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.
num (2-20)?
2
3 2
1
num (2-20)?
3
3 2 3
1 1
1
num (2-20)?
4
1 3 3 1
2 3 2
1 1
1
num (2-20)?
5
1 3 3 1 3
2 3 2 2
1 1 2
1 3
2
num (2-20)?
6
2 2 1 1 2 1
2 3 1 3 3
1 2 2 3
3 2 1
1 3
2
num (2-20)?
7
2 2 1 1 2 1 1
2 3 1 3 3 1
1 2 2 3 2
3 2 1 1
1 3 1
2 2
2
num (2-20)?
8
2 2 1 1 2 1 1 2
2 3 1 3 3 1 3
1 2 2 3 2 2
3 2 1 1 2
1 3 1 3
2 2 2
2 2
2
num (2-20)?
9
1 1 2 1 1 3 1 3 1
1 3 3 1 2 2 2 2
2 3 2 3 2 2 2
1 1 1 1 2 2
1 1 1 3 2
1 1 2 1
1 3 3
2 3
1
num (2-20)?
20
2 1 3 1 3 3 2 2 3 3 2 3 2 3 2 2 2 1 3 1
3 2 2 2 3 1 2 1 3 1 1 1 1 1 2 2 3 2 2
1 2 2 1 2 3 3 2 2 1 1 1 1 3 2 1 1 2
3 2 3 3 1 3 1 2 3 1 1 1 2 1 3 1 3
1 1 3 2 2 2 3 1 2 1 1 3 3 2 2 2
1 2 1 2 2 1 2 3 3 1 2 3 1 2 2
3 3 3 2 3 3 1 3 2 3 1 2 3 2
3 3 1 1 3 2 2 1 1 2 3 1 1
3 2 1 2 1 2 3 1 3 1 2 1
1 3 3 3 3 1 2 2 2 3 3
2 3 3 3 2 3 2 2 1 3
1 3 3 1 1 1 2 3 2
2 3 2 1 1 3 1 1
1 1 3 1 2 2 1
1 2 2 3 2 3
3 2 1 1 1
1 3 1 1
2 2 1
2 3
1
Edited on December 14, 2018, 9:42 pm
also, some random examples
