There are 40 squares in the puzzle.

Count all of the "obvious" squares first: There are 16 squares arranged in a 4 X 4 pattern. There are 8 little squares in 2 sets of 4
You've found 24 squares so far: 16 + 8

Include the 1 large square surrounding the entire puzzle and the 2 squares surrounding each set of the little squares. Now you've found 27 squares so far: 24 + 3

Then look at the 16 squares again--each set of 4 (2X2)gives you another square, and there are 9 SETS of 4 squares, so now you have found 36 squares: 27 + 9

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Each * represents a square; the above represents 4 sets of 4 squares


** **


** **
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** **

Each * represents a square; the above represents 2 additional sets of 4 squares (6 sets so far)


* ** *
* ** *

* ** *
* ** *

Each * represents a square; the above represents yet 2 more sets of 4 squares (8 sets so far)


* ** *

* ** *
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* ** *

Each * represents a square; the above represents the last set of 4 squares (in the center of the 16 squares) for a total of 9 sets of 4 squares




Then, still looking at the 16 squares, each set of 9 squares(3X3) gives you another square, and there are 4 SETS of 9 squares. Now you've found 40 squares: 36 + 4


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Each * represents a square; the above represents one set of 9 squares (3 x 3) in the upper right hand corner of the puzzle


*** *
*** *
*** *

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Each * represents a square; the above represents the second set of 9 squares (3 x 3) in the upper left hand corner of the puzzle


****

* ***
* ***
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Each * represents a square; the above represents the third set of 9 squares (3 x 3) in the lower right hand corner of the puzzle


****

*** *
*** *
*** *

Each * represents a square; the above represents the forth set of 9 squares (3 x 3) in the lower left hand corner of the puzzle