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?