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15 Chessboard Puzzles Questions and Answers

15 solved Chessboard Puzzles questions with step-by-step explanations. Includes formulas, shortcuts, and tips for placement tests and competitive exams.

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Advanced chessboard puzzles questions for experienced learners. These medium-to-hard questions test deeper understanding and are ideal for those who have already mastered the basics. Each question includes a detailed explanation.

Q1 Medium

What is the maximum number of rooks that can be placed on an 8 x 8 board so none attack each other?

  • A. 7
  • B. 9
  • C. 6
  • D. 8 ✓
Explanation: At most one rook per row and column, so maximum = 8.
Q2 Medium

In a 12 x 12 checkerboard pattern, how many black squares are there?

  • A. 76
  • B. 68
  • C. 72 ✓
  • D. 64
Explanation: Half the squares are black on even board: 144/2 = 72.
Q3 Medium

How many rectangles are there in a 2 x 3 grid?

  • A. 12
  • B. 18 ✓
  • C. 24
  • D. 8
Explanation: Rectangles = m(m+1)n(n+1)/4 = 18.
Q4 Medium

What is the maximum number of rooks that can be placed on an 7 x 7 board so none attack each other?

  • A. 5
  • B. 7 ✓
  • C. 8
  • D. 6
Explanation: At most one rook per row and column, so maximum = 7.
Q5 Medium

What is the maximum number of rooks that can be placed on an 5 x 5 board so none attack each other?

  • A. 6
  • B. 5 ✓
  • C. 3
  • D. 4
Explanation: At most one rook per row and column, so maximum = 5.
Q6 Medium

In a 8 x 8 checkerboard pattern, how many black squares are there?

  • A. 24
  • B. 28
  • C. 36
  • D. 32 ✓
Explanation: Half the squares are black on even board: 64/2 = 32.
Q7 Medium

In a 10 x 10 checkerboard pattern, how many black squares are there?

  • A. 50 ✓
  • B. 54
  • C. 46
  • D. 42
Explanation: Half the squares are black on even board: 100/2 = 50.
Q8 Medium

What is the maximum number of rooks that can be placed on an 8 x 8 board so none attack each other?

  • A. 8 ✓
  • B. 6
  • C. 9
  • D. 7
Explanation: At most one rook per row and column, so maximum = 8.
Q9 Medium

Count total squares of all sizes on a 6 x 6 chess grid.

  • A. 81
  • B. 86
  • C. 91 ✓
  • D. 96
Explanation: Total squares = n(n+1)(2n+1)/6 = 91.
Q10 Medium

How many unit squares are there on a 8 x 8 board?

  • A. 52
  • B. 56
  • C. 72
  • D. 64 ✓
Explanation: Unit squares = 8 x 8 = 64.
Q11 Medium

How many rectangles are there in a 5 x 6 grid?

  • A. 305
  • B. 321
  • C. 315 ✓
  • D. 309
Explanation: Rectangles = m(m+1)n(n+1)/4 = 315.
Q12 Medium

How many unit squares are there on a 8 x 8 board?

  • A. 64 ✓
  • B. 56
  • C. 72
  • D. 52
Explanation: Unit squares = 8 x 8 = 64.
Q13 Medium

What is the maximum number of rooks that can be placed on an 8 x 8 board so none attack each other?

  • A. 7
  • B. 6
  • C. 9
  • D. 8 ✓
Explanation: At most one rook per row and column, so maximum = 8.
Q14 Medium

What is the maximum number of rooks that can be placed on an 5 x 5 board so none attack each other?

  • A. 4
  • B. 3
  • C. 5 ✓
  • D. 6
Explanation: At most one rook per row and column, so maximum = 5.
Q15 Hard

What is the maximum number of rooks that can be placed on an 8 x 8 board so none attack each other?

  • A. 7
  • B. 8 ✓
  • C. 6
  • D. 9
Explanation: At most one rook per row and column, so maximum = 8.

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