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Evil Combinatorialist and 16 Wines: An Information Theory Puzzle

2025-08-21

Trapped in an evil combinatorialist's wine cellar, you're presented with 16 unlabeled bottles of wine, each from a different year between 0 and 15, and four binary measuring devices. Each device measures one bottle, outputting 0 or 1. The goal is to identify the year of each wine with 50 or fewer measurements. While it seems to require 64 measurements, exploiting the uniqueness of the years, a divide-and-conquer approach, starting by measuring most bottles with one device, dividing them into groups based on the result, and recursively applying the method, can solve it within 49 measurements. This puzzle cleverly combines information theory and combinatorics, showcasing how to leverage information asymmetry to reduce computational effort.

The Wallflower Fractal: A Decade-Long Mathematical Odyssey

2025-05-22

Starting from a simple geometric doodle from middle school, the author delves into a decade-long mathematical exploration. The fractal pattern, affectionately called "the wallflower," can be generated using iterative algorithms or L-systems. The author discovers subtle differences between the patterns generated by these two methods, and reveals the connection between them through the introduction of a matrix base number system and vector digits, explaining the origin of the "approximately 27-degree" rotation angle. Further, the author explores 3D and 4D extensions of the fractal and proposes a novel number system based on quaternions. This article is full of mathematical ingenuity and surprising discoveries, showcasing the beauty of mathematics and the joy of exploration.

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