8.2.6 Binary — Game [2021]

If the target decimal is an odd number , the furthest bit to the right (the 1s column) must be 1. If it's even, it must be 0.

Therefore, we posit that the "8.2.6 Binary Game" is impossible to solve in a single, simultaneous move unless the strategy space is expanded to include multi-stage signaling. 8.2.6 binary game

If your target decimal is 131, look at the largest bit (128). Does 128 fit into 131? Yes. Turn that bit ON (1) . Subtract and Move On: If the target decimal is an odd number

If Agent A plays the parity of their popcount, and Agent B does the same: If your target decimal is 131, look at the largest bit (128)

if response == 'y': print("Yay! I'm glad I was able to guess it correctly.") break elif response == 'n': print("Oops! I was wrong. Better luck next time!") break else: print("Invalid input. Please enter 'y' or 'n'.")

To understand why the game is difficult, we must define the state of nature. Let the state space be $\Omega = (8,8), (8,2), (2,8), (6,2), \dots$.