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The Checkerboard Method
Last updated at February 6, 2026 by Teachoo
Class 7 (Ganita Prakash 1, 2 & old NCERT)
Chapter 6 Class 7 - Constructions and Tilings (Ganita Prakash II)
- Constructing an Eye
- Constructing a Perpendicular Bisector
- Constructing angle 90°
- Construction Methods in Śulba-Sūtras
- Constructing Angle Bisectors
- Figure it out - Pag 144, 145
- Constructing Copy of an Angle
- Construction of a Line Parallel to the Given Line
- Constructing Arch Designs
- Constructing Regular Hexagon, Angle 60° and 6-pointed Star
- Figure it out - Pag 154, 155
- Tangrams
-
Tiling
- Figure it out - Page 160
- Tiling the Entire Plane
Transcript
The Checkerboard MethodLet’s look at our 5 × 3 grid as a checkerboard Counting the Full Grid: White (W): 8 squares Black (B): 7 squares Total: 15 squares The Golden Rule of Dominoes: Every single domino you place MUST cover exactly 1 White square and 1 Black square. Therefore, to tile any shape, you must have an equal number of Black and White squares. Now, let’s look at our question again Is the following region tileable with 2 × 1 tiles? Converting into checkerboard tile If we remove that 1 Black square, what is left? White: Still 8 (we didn't touch them). Black: Now 6 (started with 7, removed 1). The Result: You have 8 White squares and 6 Black squares. You can match 6 White with 6 Black using dominoes. You will be left with 2 White squares that have no Black neighbors to pair with. Conclusion: Impossible!
