This text discusses a classic puzzle involving a chessboard with 64 squares and coins on them. The puzzle is about finding a way for two prisoners to communicate the location of a hidden key by flipping only one coin before leaving the room. The author explores various strategies and their connections to error correction in computer science. The text also delves into the concept of coloring the corners of a high-dimensional cube to represent possible strategies and concludes by showing that certain strategies are impossible in three dimensions and beyond.
Here are the key facts extracted from the text:
1. The puzzle involves a chessboard with 64 squares, each with a coin on it.
2. Prisoners are offered a chance for freedom by solving a scheme related to the coins and a hidden key.
3. The prisoners can only flip one coin before leaving the room.
4. The goal is for both prisoners to know the key's location.
5. The warden can listen to their strategy and arrange the coins to thwart it.
6. The author first heard about this puzzle during a dinner conversation at a wedding.
7. The author explored two interesting rabbit holes related to the puzzle.
8. One rabbit hole involved proving the puzzle's impossibility in certain setups.
9. The other rabbit hole connected the puzzle to error correction and Hamming codes.
10. The puzzle's strategies can be visualized using the coloring of corners in a high-dimensional cube.
11. Strategies involve assigning colors to vertices of the cube.
12. Strategies aim to ensure that prisoners can always communicate the key's location with one coin flip.
13. The puzzle's complexity is related to combinatorial questions and coding theory.
14. The puzzle cannot be solved in three dimensions if there isn't a power of two.