In the story in the novel the maid is overheard by the husband as saying to another maid: let me clean one of the two empty rooms on floor four, while the couple are in their usual room.Age wrote: ↑Thu Sep 05, 2019 5:01 pmIn this scenario the maid KNOWS where the empty room is or rooms are. But the probability still remains the same and is NOT higher like in the game show scenario. When the maid goes into one room there is NO reason for the husband to change rooms because the probability of his wife being in the other room is NOT higher. The maid MIGHT KNOW if the other room is empty or not. But, the husband does NOT know if the maid KNOWS. Whereas, the contestant KNOWS that the game show host does KNOW which box contains the prize.duszek wrote: ↑Wed Sep 04, 2019 5:43 pmMick, I have an idea.
If wrong boxes or rooms open themselves then the room picked at first could also open itself and thus reduce the chances to 50 to 50 for the remaining two ones.
The show master opens an empty box leaving out the first choice.
That´s why the mathematician in the novel tried to improve the story this way:
The jealous husband hears two maids talking about cleaning the empty rooms on the floor in question. The husband stands at the room chosen by him (pretending that either he is a friend of the adulterous couple or he got the room and wants to check in himself).
The maid comes, passes "his" room and goes to one of the other two.
Now, can the maid replace the show master ? By a trick she was made to omit the room chosen by the husband and she goes to one of the empty ones or the only empty one.
So the husband knows that the maid knows.
One slight problem is that if a room is not clean and a guest would like to get into it the maid would not just pass but would tell him to go back to the reception desk and ask for another key.
So instead of cleaning the room it would have to be something a maid can do in a clean empty room that does not prevent a new guest from going into it.