This repository contains some simple code to illustrate how Monte Carlo methods can be used to build up mathematics intuition. Note that a state-space based analysis is relatively easy, and those who are familar with that kind of approach wouldn't need to use this applied mathematics style approach. This is intended for beginners.
The code also generates the state-space graph to help build intuition.
The puzzle is as follows:
Given a mathematical stick (infinitely thin, so modeled as a line segment), make two uniformly random cuts. This yields three sticks, the sum of the lengths of which should equal to the original, which, without loss of generality, is of length 1.
What is the probability that the three sticks can be laid down end-to-end to form a triangle?
(Alternatively, pick two points at which to install a hinge, and ...)
To see the solution, follow this link.