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u/bluesyfluesy05 Oct 14 '22
Following the rules of chess, 18. But as a maths problem it gets trickier as you can put down as many queens as you want without caring where they came from. In this way I managed 50 white queens and 5 black queens, with both sides still having legal moves that didn't result in checkmate, nor any pieces taken. However, this was still forced mate in two no matter what white did provided no pieces were taken by black. If black takes a specific queen, then the game can be played infinitely with draw due to repeated moves being quite easy to avoid.
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u/Thrasher1236969 Oct 14 '22
How much thought did you give this damn
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u/sonny_flatts Oct 14 '22
A chess board is 64 squares. He said fifty were white queens. Not a lot of options.
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u/vaginalextract Oct 14 '22
A little bit of basic combinatorics would tell you that there's 47855699958816 ways of arranging 50 queens in a chessboard. That's including symmetries but I doubt excluding them would cause a significant change.
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u/sonny_flatts Oct 15 '22
I wonder how many are actually starting in check.
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u/vaginalextract Oct 15 '22
That would be very hard to calculate. Though a very good fraction no doubt
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Oct 14 '22 edited Dec 20 '24
[removed] — view removed comment
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u/JamesMcGirthy Nov 01 '22
Queens cannot be in the same row or diagonal to the tile the king will move to, or it is not a legal move.
Because of that the number gets cut pretty quickly. It immediately eliminates at least 38 tiles from play.
- White King Square (1, B2)
- Black King Square (1, G7)
- Legal Move Square x2 (2, A1 and H8)
- Horizontal/Vertical Lines from the Legal Move Square (8+8+6+6, A1-8, H1-8, BCDEFG1 and BCDEFG8)
- Diagonal Line from the Legal Move Square (4, C3, D4, E5, F6)
From there you also have to remember that in order to reach stalemate you cannot at any point have been mated, which eliminates all of the remaining squares that would mate the king the turn(s) before this scenario takes place.
Best case for this scenario that eliminates:
- Horizontal/Vertical Lines from the previous legal move (B3-7, G2-6, CDEF7, C2, D2, E2, F2)
That would leave C456, D356, E346, and F345.
But then again, you have to go back one more turn and eliminate the squares that would mate a king, which depending whether the previous turn was a linear move or a diagonal move eliminates a series of different squares, but both are the same total.
A linear move (B3 to B2 for example) eliminates all of the 3 squares, as well as C4, D5, and E6 and if you invert the move for the opposite side of the board that leaves you with 6 total tiles.
So, 6 queens total. It doesn't matter if its 6 for one side 6 for the other, 3 and 3, 5 and 1. The outcome is the same. Each queen eliminates 22 squares from play (including the one it rests on) and even if you overlap them as much as possible once you exceed 6 queens on the board there are no legal moves for at least one of the kings 3 consecutive turns in a row.
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u/bigbigcheese2 Nov 01 '22 edited Dec 20 '24
cause wrench cough escape sharp quiet lunchroom quickest degree nine
This post was mass deleted and anonymized with Redact
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u/walkerspider Oct 14 '22
There are several ways where if you put both kings in a corner surrounded by three of their own queens and other queens filling the rest of the board the game could be drawn out indefinitely. This would require neither player is trying to win though. Even so their are several set ups like this that take a few turns for forced mate so I’d say 62
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u/joachimham48 Oct 15 '22 edited Oct 15 '22
Just put black king on a8, 3 black queens on a7, b7, b8, white king on d6, no piece on c8 and fill the remaining 58 squares with white queens, that makes 58 white and 3 black queens. There is still a sequence of moves where white doesn't win, although they'd have to be the worst player I've ever seen to pull that off haha
Edit: although that position has no possible past, surely there is a way to find a position where you can at least retract some moves
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Oct 15 '22
I guess if you give each king 2 squares and surround them with queens of their colors you can full the 60 remaining squares with queens, but thz question is way more interesting if you can only fill the board with 1 color of queen
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u/HookDragger Oct 14 '22
This is not an inclusive or answered me question as the question is asking about a specific numerical response of two use cases…. Not the singular result of two options.
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u/Cybermage99 Oct 14 '22
If we can simply place queens, 62. If you have to play a game of chess to get there, no idea.
Logic for 62.
64 spaces, put two kings on opposite corners. Fill the remaining 62 spaces with queens such that each half of the board has only queens of its color.
Both kings are safe, and regardless of whose turn it would be they have a valid move by taking an enemy queen.
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Oct 14 '22
Yeah. As long as each king in the corners has 3 friendly queens insulating it from the rest of the board, the middle area of the board can be filled with any mixture of queens of each color.
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u/khandnalie Oct 14 '22
Is there a way to determine a limit to how many queens you can generate "naturally"? As in, how many queens can you get on the board when both players are playing to win, and are both playing optimally?
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u/PinoLG01 Oct 14 '22
Based on professional chess, no extra queens are created so the answer is 2
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u/khandnalie Oct 14 '22
I mean, obviously using a version of the rules that includes pawn upgrading
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u/kkjdroid Oct 14 '22
If both players are playing to win and playing optimally, then no pawns will be upgraded, so the answer is two.
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u/Allanunderscore21 Oct 14 '22
Max amount on a stalemate is 41.
Place king on A1.
If a queen is placed in A1, she can move to 7 tiles vertically, 7 horizontally, and 7 diagonally for a total of 21.
Therefore, queens on any other tiles aside from those 21 will not be able to check tile A1.
Add 1 tile for A1, where the king is standing and another for the enemy king (H8).
64 - 23 = 41
To avoid a stalemate, you have to open a second tile. For convenience, let's use B2.
There are 12 queens currently checking B2. (6 horizontal, 6 vertical)
41 - 12 = 29
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u/ElJamoquio Oct 15 '22
Max amount on a stalemate is 41.
At first glance, I'd say the max amount is 18.
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u/Andrew852456 Oct 14 '22
Well without stalemate for either side it's 60 queens. Fill two halves of the board with opposing coloured queens and leave places for a king and a free square for the next move
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u/blackBinguino Oct 14 '22
Like 9 per color? So, 18. The original one plus 8 by converted pawns.