Gnudiff, not a cylinder. You need a torus like this one. (no financial interest) | |
| May 25, 2019 at 6:20 | comment | added | Gnudiff | Can it be solved if you join the sides of the paper in a cylinder? | |
| May 25, 2019 at 3:33 | comment | added | user2357112 | Proving that $K_{3,3}$ is nonplanar isn't that hard. Even without the Jordan curve theorem, the Wikipedia page on the three utilities problem includes a short proof based on Euler's formula for planar graphs. | |
| May 25, 2019 at 3:17 | comment | added | user2357112 | Kuratowski's theorem is way stronger than the statement that this puzzle is impossible, and way harder to prove than proving that this puzzle is impossible. Kuratowski's theorem is a characterization of all finite graphs, while this puzzle only requires proving one specific graph nonplanar. | |
| May 24, 2019 at 12:46 | comment | added | hexomino | I would say it is not too difficult to prove once you can assume the Jordan curve theorem. I've essentially outlined the argument in my answer which I think is what they are referring to here | |
| May 24, 2019 at 12:23 | history | answered | Glorfindel | CC BY-SA 4.0 |