Question 1162655
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The top left unit square is shaded.<br>
The other 8 unit squares are either shaded or unshaded.  That is 2 choices for each of the 8 squares, for a total of 2^8=256 different grids with the top left unit square shaded.<br>
With the top left unit square shaded, there are 3 sets of four unshaded unit squares that form a 2x2 square.<br>
For each of those three sets of four unit squares, with the top left unit square shaded there are four unit squares left that are either shaded or unshaded.  That is 2^4=16 possible combinations.<br>
So, with the top left unit square shaded, there are 3*16=48 grids which DO contain an unshaded 2x2 square.<br>
And so the number of grids with the top left unit square shaded that do NOT contain an unshaded 2x2 square is 256-48 = 208.<br>