How many distinct chess games are possible, and which is the longest?
Seven queens on a board is possible: Granted I've only spent a few minutes on this, but I don't think eight is possible. Very interesting discussions you all have on this thread.
No matter how I attack this, at best I keep coming down to two free squares side by side after six queens are placed. Thus, wherever I place the seventh queen, both squares are taken. Alternatively, placing queens on "knight move" opposition allows you to maximize squares, but after b1 -- d2 /a3 queen satalites and f7root and e5/c6 satalites only h4 is a valid square.
You are correct LoekBergmen. Had I thought a little bit deeper on my knight/space queen idea, I'd have seen it quicker. The starting square is Qc1.
Hi, I believe I have 33^49 as an upper bound which is approximately 2.6 x 10^74, which is considerably less than Shannon's number 10^120. How does this compare to other upper bounds? I'm not certain what the reigning (lowest) upper bound we have so far.
I just found a new upper bound. (16^50‐1)/15 which is roughly 10^59. What is the best upper bound known so far?