Yeah, I&#x27;m surprised more comments aren&#x27;t pointing this out. To spell it out further:<p>&gt; the number of valid positions [of a game on a 19 x 19 board] is 19 x 19 in base 3<p>This statement is true when replacing 19 with <i>any number</i>, since the number of <i>legal and illegal</i> configurations is exactly 3^(n*n).