The Circular Problem

It will be easier to draw the radii inside the circles to find the areas of the circles and the diamonds. If the area of the square = 49 square units, then the measure of one side of the square = 7 units.

Therefore, the measure of the radius = $\frac{7}{4}$ units. Therefore, the area of the circle = $\frac{22}{7}$ * $\frac{7}{4}$ * $\frac{7}{4}$ = $\frac{77}{8}$ . Therefore, the total area of all the circles = $\frac{77}{8}$ * 4 = $\frac{77}{2}$ .

The total area of one quarter of a diamond = $\frac{1}{2}$ * $\frac{7}{4}$ * $\frac{7}{4}$ = $\frac{49}{32}$ . Therefore, the area of a diamond = $\frac{49}{32}$ * 4 = $\frac{49}{8}$ . Therefore, the total area of all the diamonds = $\frac{49}{8}$ * 4 = $\frac{49}{2}$ .

Therefore, the total area of the regions marked as 'x' = $\frac{77}{2}$ - $\frac{49}{2}$ = $\frac{28}{2}$ .

Therefore, the total area of the regions marked as 'y' = 49 * $\frac{2}{2}$ - $\frac{77}{2}$ = $\frac{98}{2}$ - $\frac{77}{2}$ = $\frac{21}{2}$ .

Therefore, $\frac{28}{2}$ / $\frac{21}{2}$ = $\frac{28}{2}$ * $\frac{2}{21}$ = $\frac{4}{3}$

Therefore, $\frac{4}{3}$ * 6 = 8

Therefore, 8! = 40320