Begin with a finite sequence of blocks in a row, each in one of 3 colors: red, blue, yellow.
Below each pair of neighboring blocks place a new block with the color rule: If the blocks are the same color use that color but if they are different use the third color.
r b y y b
y r y r
b b b
How can the color of the last block be easily predicted from the top row?
Note: I don't know the full answer but can solve special cases.