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?

• In a 6x6 square grid having 9 tiles
  then each tile can be painted in either red(or)blue color,and there is one condition that is the tile having same color by rotating the grid then the spotted tile.
  R B R
  B R B RR,BB,RR,BB,R
  R B R
  there fore there are mainly 5 such pairs are obtained and each pair having total two possibilities
  finally there are painted in 2^5 ways.
• 5 years agoHelpfull: Yes(4) No(1)
• 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.
• 5 years agoHelpfull: Yes(1) No(4)
• For odd nos. the ways will be 2^(no of grids in 2 diagonals -1), 1 is subtracted for the common grids in diagonals.
  For even no the ways will be 2^(no of grids in 2 diagonals).
  
  No of ways 2^(6+6)= 4096
• 5 years agoHelpfull: Yes(1) No(0)
• This grid even rotated 180 degrees the relative positions of the tiles do not change. So we paint tile number 1's with red or blue (only one color should be used) , 2's with red or blue.....tile 5 red or blue. Then total possibilities are 2^5 = 32
• 5 years agoHelpfull: Yes(0) No(0)
• 5main possibles is their and each pair having 2 possibles,so finally painted is 2^5
• 5 years agoHelpfull: Yes(0) No(0)