A repository for sharing my own math explanations, problems and more.
By Dylan Tintenfich.
The Binary Tree Lottery Problem
The Binary Tree Lottery is a game where $k$ different nodes are randomly selected from a perfect binary tree of height $h$. You win the lottery if the $k$ selected nodes belongs to the same level of the tree.
The problem consists in finding the probability of winning the binary tree lottery as a function of $h$ and $k$.
Consider a circle of radius one centered at the origin of a complex plane. Given an $n \in \mathbb{N}$ and $\theta_0 \in \mathbb{R}$, find the product of the $n$ complex numbers $z_1, \dots, z_{n}$ that represent the $n$ equal parts into which the circle is divided, considering all possible rotations of these parts by $\theta_0$, the angle between the x-axis to the last complex number $z_{n}$ (i.e., $z_{n} = \cos\theta_0 + i \sin\theta_0$).
