How my solution works:
For each new character, look at the character immediately above and to the left of that character. If they are the same, use 0. If they are different, use 1. If you go off of the board, assume the character is 0.
In short:
0 0
? 0
1 1
? 0
1 0
? 1
0 1
? 1
Is the rule table. I believe this works, yes?
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No amount of planning will ever replace dumb luck.