Puzzle 1

Kevin and Stuart have some bananas. Each banana has the same size and shape, and they are all two-dimensional. Each one consists of the area between two circular arcs. The two circular arcs meet at either end of the banana at an angle of \(\pi/9\).

Kevin has 12 more bananas than Stuart. Kevin can use all of his bananas to form a perfect circle from circular arcs. Stuart can also use all of his bananas to form a perfect circle from circular arcs. How many bananas does Kevin have?

Note, the angle in the above problem is given in radians. If you're not familiar with radians, think of it as 20 degrees.