Question

Count the number of squares in the given figure. 

Hint:

Break complex “star/rosette” pictures into identical halves, count by size inside one half, and then correct for any shared square(s) at the join.

Answer 1

The drawing is made of two identical “rosette” blocks (left and right) that touch at one small diamond–square in the middle. Count squares by size inside one rosette and then use symmetry.
Step 1: Squares inside a single rosette
Within one block we find:
1 largest outer tilted square (the diamond boundary).
4 medium axis–aligned squares (one facing each cardinal direction).
4 medium tilted squares (set at $45^\circ$ within the arms).
4 small axis–aligned corner squares around the star.
5 tiny squares in the central star (the middle one plus four around it).
Thus one rosette contributes \[ 1+4+4+4+5=18 \text{ squares}. \] Step 2: Use symmetry and subtract/ add overlaps
There are two identical rosettes $⇒ 2\times 18=36$ squares.
They meet at exactly one small diamond–square that sits on the joint and belongs to the whole figure (not double–counted across the two lists). Adding this shared square gives \[ 36+1=\boxed{37}. \]