Timeline for Ants on a rod puzzle
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 15, 2010 at 21:30 | comment | added | Sam Nead | Throwing my hat into the ring: We could formalized the proof a little bit by looking at the time/space diagram. Here all of the ants move with constant speed along lines of slope $\pm 1$ and reflect off of each other. If an ant A is still on the rod after time 1 then we can follow the negative of A's tangent direction and find that some ant B entered from the edge of the rod at a time $t > 0$, a contradiction. This set-up also allows you to "see" the number of collisions -- simply count the number of intersections of all the lines of slope $\pm 1$. | |
| Mar 15, 2010 at 21:21 | comment | added | Anonymous | The hats-switching proof is not only mathematically correct but also goes to the essence of the matter. Hence it can also easily answer other related questions such as how many head-bumps occurred before all the ants fell of the rod. | |
| Mar 15, 2010 at 21:17 | comment | added | Sam Nead | There are formal proofs of the Jordan curve theorem. For a discussion see Hales' paper "The Jordan curve theorem, formally and informally". | |
| Mar 15, 2010 at 20:53 | comment | added | Sergei Ivanov | There are no fully formalized proofs except for the most basic, algebraic-style things - search for "formalized mathematics" or "machine verified proofs". A practical definition of a mathematical proof is "a text that an expert mathematician can formalize down to any level of detail if paid enough". Ants switching hats is a perfect proof, that every sensible person would prefer over a long and messy series of symbols expressing the same idea in a formalized language. | |
| Mar 15, 2010 at 19:43 | comment | added | Ashish | The intuitive answer which I knew is this one. i.e one can assume that ants pass freely without collision. But I am somehow not convinced of this being a formal proof for this problem. But yes, assuming that there is such a proof, one can say on its basis that it appears as if the ants move on freely without collision. | |
| Mar 15, 2010 at 18:37 | comment | added | Sergei Ivanov | Sorry, I did not update the browser window and did not notice that the puzzle is already solved in comments. | |
| Mar 15, 2010 at 18:29 | history | answered | Sergei Ivanov | CC BY-SA 2.5 |