Explore the pigeonhole principle through a 29-minute video lecture featuring several examples, including a famous problem from Erdos and one from the 1994 Putnam Exam. Delve into problem-solving techniques as the instructor introduces the concept and demonstrates its application in various scenarios, such as picked socks, pigeon holes, and linear algebra. Gain valuable insights into this fundamental mathematical principle and enhance your problem-solving skills through clear explanations and practical examples.