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)
xdog's rule, as stated, might work for an even number of blocks. For an odd number of blocks, the rule should be modified to just take the result from step 2, mod 3. I have not done any real testing of this, but that seems to work better.
For instance,
1 resolves to 1, not 2
2 resolves to 2, not 1
010 resolves to 2, not 1
re: proposed solution
