Timeline for Prime lights out
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 2, 2023 at 3:38 | history | bounty ended | msh210 | ||
| Aug 9, 2022 at 11:38 | comment | added | Falco | @WhatsUp you are right. I was thinking of a 2x2 grid, which can be turned to all 1 in a classical lights-out, but which will have all 3s when you try to get all equal. And this cannot be removed to all-1 even with negative moves, since you can only get multiples of 3 with a 2x2 grid and all equal. | |
| Aug 5, 2022 at 16:00 | comment | added | Ben Reiniger | @WhatsUp, I think that argument requires negative moves? But that's fine, just crank up the binary representation grid with more moves. | |
| Aug 5, 2022 at 14:56 | comment | added | WhatsUp | @Falco A $2\times 3$ grid can be filled with all-one by making moves in two opposite corners. With small modification, this method also works if one can produce an "all-equal" result, which is equivalent to saying that the "all-one" vector lies in the $\Bbb Q$-vector space generated by the basis vectors. I have checked every rectangular grid up to $20\times 20$ that this is always true. Perhaps there is a general argument to prove that. | |
| Aug 5, 2022 at 8:59 | comment | added | Dmitry Kamenetsky | @Falco ok. Can we say that solutions exist for all grids NxN with N>=3? I can confirm that the 5x5 solution exists. | |
| Aug 5, 2022 at 8:48 | comment | added | Falco | I especially like this answer, because it found the solution (16) without actually searching for any specific primes. | |
| Aug 5, 2022 at 8:47 | comment | added | Falco | @DmitryKamenetsky I don't think that's true. This answer requires a set of moves which produce 1 on all cells. Such a move does not exist for any grid. E.g. a 2x3 grid cannot be filled with all 1s. | |
| Aug 3, 2022 at 23:40 | comment | added | Dmitry Kamenetsky | This is a very nice generalisation. It means we can find solutions for a grid of any size. | |
| Aug 3, 2022 at 17:11 | history | answered | WhatsUp | CC BY-SA 4.0 |