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.
All the 5 position cases are represented, with the final color, using digits to represent the colors:
11111 1
11112 2
11121 2
11122 3
11123 1
11211 1
11212 2
11213 3
11221 2
11222 3
11223 1
11231 3
11232 1
11233 2
12111 2
12112 3
12113 1
12121 3
12122 1
12123 2
12131 1
12132 2
12133 3
12211 2
12212 3
12213 1
12221 3
12222 1
12223 2
12231 1
12232 2
12233 3
12311 2
12312 3
12313 1
12321 3
12322 1
12323 2
12331 1
12332 2
12333 3
|
|
Posted by Charlie
on 2018-12-14 21:26:20 |
in case this helps guide the analysis
