user> here's a cool puzzle. There are 16 light bulbs. Some are on, some are off. It's random. You must flip exactly one switch. You and a friend have agreed beforehand on a communication scheme. How many distinct messages is it possible to send?
deepseek-o3>
Alright, let's tackle this puzzle step by step. I'm going to think aloud as I work through the problem to understand how many distinct messages can be sent using the given setup.
We have:
- 16 light bulbs, each can be either on (1) or off (0). The initial state is random.