$$\bf \text{First problem }$$
100 thinking robots are given a challenge : they will communicate only by means of a single light bulb which can be either in the state 1 (light on) or in state 0 (light off). Each second a randomly chosen $$\bf ONE\quad single$$ robot can see the bulb (others don't- in that second) and keep it in the previous state or change it to opposite state. Bulb is On at first.
Each second one chosen randomly out of 100.
The challenge is to know -WHEN every one of them has been at the bulb at least once (or more) times.
This info has to reach all of 100 eventually.

Question

$$\bf \text{First problem }$$
100  thinking robots  are given a challenge : they will communicate only by means of a single light bulb which can be either in the state 1 (light on) or in state 0 (light off). Each second a randomly chosen  $$\bf ONE\quad single$$ robot can see the bulb (others don't- in that second) and keep it in the previous state or change it to opposite state.  Bulb is On at first.
Each second one chosen randomly out of 100.
The challenge is to know -WHEN every one of them has been at the bulb at least once (or more) times.
This info has to reach all of 100 eventually.

anonymous · Answer

Consider it given that there does occur a visit of each to the bulb. THIS IS NOT THE QUESTION !! 
The question is to communicate that event AFTER IT HAPPENNED JUST USING THE BULB !

anonymous · Answer

Thanks

anonymous · Answer

1st time the robot is chosen, turn off. After that, if they are chosen, turn it on. Count 100 turn-offs.