The Pigeonhole Principle [Math Mondays]

One of the most obvious concepts- that ends up being useful everywhere

Apr 11, 2023

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Mondays are dedicated to theoretical concepts. We’ll cover ideas in Computer Science💻💻, math, software engineering, and much more. Use these days to strengthen your grip on the fundamentals and 10x your skills 🚀🚀.

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There is a lot of power found in simplicity.

If you have spent any time working on algorithm design, you will often see that some of the biggest breakthroughs are found in some of the ‘simplest’ insights.

In today’s post, I will teach you about one such principle- called The Pigeonhole Principle. It is among the legendary concepts in theoretical computer science and will help you a lot when it comes to algorithm design, system safety, and more. It seems obvious and almost trivial, but it can be used to prove some non-trivial results in mathematics and computer science.

Key Highlights

What is The Pigeonhole Principle?- The Pigeonhole Principle (also sometimes called the Dirichlet Drawer Principle) states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.
How can The Pigeonhole Principle help us in software engineering- In software engineering, the Pigeonhole Principle is often used to ensure the correctness and efficiency of algorithms. When it comes to large-scale system design, you want to ensure that your components behave correctly to limit side effects. This principle can be used to prove certain properties about your components.
Pigeonhole principle and proving non-existence- One of the most useful applications of the principle will show when you want to see if problems are not solvable. For example, it has been used to show the non-existence of a universal lossless compression algorithm and as a basis for the pumping lemma.

For a great introduction to the topic, make sure you watch the video below. It covers the concepts in a robust but comprehensive manner.

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