Give everyone a unique number during the planning phase. Have everyone scratch their number into the wall. Leave the light on.
When all numbers are on the wall, you are done.
When all numbers are on the wall, you are done.
The premise of the problem is very clear: How do you tally the presence of 100 unique events, some of which may repeat themselves, when you may use one and only one bit to register the state of the system?
Or use names, symbols, it doesn't matter. Just wait until there are 99 different ones on the wall.
Clearly, this would be a form of communication between the prisoners.
Reminds me of this:
http://blogs.msdn.com/b/ericlippert/archive/2011/02/14/what-...