Click on the left links to find tables for L(m,n).
| n | number of legal n*n positions |
| 1 | 1 |
| 2 | 57 |
| 3 | 12675 |
| 4 | 24318165 |
| 5 | 414295148741 |
| 6 | 62567386502084877 |
| 7 | 83677847847984287628595 |
| 8 | 990966953618170260281935463385 |
| 9 | 103919148791293834318983090438798793469 |
| 10 | 96498428501909654589630887978835098088148177857 |
| 11 | 793474866816582266820936671790189132321673383112185151899 |
| 12 | 57774258489513238998237970307483999327287210756991189655942651331169 |
| 13 | 37249792307686396442294904767024517674249157948208717533254799550970595875237705 |
| 14 | 212667732900366224249789357650440598098805861083269127196623872213228196352455447575029701325 |
| 15 | 10751464308361383118768413754866123809733788820327844402764601662870883601711298309339239868998337801509491 |
| 16 | 4813066963822755416429056022484299646486874100967249263944719599975607459850502222039591149331431805524655467453067042377 |
| 17 | 19079388919628199204605726181850465220151058338147922243967269231944059187214767997105992341735209230667288462179090073659712583262087437 |
| 18 | ~0.017322427762 * 3^324 ~ 6.697231143 * 10^152 |
| 19 | ~0.011957528698 * 3^361 ~ 2.081681994 * 10^170 |
The results for n=14,15,16 and 17 were obtained in a joint effort between Michal Koucký and John Tromp.
A preliminary version of our paper ``Combinatorics of Go'' that contains these and many other results.
This gzipped tar contains various programs used to compute the exact numbers. Many thanks to Gunnar Farnebäck and Michal Koucký for their contributions. Gunnar wrote a legal counting program in pike, while Michal suggested the use of Chinese Remaindering and implemented a file based program.
This small program approximates the probability of a random n*n position being legal.
Additions and corrections are welcome. tromp@cwi.nl