Evil Combinatorialist and 16 Wines: An Information Theory Puzzle

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.