Question

In a 3*3 square grid comprising 9 tiles each tile can be painted in red or blue color. When the tile is rotated by 180 degree, there is no difference which can be spotted. How many such possibilities are there?

a.16 b)32 c)64 d)256

Answer 1

Answer:

b) 32

Step-by-step explanation:

Area of grid = 3 × 3 (Given)

Number of tiles = 9 (Given)

Rotation degree = 180° (Given)

The grid so formed will be -

2 3 1

4 5 4

1 3 2

Thus, this grid even when rotated at 180°, then the relative positions of the tiles will not change.

Thus, we will paint tile number 1's with the colour red or blue (only one color should be used) , and the tile 2's with red or blue.....tile 5 red or blue.  Then total possibilities of the grid will be -  

2`5

= 32

Answer 2

Answer:

Step-by-step explanation:

Number of tiles = 9 (Given)

Rotation degree = 180° (Given)

The grid so formed will be -

2 3 1

4 5 4

1 3 2

Thus, this grid even when rotated at 180°, then the relative positions of the tiles will not change.

Thus, we will paint tile number 1's with the colour red or blue (only one color should be used) , and the tile 2's with red or blue.....tile 5 red or blue. Then total possibilities of the grid will be -

2`5

= 32