The nerd snipers problem

TL;DR

This paper investigates the 'nerd snipers problem,' analyzing the expected proportion of nerds remaining unscathed after each targets their nearest neighbor in a large, uniformly distributed population.

Contribution

It provides a corrected analysis of the problem, offering new insights into the behavior of nearest neighbor interactions in large random distributions.

Findings

Expected unscathed proportion converges as N approaches infinity.

Provides corrected mathematical framework for the problem.

Analyzes the probabilistic behavior of nearest neighbor targeting.

Abstract

We correct errors that appear throughout "The vicious neighbour problem" by Tao and Wu. We seek to solve the following problem. Suppose $N$ nerds are distributed uniformly at random in a square region. At 3:14pm, every nerd simultaneously snipes their nearest neighbor. What is the expected proportion $P_N$ of nerds who are left unscathed in the limit as $N\to\infty$?