Timeline for Klarner's theorem
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| May 14, 2018 at 18:03 | comment | added | Per Alexandersson | @AndreasThom: Right, each square must be covered, so one can recursively try to add a piece on the lex-smallest square. If no piece at all fit, then there is no need to continue - a human would stop there as well (I hope). | |
| May 14, 2018 at 15:37 | comment | added | Andreas Thom | In your count you are missing (on purpose) the $6^{10}$ cases that are maximal too, but unreasonable because you leave holes in the pattern already during the process. | |
| May 14, 2018 at 15:36 | vote | accept | Andreas Thom | ||
| May 14, 2018 at 15:36 | comment | added | Andreas Thom | Ok, thank you. Then a reasonable trial-and-error can be done by checking $3086$ patterns. I count that as an answer to my question. If you need say $1$ minute to do one pattern by hand, then you need about $2$ days (and a good memory); so the abstract argument is worth it. | |
| May 14, 2018 at 13:14 | history | edited | Per Alexandersson | CC BY-SA 4.0 |
added code
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| May 14, 2018 at 13:10 | comment | added | Per Alexandersson | @AndreasThom: One can of course just try all possible ways to add a piece, and then stop when it is not possible to add more. You can do a computer-program that count the number of such "dead-ends". I got it to 3086. | |
| May 14, 2018 at 12:28 | comment | added | Andreas Thom | Thanks for your answer. I would expect it is less than $5 \cdot 10^8$. The only real flexibility arises when all tiles are parallel and you have $2$ in each column. There are six configurations of two tiles in a column, hence $6^{10}$ such patterns. This gives about $60$ million configurations and I do not think that there is more than $500$ million in total. However, all the ones I described are obviously not solving the puzzle -- so how many does one really have to check if one searches systematically? | |
| May 12, 2018 at 14:25 | history | answered | Per Alexandersson | CC BY-SA 4.0 |