Chessboard queen stalemate

Logic Level 2

On a typical 8 x 8 chess board, what is the most amount of queens can be placed on a chess board, where the opponent has not been checkmated?

Note: Only one king on the board with the opponent only having queens.

The answer is 42.

4 solutions

Kunal Verma
Jul 9, 2015

Let's assume our king is at the bottom right corner. I cannot obviously place a queen in the same row or column. So I can occupy my queens in $7 \times \ 7$ square. But since queens cannot also occupy diagonal squares, $7$ queens will be removed again. Hence the answer $42$

Bonus question :- What will be the maximum number of queens if you were to surely checkmate your opponent by the formation of a queen in the next move and not let him enforce a stalemate.

Hi sir, good solution to my problem! I am confused by your bonus question though, do you mean to add an extra queen and end up with a 43 queen on the board enforcing checkmate, or did you mean moving one of the 42 queens (which wouldn't be possible as the king is already in a stalemate). Sorry for asking, but could you clarify?

Jack Barker - 5 years, 11 months ago

I mean the opponent shouldn't be in a stalemate before you move to your victory next move.

Kunal Verma - 5 years, 11 months ago

62 beacuse our king and oppont king's place

Mithil Yaganti - 5 years ago

Why can't the queen be in the same row as the king? Yes, it would be a check, but not checkmate yet. Alas, the square which must not be attacked is the one adjacent with the king. The answer is the same actually.

William Nathanael Supriadi - 4 years, 6 months ago

Ananth D
Jul 8, 2015

If we place the king at some position on the chessboard, queens can not be placed in the row, column or diagonal(s) corresponding to the king's position. To minimize the number of such positions, we place the king at a corner position. Queens of the opposite colour can now be placed at all positions except on the row, column and diagonal corresponding to the king's position. i.e., 42 positions

Moderator note:

Bonus question : What would the answer be I replaced the word "queens" with "bishops" instead?

forgot to remove the diagonals! good one!

michael bye - 5 years, 11 months ago

Good bonus! And 56 bishops to avoid mate. Try doing the sum of all pieces placed like this on the board -> pawns + rooks + knights + bishops+ queens (not including number of kings to summation).

Jack Barker - 5 years, 11 months ago

bonus ques --( 63-7)=56

ommkar priyadarshi - 4 years, 7 months ago

Bhavya Singhania
Apr 30, 2019

I placed the king at e1 if the king faces a check the queen should be in the same diagonal , rank or file as the king. But if the king faces a check it would be the move of the player with the king. Hence counting the remaining squares I reached 42. But I definitely am not certain how is my answer correct. Please explain me

Mimi Lica
Dec 18, 2016

In general for nxn we have: nxn-1(KING)-3(n-1)

Chessboard queen stalemate

The answer is 42.

4 solutions

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