Showing posts tagged puzzles

Numberphile video on the Josephus Problem

Recently, the following Numberphile video on the Josephus Problem has been making the rounds on math-related social media. I watched the video, and I thought Daniel Erman did a remarkably good job at explaining how to solve a mathematical problem. Daniel’s approach is similar to the techniques described in Polya‘s “How to Solve It.” Yet the particular story that Daniel tells also has an appealing narrative arc. Daniel’s video adheres to the following principles, which I think are fairly universal in mathematical problem solving. Start with a…

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The Aura of Interactive Proofs

In his essay The Work of Art in the Age of Mechanical Reproduction, Walter Benjamin introduces the idea that original artwork has an aura — some ineffable something that the work’s creator imbues into the work, but which is lost in reproductions made by mechanical means. There is something unique about an original work. Let us imagine that Walter is able to read the aura of work of art, or sense its absence. Thus, he has the seemingly magical ability to tell original art from mechanical forgery. Andy Warhol is…

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The Pop Quiz Paradox

This is one of my all-time favorite paradoxes: On Friday, a teacher announces to his class that there will be a pop quiz one day during the following week. In order to uphold the integrity of the quiz, it must satisfy the following two conditions: The quiz will be handed out at the beginning of class one day the following week (Monday through Friday). The students will not be able to (logically) deduce which day the quiz will be held before they are actually given the quiz. After making this…

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