The 8 queen question

hi everyone! today we are going to play a game that is related to chess (and some math): The 8 queen question.

The rules

here are the rules: pick a Standard chessboard and 8 queens (the color doesn’t matter in this case), Place the queens on the board.

but the queens cannot attack each other, The queens cannot capture each other,no matter the color.
for example this position is forbidden:
lichess.org/editor/8/8/4Q3/2Q4Q/5Q2/3Q4/1Q4Q1/Q7_w_-_-_0_1?color=white
the a1,b2,and g2 queens Touched. (this is like that game sudoku)
The question is how many ways could you do this? how many positions could the queens form?

The answer

let’s first take a step back. first let’s think about how many positions could the queens form but without the one rule?

The answer turns to be 4,426,165,368 so is that the answer? there are 4,426,165,368 different ways?
of course no, A lot of the 4,426,165,368 position’s queens attacked each other.
so how many of the 4,426,165,368 positions do indeed follows the rule?
it turns out to be only 92 positions! think of the percentage! 92/4,426,165,368 is about 0.0000000000208%! (10 zeros!)
but that’s not over! A lot of the positions are rotated or backfliped positions of another position. so the answer turns out to be only 12 positions! 12/4,426,165,368≈0.00000000000271% (11 zeros) ......
so that’s your answer! 12! (not 12 factual lol) and here’s one of them:
lichess.org/editor/2Q5/4Q3/1Q6/7Q/Q7/6Q1/3Q4/5Q2_w_-_-_0_1?color=white
could you find the others?
you can make your own Version of this game! Like swap the 8 queens with 8 rooks or 8 Knights ! and I’ll leave it your turn to figure out how many positions 8 Bishops could make.

Feedback video

for more details, Watch this video:
https://www.youtube.com/watch?v=jPcBU0Z2Hj8

Goodbye!

bye everyone! i hope you all had some fun! thanks for viewing this blog! see you in my next blog!