Timeline for Dominoroto-toto
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 11, 2020 at 13:45 | vote | accept | Paul Panzer | ||
| Aug 4, 2020 at 6:26 | comment | added | justhalf | @happystar Yes, so I think you should write w.l.o.g. N is even. | |
| Aug 4, 2020 at 5:55 | comment | added | happystar | I assumed w.l.o.g. the board is 7 x 8 because the proof is unchanged if there are M rows and N columns, where N is even. Hope that clears any confusion. | |
| Aug 4, 2020 at 5:33 | comment | added | tehtmi | Essence of this seems correct. Parity argument would be e.g. checkboard coloring of rows above the middle of the chosen vertical domino. Chosen domino creates an unbalance of remaining colors in this region which must be compensated by another vertical domino in the same rows covering the opposite color (which will be even distance away). | |
| Aug 4, 2020 at 3:01 | comment | added | Paul Panzer | I s'pose so @justhalf (if I understand and second guess the argument correctly). | |
| Aug 4, 2020 at 2:53 | comment | added | justhalf | @Paul, that's true. Or perhaps it's used in the two vertical dominos proof. Either way, that part definitely needs to be part of the explicit proof. I guess the w.l.o.g. should be the number of columns is even, then. Right? | |
| Aug 4, 2020 at 2:49 | comment | added | Paul Panzer | @justhalf I agree that the two vertical dominos argument should be made more explicit, given how central it is. I don't see where the odd number of rows comes in, though. Isn't all that'S used (and that's necessary for the argument to work) that the number of columns is even? | |
| Aug 4, 2020 at 2:44 | comment | added | justhalf | Also, the argument will be much nicer if you instead take "the two vertical dominos with the least nonzero gap", and show that the gap must be zero, a contradiction. I think this would make a very nice argument, much better than Victor's. (Also I think the part that proves that there should be two vertical dominos covering the same two columns need to be made more rigorous) | |
| Aug 4, 2020 at 2:41 | comment | added | justhalf | I think what you want is w.l.o.g. the number of rows is odd, which can be proven by the first few steps of Victor's answer. | |
| Aug 3, 2020 at 23:06 | comment | added | Paul Panzer | How can you assume $7 \times 8$ w.l.o.g.? | |
| Aug 3, 2020 at 22:26 | history | answered | happystar | CC BY-SA 4.0 |