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.

Example:

r b y y b
y r y r
b b b
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.

If the top line is symmetric with respect to two of the letters, then the final result cannot be either of those two, so it must be the third.

For example, the following all must result in a "b":

y y r r

y r y r

b r y b

y b b r

b b b b

y y b r r

y r b y r

b r b y b

y b b b r

b b b b b