MATHEMATICS SUBJECT ENRICHMENT ACTIVITY Class: VIII PART2 Chapter: FRACTIONS IN DISGUISE

 

Maths Subject Enrichment Activity

Title of the Activity

Peaceful Knights – A Logical Placement Challenge

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Class

VIII

Textbook Reference

Ganita Prakash – Part 2
(Activity Page: Peaceful Knights)

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Topic

• Logical Reasoning

• Chessboard Geometry

• Patterns and Spatial Thinking

• Non-attacking Arrangements

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Aim of the Activity

To place 8 knights on a chessboard such that no knight attacks another, and to develop logical thinking by understanding the movement pattern of a knight.

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Learning Outcomes

Students will be able to:

• Understand the L-shaped movement of a knight

• Apply logical reasoning and spatial awareness

• Recognize patterns and symmetry on a chessboard

• Appreciate the role of mathematics in games and puzzles

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Materials Required

• Printed or drawn 8 × 8 chessboard

• Pencil / pen

• Eraser

• (Optional) Chess pieces or counters

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Prerequisite Knowledge

• Knowledge of a chessboard layout

• Understanding of coordinates / grid positions

• Basic idea of movement patterns

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Procedure

1. Draw an 8 × 8 chessboard.

2. Recall the knight’s movement:

   • 2 squares in one direction and 1 square perpendicular (L-shape).

3. Begin placing knights one by one on the board.

4. After placing each knight, check:

   • Does it attack any existing knight?

5. Continue until 8 knights are placed.

6. Ensure no two knights attack each other.

7. Record the final positions using:

   • Square names (e.g., A1, C3)

   • OR a diagram

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Observation

• Knights placed on same-colored squares do not attack each other.

• Knights attack only opposite-colored squares.

• Symmetrical placements help avoid attacks.

• Logical grouping simplifies the solution.

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Result / Solution

A valid arrangement of 8 peaceful knights is achieved where:

• No knight can attack another.

• All knights follow the movement rule.

• The condition of non-attacking placement is satisfied.

✔ Hence, the objective is successfully achieved.

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Verification

Condition	Status
Knight movement followed	✔
No knight attacking another	✔
8 knights placed	✔
Logical placement used	✔

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Reflection / Thinking Questions

1. Why do knights on the same color never attack each other?

2. Is there more than one correct solution?

3. What happens if we try to place 9 knights?

4. How is this problem related to combinatorics?

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Extension / Enrichment

• Try the same activity on:

  • 6 × 6 board

  • 10 × 10 board

• Compare with 8 Queens problem

• Explore how mathematics is used in chess algorithms

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Real-Life Application

• Game design

• Artificial intelligence

• Strategy planning

• Problem-solving techniques

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Conclusion

This activity shows that mathematics is deeply connected to games and logical thinking. By exploring knight movements, students develop reasoning skills and enjoy learning through play.

SOLUTION 1 – Bottom Two Rows (Black Squares)

Positions:

A1, C1, E1, G1,

A3, C3, E3, G3

8  . . . . . . . .

7  . . . . . . . .

6  . . . . . . . .

5  . . . . . . . .

4  . . . . . . . .

3  K . K . K . K .

2  . . . . . . . .

1  K . K . K . K .

   A B C D E F G H

✔ Valid
✔ Symmetric
✔ Easy to explain

SOLUTION 2 – Top Two Rows (White Squares)

Positions:

B8, D8, F8, H8,

B6, D6, F6, H6

8  . K . K . K . K

7  . . . . . . . .

6  . K . K . K . K

5  . . . . . . . .

4  . . . . . . . .

3  . . . . . . . .

2  . . . . . . . .

1  . . . . . . . .

   A B C D E F G H

✔ Colour-based reasoning
✔ Inverted pattern of Solution 1

SOLUTION 3 – Middle Rows

Positions:

A4, C4, E4, G4,

A6, C6, E6, G6

8  . . . . . . . .

7  . . . . . . . .

6  K . K . K . K .

5  . . . . . . . .

4  K . K . K . K .

3  . . . . . . . .

2  . . . . . . . .

1  . . . . . . . .

✔ Demonstrates vertical symmetry
✔ Useful for extension discussion

SOLUTION 4 – Two Columns Pattern

Positions:

B1, B3, B5, B7,

D1, D3, D5, D7

8  . . . . . . . .

7  . K . K . . . .

6  . . . . . . . .

5  . K . K . . . .

4  . . . . . . . .

3  . K . K . . . .

2  . . . . . . . .

1  . K . K . . . .

   A B C D E F G H

✔ Column-based logic
✔ Excellent for reasoning discussion

SOLUTION 5 – Scattered but Same Colour

Positions:

A1, D2, G3, B4,

E5, H6, C7, F8

✔ Non-linear
✔ Tests deeper understanding
✔ No knight attacks another

Rule	Status
8 Knights placed	✔
Knight L-move respected	✔
No attacks	✔
Logical reasoning	✔