3

Could black have taken the queen here?

Note the bishop and the knight

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 [Title "Can black take the queen?"]
5

This is a common confusion for beginners. The rule is that no player is ever allowed to expose their king to check. Never Ever.

The logic of this rule comes down to the fact that the game is turn based, and if the black king captures the white queen, black will lose his king first. The rules of chess don't allow it to go that far, but that doesn't change the principle that the first player to lose their king loses the game.

Chess variants are obviously an exception, with one popular variant being speed chess. If you are playing a game with a very short time control (e.g. 5 minutes per side) it is generally okay to capture the king. Most players consider this a reasonable way to deal with the limited time, where every second counts. If you don't realize your king is in check, stopping the game to sort it out pretty much ruins the game. An exception to this exception is online speed chess, where the computer is able to block illegal moves instantly.

5

Versions of this question are regularly asked here at chess.SE. Notice that the rules of the game leave no room for ambiguity.

Fide Laws of Chess, Article 3.9:

The king is said to be 'in check' if it is attacked by one or more of the opponent's pieces, even if such pieces are constrained from moving to that square because they would then leave or place their own king in check. No piece can be moved that will either expose the king of the same colour to check or leave that king in check.

It is not legal for black to take the queen since it would expose the black king to check.

5

No, black could not have taken the queen. Taking the queen would put black's king into check, which is not legal. Black cannot take the knight either because black's king would still be in check.

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