To me, all the description points to a somehow binary counting… if they can move 1 switch at a time it means they can count 01, 11, 10, 00 over and over again, I think the key is the number of prisoners “23” because then there must be a way to find out a match between the counting of the switches with the counting of the prisioners multiplied by X number of repetitions (remember the end is when each prisioner visited the room as many times as everyone else) it means it can be 23, 46, 69, 92… and so on.
I will keep trying to figure out how to do it :-D
remember the end is when each prisioner visited the room as many times as everyone else
No — the end comes when any prisoner claims to be able to tell that they’ve all visited at least once. If prisoner A visits the room five times in a row, followed by prisoners B through W, once each in any order, and one of the prisoners announces that they’ve all visited, they win.
The description does suggest some sort of binary coding with the switches, but with only two switches, you can only encode four states, which certainly doesn’t seem like enough to discern when all 23 prisoners have visited the room.
Another complicating factor is that the switch state is required to change on each visit. Prisoners aren’t allowed to not change them.
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