Question

In a 6x6 square grid comprising 9 tiles, each tile can be painted in red or blue color. When the tile is rotated by 1800, there is no difference which can be spotted. How many such possibilities are there?

Answer 1

If we rotate 180 degree in 5 possible place in 2 colors.

Assume 3*3 grid

b d c

e a e

c d b

So, we can say that a,b,c,d,e colored red or blue.

There is no difference by rotating

Hence,

$2^{5} =32$

Total possibilities are 32.

Answer 2

Answer:

2^5

Step-by-step explanation:

here 6*6 square comprises of 9 tiles which means each tile is a 2*2 square grid. The problem can be viewed as a 3*3 square grid. Here after rotating by 180 degrees there shouldn't be any difference. So 5 pair of positions are there in total. these can be painted in 2^5 ways.