In a game of chess with standard rules, what is the maximum number of queens, rooks, bishops, knights, and kings both black and white that can be on the board?
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4
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$\begingroup$ by 'can be on the board' you mean with or without any check-mate situation? $\endgroup$– Emre UnsalCommented Jul 5, 2018 at 10:59
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3$\begingroup$ Is the question for queens equivalent to this one on chess stack exchange: chess.stackexchange.com/questions/4123/… ? $\endgroup$– hexominoCommented Jul 5, 2018 at 11:00
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$\begingroup$ @EmreÜnsal it can end in a checkmate or it cannot but it plays by normal rules so you can't ignore a check or anything like that $\endgroup$– Jon.GCommented Jul 5, 2018 at 12:03
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$\begingroup$ @hexomino I believe this number would by higher as you are not forced to sacrifice all your bishops and knights like you do in the queen example $\endgroup$– Jon.GCommented Jul 5, 2018 at 12:06
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1 Answer
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8
The anwser is:
28
My first though was
32 (every pawn is promoted to another piece by reaching the bank rank)
But the pawns can't pass trough the enemy pawns that are on the same file. All the other pieces can move away though.
So:
The pawns can side step the enemy by capturing (lets say from the a-file to the b-file).
Which will reduce the total by one. But will let the enemy pawn on the a-file through and let the two friendly pawns on b-file through.
So one pawn is sacrificed, allowing the remaining a-file and b-file pawns to be promoted.
Now we just repeat this:
pawn on c-file hits pawn on d-file
pawn on e-file hits pawn on f-file
pawn on g-file hits pawn on h-gile
So in total:
We have to sacrifice 4 pawns which gives us a total of 28 non-pawn pieces.
answered Jul 5, 2018 at 11:08
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$\begingroup$ This is just getting the pawns to the other side of the board, this doesn't say where to move the rest of the pieces to avoid a checkmate in that situation. $\endgroup$– Jon.GCommented Jul 5, 2018 at 12:08
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2$\begingroup$ @Jon.G That wasn't part of the question. But, by keeping each colour's Kings, Rooks & Knights to opposite corners of the board, putting Bishops & Queens in the remaining two corners, the options for two cooperating players to achieve this without checkmate are essentially trivial - only Queens can then threaten the King, and the Rooks/Knights can be use as a wall to prevent Check $\endgroup$ Commented Jul 5, 2018 at 12:42
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$\begingroup$ @Chronocidal standard rules include checkmate. $\endgroup$– Jon.GCommented Jul 5, 2018 at 12:52
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$\begingroup$ @Jon.G Standard rules include Checkmate as a winning/losing position. However, the Standard Rules don't actually say that you have to play to win. Both players may intentionally be avoiding checkmate. $\endgroup$ Commented Jul 5, 2018 at 12:55
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$\begingroup$ @Chronocidal this is intended for cooperative play, it doesn't make much sense if you were playing to win $\endgroup$– Jon.GCommented Jul 5, 2018 at 12:59