Welcome to the first homework session of Statistical Mechanics: Algorithms and Computations. During the lecture, we have seen two powerful methods to compute π using Monte Carlo algorithms the homework consists of three parts, and you can find them on the Coursera website. In part 1, you will evaluate errors associated to direct sampling like in the children's game at the Monte Carlo beach. In part 2, you will see that the performance of the Markov chain algorithm played by adults in the heliport depends on how far you can throw the pebble. You will find that the best performance is approximately reached using the very famous 1/2 thumb rule. In part 3, you will study an advanced automatic method to evaluate errors in a smart way in Markov Chain algorithm, it's named the bunching method.