Hi Michael, Gunnar Farnebäck and myself have also verified these numbers. We used a modified version of our program for counting the number of legal go positions. Our results are as follows
1 1- 1 = 0 2 4- 2 = 2 3 9- 3 = 6 4 16- 4= 12 5 25- 7= 18 6 36-10= 26 7 49-12= 37 8 64-16= 48 9 81-20= 61 10 100-24= 76 11 121-29= 92 12 144-35=109 13 169-40=129 14 196-47=149 15 225-53=172 16 256-60=196 17 289-68=221 18 324-76=248 19 361-84=277 20 400-92=308 21 441-101=340 22 484-111=373 23 529-121=408 (took over a week on a 1.4Ghz opteron using 13GB of memory) which confirm yours. we also found a general formula n^2 - floor((n^2+4n-16)/5) derivable from 5 optimal "edge-patching" patterns. we conjecture that the only exceptions occur at n=1,2,3,4,5,6, and 13. here's a nice symmetric 19x19 position with 277 strings: X O . O . O X O . O . O X O . O . O X . X O X O X . X O X O X . X O X O X . X O X . X O X O X . X O X O X . X O X O . O X O . O . O X O . O . O X O . O X O X . X O X O X . X O X O X . X O X . X O X O X . X O X O X . X O X O X . X O . O . O X O . O . O X O . O . O X . X O X O X . X O X O X . X O X O X . X O X . X O X O X . X O X O X . X O X O . O X O . O . O X O . O . O X O . O X O X . X O X O X . X O X O X . X O X . X O X O X . X O X O X . X O X O X . X O . O . O X O . O . O X O . O . O X . X O X O X . X O X O X . X O X O X . X O X . X O X O X . X O X O X . X O X O . O X O . O . O X O . O . O X O . O X O X . X O X O X . X O X O X . X O X . X O X O X . X O X O X . X O X O X . X O . O . O X O . O . O X O . O . O X regards, -John On 12/7/06, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote:
I have independently verified the MSP (maximum number of living strings on a board) results for board sizes up to 16 that Youhei Yano created and that Hiroshi Yamashita reported on in this mail group about a month ago.
_______________________________________________ computer-go mailing list computer-go@computer-go.org http://www.computer-go.org/mailman/listinfo/computer-go/
