The Light Switch Problem

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.

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