Sixteen Bottles of Wine Riddle
7 days ago
- #combinatorics
- #binary
- #puzzle
- A prisoner must solve a riddle involving identifying the year of 16 unlabeled wine bottles using 4 measuring devices, each providing a binary output.
- Each device corresponds to a bit in the binary representation of the year, allowing the year to be deduced by converting the binary output to decimal.
- The challenge is to identify all 16 unique years in 50 measurements or fewer, leveraging the uniqueness constraint to reduce the required number of measurements.
- A divide-and-conquer strategy is proposed, starting with simpler cases (2, 4, and 8 bottles) and scaling up to 16 bottles, using 49 measurements.
- The solution involves inferring some measurements based on prior results, reducing the total number of required measurements.
- Alternative strategies, such as a greedy information gain approach, are mentioned but not explored in depth.
- The problem is compared to radix sort and raises questions about optimal strategies for larger numbers of bottles.
- Visualizations and probabilistic approaches are suggested for understanding the problem, though computational limits are noted.