Question 68
We want to colour the 36 squares of a $6 \times 6$ board. Every square must be coloured white, grey, or black, and the following requirement must be met:
Three adjacent squares in the same row or column, must always have three different colours.
We say that two colourings are *truly different* if you cannot get one from the other by rotating the board. Below, you can see three colourings that meet the requirement. The first and second colouring are truly different, but the third is the same as the second after rotating.
How many truly different colourings meet the requirement (including the two from the figure)?
Three adjacent squares in the same row or column, must always have three different colours.
We say that two colourings are *truly different* if you cannot get one from the other by rotating the board. Below, you can see three colourings that meet the requirement. The first and second colouring are truly different, but the third is the same as the second after rotating.
How many truly different colourings meet the requirement (including the two from the figure)?