This is a clever and practical idea, in the sense of having Indiana Jones just shoot the guy with his pistol, instead of engaging in an elaborate sword fight, but it violates the spirit of the problem. If we solved all of our problems like this, we would kill the patients instead of curing the diseases.

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?

It depends on the disease, doesn't it? At this point (for some diseases) it's much more cost-effective to kill the patient that would have gone towards prolonging a state of suffering. Then send the funds towards Against Malaria or something else. ;-)

Heck, you don't even need to pick numbers in advance. Just pick a number the first time you go in the room, that isn't already on the wall.

Or use names, symbols, it doesn't matter. Just wait until there are 99 different ones on the wall.

"they won’t be able to communicate again until the game is over."

Clearly, this would be a form of communication between the prisoners.

So is the light.

Reminds me of this:

http://blogs.msdn.com/b/ericlippert/archive/2011/02/14/what-...

This is an amazing solution. Of course the light is needed or they couldn't see the wall!