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.
(In reply to
proposed solution by xdog)
I think you got it. I didn't think working with numbers would work because 0+1=2, 0+2=1, 2+1=0 isn't recognizeable.
But because the sum is always 0 mod 3, your idea works.
You can even streamline your process further by doing eveything mod 3.

Posted by Jer
on 20181218 11:07:19 