Practice30Create account

On an chessboard, the two opposite corner squares (both white) are removed. Why can't tiles cover the 62 squares that remain?

Class 7Tiling PatternsGeometry
  • A62 is an odd number
  • BEach tile covers 1 black and 1 white, but 32 black and 30 white remain
  • CCorner squares are needed to start
  • DAn board cannot be tiled at all

Step-by-Step Solution

Any tile on a chessboard covers one black and one white square. 31 tiles would need 31 black and 31 white, but 32 black and only 30 white are left. (62 is even, so counting alone does not settle it.)
Answer: B) Each tile covers 1 black and 1 white, but 32 black and 30 white remain

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Tiling Patterns practice questions

More Class 7 Tiling Patterns practice

Covering a flat surface with copies of shapes so that there are no gaps and no overlaps…Look at the square tiling. How many tiles meet at each corner point inside the pattern?In this tiling of equilateral triangles, how many triangles meet at each inside vertex?A honeycomb is a tiling of regular hexagons. How many hexagons meet at each vertex?Each angle of a square is 90°. Why do four squares fit exactly around a point?