Life In 19x19

Posted: **Mon Mar 09, 2015 1:17 am**

Number of legal 18x18 Go positions

So the number included all symmetrical positions.

Click Here To Show Diagram Code: [go]$$ $$ . . ? X . ? . X ? . . ? . . ? O . ? . O ? . . ? . . ? X X $$ . . ? . . ? . . ? . X ? X . ? . . ? . . ? . O ? O . ? . . $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ . X ? . . ? X . ? X . ? . X ? O O ? . O ? . . ? O . ? O . $$ . X ? X X ? X . ? . X ? X . ? . . ? . O ? O O ? O . ? . O $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ . O ? X O ? . X ? . . ? O . ? O X ? . O ? . . ? X . ? X . $$ O . ? . . ? . O ? O X ? X . ? . . ? . X ? X O ? O . ? . O $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ . X ? O . ? . O ? X X ? . X ? X . ? X X ? O O ? . O ? O . $$ O . ? . X ? X . ? . X ? X X ? X X ? . X ? . O ? O O ? O O $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ O O ? X X ? . X ? O . ? X O ? X X ? O X ? . O ? X . ? O O $$ O . ? . O ? O X ? X X ? X . ? O . ? . X ? X X ? X O ? . X $$ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? $$ . O ? X . ? O X ? O O ? X O ? . X ? O . ? ? ? ? ? ? ? ? ? $$ X O ? O O ? O . ? X . ? . O ? O O ? O X ? ? ? ? ? ? ? ? ?[/go]

I'll leave the 12,675 cases of the 3x3 for others. :mrgreen:

Posted: **Mon Mar 09, 2015 1:42 am**

Here are the possible states, it seems they add up to 57:

Click Here To Show Diagram Code: [go]$$ 1 (empty board) $$ -- $$ | . . | $$ | . . | $$ --[/go]

Click Here To Show Diagram Code: [go]$$ 4 (a single black stone) $$ -- $$ | X . | $$ | . . | $$ --[/go]

Click Here To Show Diagram Code: [go]$$ 4 (two adjacent black stones) $$ -- $$ | X X | $$ | . . | $$ --[/go]

Click Here To Show Diagram Code: [go]$$ 2 (black diagonal) $$ -- $$ | X . | $$ | . X | $$ --[/go]

Click Here To Show Diagram Code: [go]$$ 4 (three black stones) $$ -- $$ | X X | $$ | X . | $$ --[/go]

Click Here To Show Diagram Code: [go]$$ 4 (single white stone) $$ -- $$ | O . | $$ | . . | $$ --[/go]

Click Here To Show Diagram Code: [go]$$ 4 (two adjacent white stones) $$ -- $$ | O O | $$ | . . | $$ --[/go]

Click Here To Show Diagram Code: [go]$$ 2 (white diagonal) $$ -- $$ | O . | $$ | . O | $$ --[/go]

Click Here To Show Diagram Code: [go]$$ 4 (three white stones) $$ -- $$ | O O | $$ | O . | $$ --[/go]

Click Here To Show Diagram Code: [go]$$ 12 (one black, one white) $$ -- $$ | X O | $$ | . . | $$ --[/go]

Click Here To Show Diagram Code: [go]$$ 8 (two black, one white) $$ -- $$ | X X | $$ | O . | $$ --[/go]

Click Here To Show Diagram Code: [go]$$ 8 (two white, one black) $$ -- $$ | O O | $$ | X . | $$ --[/go]

Posted: **Mon Mar 09, 2015 1:44 am**

oh seems EdLee edited away his question about how to get 57 for n = 2

Posted: **Mon Mar 09, 2015 1:53 am**

You forgot 1 white 1 black diagonal.
edit: Oh I see you count it. Thought you wanted to deal with symmetry as well.

Posted: **Mon Mar 09, 2015 1:59 am**

Sennahoj wrote:oh seems EdLee edited away his question about how to get 57 for n = 2

Yea, instead of asking, I just brute forced it.

kivi wrote:You forgot 1 white 1 black diagonal.

Do you mean Sennahoj ? He counted them, under "12 for 1 :black:

and 1

"

An interesting factoid is the number of unique 2x2 positions would have been the number of Sennahoj's diagrams, 12,
except for the above case, so it's actually 1 more, at 13.

(Because he merged the adjacent and diagonal cases into 1 diagram; but he kept them separate for 2 stones of the same color.

)

Posted: **Mon Mar 09, 2015 2:54 am**

If they could just make that diagram on page 5 of their paper for 19x19 and figure out a way for me to memorize it perfectly, that would be nice.

Posted: **Mon Mar 09, 2015 3:18 am**

EdLee but if we are talking about symmetries, then these should also be considered the same:

Click Here To Show Diagram Code: [go]$$ $$ -- $$ | O . - X . | $$ | . . - . . | $$ --[/go]

So there are only 8 "essentially unique" positions

Click Here To Show Diagram Code: [go]$$ $$ -- $$ | . . - X . - X X - X . - X X - X O - X . - X X| $$ | . . - . . - . . - . X - X . - . . - . O - O .| $$ --[/go]

Life In 19x19

Number of legal 18x18 Go positions

Number of legal 18x18 Go positions

Re: Number of legal 18x18 Go positions

Re: Number of legal 18x18 Go positions

Re: Number of legal 18x18 Go positions

Re: Number of legal 18x18 Go positions

Re: Number of legal 18x18 Go positions

Re: Number of legal 18x18 Go positions