Summary of The hardest problem on the hardest test

00:00:00 - 00:05:00

The video discusses a difficult problem on the Putnam math competition, which is a test consisting of 12 questions of varying difficulty. The problem discussed in the video is a 2D problem that can be approached in a number of ways. The video shows one way to solve the problem and emphasizes the importance of deep understanding in mathematical problem-solving.

• 00:00:00 The Putnam is a math competition for undergraduate students that consists of 12 questions, each with a 1-10 difficulty scale. Despite being difficult, the median score is around 1 or 2. One of the 6 questions on the test is a difficult problem that involves solving a problem in 2 dimensions. The problem can be approached in a number of ways, and the video shows one way to find the solution.
• 00:05:00 In the 2D case of the Triangle Problem, it is easier to think about the average size of the section of the sphere that the triangle will contain if you start by thinking about two random lines that pass through the center of the sphere and then flip a coin to choose which of those two points is P1. However, it is still difficult to solve this problem, and it is important to have a deeper understanding of mathematical problem-solving in order to be able to articulate that understanding more formally.