a 3x3 grid is painted with red and blue... in how many ways can it be painted in such a way that even if the grid is rotated 180 degrees it looks as the one before rotating..

• in a 3x3 grid we have 9 tiles [1 2 3] on rotating 180deg we get [9 8 7]
  [4 5 6] [6 5 4]
  [7 8 9] [3 2 1]
  so that 1=9,8=2,7=3,6=4,5=5 for each combination 2ways of colors are possible
  therefore for 5 combinations 2x2x2x2x2=32 ways are possible
• 11 years agoHelpfull: Yes(28) No(5)
• we have 123
  456
  789
  after rotation
  987
  654
  321
  now we can pain 123 in 2*2*2=8 ways.. and in which way we pain 123 we have to paint 789 in reverse way so that after rotation it will becom same as 123
  now 456 and 654 shoul be same
  there are possible combinations
  rrr,bbb,rbr,brb only 4
  so total combination will be 8+4=12
  12 is ans
  
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• Hey Sruthi...can u mail me ques u hv remembred...my id z mainapnifavoritehoon11@gmail.com
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• 32.... 9 grids can be imagined as below
  
  123
  456
  789
  
  SO when it is rotated 180 it becomes
  
  987
  654
  321
  
  so positions (1,9);(2,8);(3,7);(4,6) must be same and as there are 2 colors its becomes 2 combinations each making total possible ways as 2*282*2=16 and in block 5 we can have 2 combinations for each of these 16 combinations.. so total possible combinations is 32
  
  ANS:-32
  
  
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• 2^5=32
  as no of combinations are 5...for each 2 ways of color are possible
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