Person A will be the decider. They will only turn on the light when it is off.
Person B will only turn the light off if it is on once. All other times they do nothing.
Person C will do the same as Person B
Once Person A has turned the light on twice they can definitively claim all 3 have been in the room.
Three people are offered an opportunity. They will be brought at random and one at a time into a room that contains a simple light switch and a working light. Any of the three may be brought into this room multiple times, even multiple times in succession. If any one of the three is able at any time to correctly deduce that all three of them have been brought into this room, they will win 1 million dollars. If the deduction is incorrect, they will each have to pay $10,000. If they are allowed to meet and confer together before the random procedure begins, what plan will ensure they win the money and not run the risk of having to pay? Assume that the light is on at the beginning and that only the three people are allowed to flip the light switch.