The solution requires agents to abandon the attempt to solve for the "correct number" individually. Instead, they must adopt a convention—a pre-agreed mapping of value-to-bit. Whether through a "High/Low" threshold strategy or a "Popcount Parity" strategy, the agents succeed not by calculating the answer, but by agreeing on a language.
The computer uses a binary search algorithm to narrow down the possible range of numbers. It asks yes or no questions about the number's binary representation, effectively dividing the search space in half with each question. The computer continues to ask questions until it is able to guess the number correctly. 8.2.6 binary game
Think of a number between 1 and 255. I'll try to guess it by asking yes or no questions about its binary representation. Is the number's binary representation greater than 01111111? (y/n) y Is the number's binary representation greater than 10111111? (y/n) n Is the number's binary representation greater than 10011111? (y/n) y ... I'm going to take a guess: 150. Am I correct? (y/n) y Yay! I'm glad I was able to guess it correctly. The solution requires agents to abandon the attempt
low = 0 high = 255