Problems

Age
Difficulty
Found: 2

James furiously cuts a rectangular sheet of paper with scissors. Every second he cuts a random piece by an unsystematic rectilinear cut into two parts.

a) Find the mathematical expectation of the number of sides of a polygon (made from a piece of paper) that James randomly picks up after an hour of such work.

b) Solve the same problem if at first the piece of paper had the form of an arbitrary polygon.