troydaniels: It's not that simple. There are a lot more cases to consider. For instance:

  +---+---+---+---+---+
6 |   |   | 0 |   |   |   
  +---+---+---+---+---+
5 | 0 |   |   |   |   |
  +---+---+---+---+---+
4 |   | 1 |   |   | 0 |   
  +---+---+---+---+---+
3 |   | 1 |   | 1 |   |   
  +---+---+---+---+---+
2 |   |   |   |   |   |   
  +---+---+---+---+---+
1 |   | 0 |   |   |   |
  +---+---+---+---+---+

If shooting on a2 reveals a 1, it can be determined that d4 must be a zero.