Timeline for The Erasmus rook tour
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 14, 2015 at 19:13 | vote | accept | Gamow | ||
| Feb 3, 2015 at 20:11 | comment | added | Joel Rondeau | @KSmarts I started with larger shapes that I'd have to join together. When I was trying to simplify that, I discovered that every one could be created from $2x2$ squares. Made the problem much simpler. | |
| Feb 3, 2015 at 20:03 | comment | added | KSmarts | Okay, I get it. I was thinking along these same lines, but you beat me to it. Also, I wasn't sure if it covered all tours. | |
| Feb 3, 2015 at 19:50 | comment | added | Joel Rondeau | @KSmarts Take 2 squares at A1:B2 and C1:D2. To join them together, you remove the vertical lines (moves) at B1:B2 and C1:C2 and replace them with horizontal lines (moves) at B1:C1 and B2:C2. The joining can always be the replacement of 2 vertical lines with 2 horizontal lines of a $2 x 2$ square (or 2 horizontal with 2 vertical lines). | |
| Feb 3, 2015 at 19:41 | comment | added | KSmarts | I'm not sure what you mean here, by "when [joining 2 shapes], you will alter both the horizontal and vertical moves by 2." | |
| Feb 3, 2015 at 19:22 | comment | added | Joel Rondeau | @Lopsy, I'm reasonably certain that every rook tour can be made this way for any $m x n$ board where $m$ and $n$ are both even. | |
| Feb 3, 2015 at 19:13 | comment | added | Lopsy | Re your proof: not every possible rook tour can be made by joining 2x2 squares together, right? | |
| Feb 3, 2015 at 18:58 | history | edited | Joel Rondeau | CC BY-SA 3.0 |
Included proof.
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| Feb 3, 2015 at 18:06 | comment | added | KSmarts | I'm in the same place as you. But, "I can't find one" doesn't mean, "there isn't one". I'm pretty sure there isn't, but I'm trying to prove it. | |
| Feb 3, 2015 at 17:55 | comment | added | Joel Rondeau | I do not have a full proof for the 8x8 board. Given what I tried with the 4x4 and then 6x6 board and the fact that similar answers didn't get me any closer than 4 for the 8x8, I believe it to be correct. I'll see if I can put something together later. | |
| Feb 3, 2015 at 17:51 | comment | added | Trenin | What is the proof for the 8x8 board? | |
| Feb 3, 2015 at 17:47 | history | answered | Joel Rondeau | CC BY-SA 3.0 |