I'm working on a solution using the current day (modulo the population) as a kind of covert channel to keep track of the number of prisoners who already visited

I'm working on a solution using the current day (modulo the population) as a kind of covert channel to keep track of the number of prisoners who already visited the room (the basic idea is that, if the light is on on day 64, at least 64 people have visited the room). I still have a bug in my algorithm and I'm not even sure it will really work.