Problem 1966. Kaggle: Reverse Game of Life - Single Move to One Cell Case

Kaggle's Conway's Reverse Game of Life contest inspires this Single Reverse step in Life challenge. The kaggle contest runs from Oct-14-2013 thru Mar-02-2014. References: Game of Life at Wolfram. Wiki Life.

1. Any live cell with fewer than two live neighbors dies, as if caused by under-population.
2. Any live cell with two or three live neighbors lives on to the next generation.
3. Any live cell with more than three live neighbors dies, as if by overcrowding.
4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.
5. No wrap around. Beyond edge is zero. Eight Neighbors.

Find all the 4x4 Life matrices that upon one evolution produce a single living cell. This is a single evolution reversal set. The 4x4 gets appended by a ring of zeros for processing. The single living cell may be anywhere in the final 6x6 matrix, but none are expected to occur in the outer ring for a valid solution.

Input: None

Output: Cell array of unique 4x4 matrices that evolve to a single cell

Scoring: 600 - (Number of valid unique 4x4 matrices)

Examples: A few valid matrices that produce a single cell

0000  0010  1101
0001  1000  1110
0000  0000  0100
0101  0110  1001