Paint the town red!
You paint the grid red, one square at a time. You can only paint a square red if it shares an edge with 1 or 3 blue squares (diagonals don't count).
If you continue until there is no more blue square left to be painted red according to the rule above, what's the minimum possible number of squares you can color?
Below right is an example of a sequence of how you might paint the first 4 squares.
Clarification:
The square colored red with sequence number 3 now borders two blue squares, but it was bordering three blue squares at the time of coloring.
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1 solution
Here is one way you could paint 8 squares (in the order given):
Will try to come up with a rigorous proof as to why this is the minimum you can do... Stay tuned!
In the meantime, in case you are bored, can you come up with the general solution for an m × n grid? :0)