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November 20, 2025 9:37 pm (EST)
The Pigeonhole Principle
The pigeonhole principle is based on a very simple idea but is very powerful in mathematical problem solving. Here is the principle: Pigeonhole Principle: If there are objects to be placed in boxes, then at least one box must contain at least objects. The proof is straightforward. We can proceed by contradiction. Specifically, if…
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November 20, 2025 9:37 pm (EST)
Telescoping series
One of my favourite tricks in mathematical problem solving is the idea of a telescoping series. Consider the following problem: Find the sum of This seems to lead to an ugly expression without any insights into the problem. But now this is where a beautiful observation comes in: This allows us to…
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November 20, 2025 9:37 pm (EST)
The genius of Gauss
One of the most famous stories in mathematics is related to Gauss when he was a little boy. It went as follows: “It was said that to punish the kids for misbehavior, a teacher asked all students in the class to find the sum of all the natural numbers from 1 to 100. Gauss got…