64 farmers each have square farms arranged in an 8 \(\times\) 8 grid. The farmers all want to grow crops. If on one day a farmer is not already growing crops, then the next day s/he will start growing crops if at least two of his/her adjacent neighbors are already growing crops
. (Note we mean adjacent by a side, not a corner.)
If on some day the 8 farmers on a diagonal are all growing crops, eventually (after 7 days) all farmers will be growing crops. If on some day exactly 7 farmers are growing crops, is it possible that eventually all farmers will be growing crops?
This problem is not original.