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10 Chessboard Puzzles Questions and Answers

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

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Practice chessboard puzzles questions with detailed explanations. These solved examples cover the most frequently asked patterns in placement and competitive exams.

Q1 Easy

Count total squares of all sizes on a 8 x 8 chess grid.

  • A. 199
  • B. 194
  • C. 204 ✓
  • D. 209
Explanation: Total squares = n(n+1)(2n+1)/6 = 204.
Q2 Easy

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

  • A. 18 ✓
  • B. 24
  • C. 8
  • D. 12
Explanation: Rectangles = m(m+1)n(n+1)/4 = 18.
Q3 Easy

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

  • A. 64 ✓
  • B. 72
  • C. 52
  • D. 56
Explanation: Unit squares = 8 x 8 = 64.
Q4 Easy

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

  • A. 28
  • B. 24
  • C. 32 ✓
  • D. 36
Explanation: Half the squares are black on even board: 64/2 = 32.
Q5 Medium

How many unit squares are there on a 10 x 10 board?

  • A. 92
  • B. 108
  • C. 88
  • D. 100 ✓
Explanation: Unit squares = 10 x 10 = 100.
Q6 Medium

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

  • A. 64
  • B. 72 ✓
  • C. 68
  • D. 76
Explanation: Half the squares are black on even board: 144/2 = 72.
Q7 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.
Q8 Medium

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

  • A. 42
  • B. 46
  • C. 54
  • D. 50 ✓
Explanation: Half the squares are black on even board: 100/2 = 50.
Q9 Hard

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. 5 ✓
  • C. 3
  • D. 6
Explanation: At most one rook per row and column, so maximum = 5.
Q10 Hard

How many unit squares are there on a 6 x 6 board?

  • A. 28
  • B. 44
  • C. 36 ✓
  • D. 24
Explanation: Unit squares = 6 x 6 = 36.

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