A 3*3 grid is coloured using red,green and blue colour such that if we rotate the grid about its centre in the plane by 180 degree,the grid looks the same.the number of ways to colour the grid this way is-

• there are 9 tiles( number it in horizantal way 1 2 3....to9)pls draw fig
  blue or red
  1)consider 1 and 9 blocks 2^1=2ways(i.e red or blue)
  2)consi 3 and 7(again 2^1=2ways)
  3)nw 2 and 8(2ways)
  4)nw 4 and 6(2ways)
  5)centre i.e 5(2ways)
  total=2x2x2x2x2=32ways
  
• 10 years agoHelpfull: Yes(23) No(7)
• A B C
  D E F
  G H I
  
  rotate
  
  I H G
  F E D
  C B A
  
  
  conditions:
  A=I;
  B=H;
  C=G;
  D=F;
  
  lets color A,B,C,D,E first
  total ways=3*3*3*3*3 (for A,b,C,D,E)
  now after coloring these,the only way you can color the rest is 1..
  
  So ans is 243
• 10 years agoHelpfull: Yes(21) No(11)
• it is 3^5=243
• 10 years agoHelpfull: Yes(14) No(13)
• arrange red at corners , green at space between reds and blue at center 3!=6
  
• 10 years agoHelpfull: Yes(10) No(9)
• No of ways= 3*3*3=27.
  Consider initial grid as 123
  456
  789
  On rotating by 180 degrees, new grid,
  741
  852
  963.
  Therefore in the initial grid 2,4,6 and 8 must have same color. Therefore they can have any 1 of the 3 colors.
  Similarly 1,3,7 and 9 must have same color. Therefore they can also have any 1 of the three colors.
  5 can have any one of the three colors.
  Therefore no of ways to color the grid=3*3*3=27.
  
• 10 years agoHelpfull: Yes(3) No(13)
• divide the whole grid into 12 parts i.e 90/3=3*4=12
  so in 1st 90 degrees color with red,green and blue respectively.
  similarly repeat the same process for remaining.
  so it is the only way..
• 10 years agoHelpfull: Yes(0) No(3)
• answer this questionnn
  
• 9 years agoHelpfull: Yes(0) No(0)
• 64
  
  
  
  
  The
• 9 years agoHelpfull: Yes(0) No(0)