Question

If the queen is at c5, and the other pieces at positions c2, gl, g3, g5 and a3, how many are under attack by the queen? There are no other pieces on the board.

• A. 2
• B. 3
• C. 4
• D. 5
• A. f8
• B. a7
• C. c1
• D. d3
• A. 0
• B. 3
• C. 4
• D. 6
• A. 32
• B. 35
• C. 36
• D. 37

Answer 1

The Correct Option is C

To determine how many pieces are under attack by the queen, we analyze the position of the queen and other pieces on the board.

Queen's Position: c5 

Other Pieces: c2, g1, g3, g5, a3

Queen's Attack Pattern: The queen can attack in her row, column, and diagonals.

1. Same Column (c):The queen at c5 can attack any piece in the same column. The piece at c2 is directly in her path.
   Pieces attacked: c2
2. Same Row (5):There is a piece at g5 in the same row.
   Pieces attacked: g5
3. Main Diagonal (a1-h8):The queen at c5 can attack diagonally. The piece at a3 is on the same diagonal.
   Pieces attacked: a3
4. Other Diagonals: Piece at g3 is on the other diagonal (h1-a8 direction).
   Pieces attacked: g3

Hence, the pieces at positions c2, g5, a3, g3 are under attack by the queen. In total, 4 pieces are attacked.

Answer 2

The problem requires determining from which starting position the queen will attack the maximum number of other pieces. The pieces are located at positions: a1, a3, b4, d7, h7, and h8. We'll evaluate each choice:

Option: f8

• Row attacks on h7.
• Column and diagonal attacks are blocked by lack of accessibility from f8.
• Total: 1 piece attacked.

Option: a7

• Row attacks on h7.
• Column attacks on a3.
• No diagonal attacks possible due to absence of pieces.
• Total: 2 pieces attacked.

Option: c1

• Row attack on none.
• Column attack is blocked by lack of targets.
• Diagonally, b4 is threatened.
• Total: 1 piece attacked.

Option: d3

• Row attacks on no pieces directly in d3.
• Column attacks on d7.
• Diagonally, b4 (to the bottom-left) and h7 (to the top-right) are attacked.
• Total: 3 pieces attacked.

Hence, placing the queen at d3 allows her to attack the maximum number of pieces (3 pieces).

Answer 3

To solve this problem, we must determine from how many positions a queen cannot attack any given piece on the chessboard. The positions of the pieces are: a1, a3, b4, d7, h7, and h8. Let's analyze each of these situations on a chessboard: 

• A queen on a1: This position covers all of column 'a', row '1', and both diagonals originating from a1. Pieces a3 and b4 are within the attack range on column and diagonals respectively.
• A queen on a3: This position covers all of column 'a', row '3', and both diagonals from a3. Piece a1 is on the same column and b4 is on a diagonal.
• A queen on b4: Covers column 'b', row '4', and both diagonals. Pieces a1, a3, d7, and h7 are on diagonal/column paths.
• A queen on d7: Covers column 'd', row '7', and both diagonals. Pieces a3, b4, h7, and h8 are within attacking paths.
• A queen on h7: Covers column 'h', row '7', and both diagonals. Pieces d7, b4, and h8 are within attacking range.
• A queen on h8: Covers column 'h', row '8', and both diagonals. Piece h7 is on the same column as h8.

Analyzing positions not threatening any other piece. Consider the logical exclusions of overlapping attack vectors:

Position	Reason
c5	No pieces on c column, 5th row, and its diagonals.
d1	Free from pieces along column, row, nor its direct diagonals because d7 is blocked.
g3	Lacks pieces on g column, 3rd row, or direct diagonals.
f8	Uninterrupted and free from paths or direct diagonals targeting from known pieces.

Based on these observations, there are 4 positions (c5, d1, g3, f8) from which the queen cannot attack any of the pieces. Hence, the correct answer is 4.

Answer 4

Step 1: Total squares on the board

An \(8 \times 8\) chessboard has: \[ 8 \times 8 = 64 \ \text{squares} \]

Step 2: Attackable squares from position d5

• Same row (5th rank): The queen attacks 7 other squares in this row.
• Same column (d-file): The queen attacks 7 other squares in this column.
• Diagonal \ (top-left to bottom-right): From d5, squares are: a2, b3, c4 (towards bottom-left) and e6, f7, g8 (towards top-right), totaling \(3+3=6\) squares.
• Diagonal / (top-right to bottom-left): From d5, squares are: a8, b7, c6 (towards top-left) and e4, f3, g2, h1 (towards bottom-right), totaling \(3+4=7\) squares.

Step 3: Adding attackable squares

Total attackable: \[ 7 \ (\text{row}) + 7 \ (\text{column}) + 6 \ (\text{diagonal } \backslash) + 7 \ (\text{diagonal } /) = 27 \]

Note: The square d5 itself is not included in these counts.

Step 4: Safe squares calculation

\[ \text{Safe squares} = 64 - (\text{Attackable squares} + 1 \ \text{(queen’s own square)}) \] \[ = 64 - (27 + 1) = 64 - 28 = 36 \]

Final Answer:

\[ \boxed{36} \]