On Thu, Mar 5, 2009 at 10:25 AM, Lone Locust of the Apocalypse <[email protected]> wrote: > On Thu, 5 Mar 2009 [email protected] wrote: >> What would the space be if we didn't care about the validity of the >> words? How many possible ways can 100 tiles fit on a 225 square grid? >> That would seem like the upper bound. > > With Steven's correction about 99, wouldn't the answer just be 225C99? > That comes out to: > > 568853103883032620228431773543075693828810926090255948388293937600 > > But even that wouldn't be an upper bound, because there are multiple > ways to reach the same position of tiles on the board depending which > "words" are formed when, and by which hooks/extensions etc. > > -- S. Spencer Sun > Interestingly, this still comes out to be 10 to the sixty-somethingth power.
Other complications: - the squares on the board would have to be connected (no islands), making it smaller, - the center square would have to be occupied (224C98 ?), making it smaller, and - the number of unplayed tiles could be any number between 1 and 7, making it larger (assuming no resignations or 6 consecutive passes).
