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Very Difficult Logic Problems
There are 100 prisoners.

Tue Aug 30, 2016 4:50 am  by tartle

There are 100 prisoners. At random times one prisoner is chosen uniformly at random and led into a room with a single lamp. The prisoner can choose to switch it on or off or leave it as the last visiting prisoner left it. Apart from the state of the lamp he must leave the room unchanged.
After visiting the room, each prisoner is asked if every prisoner has visited the room by now. If he answers 'Yes' and indeed everyone has been to the room at least once, then everybody is freed immediately. Otherwise they are all executed ;) He can answer 'I don't know' without any consequences.
Apart from the lamp being on or off the prisoners have no way of communication at all, but of course as is customary in such puzzles they can plot a strategy in advance and everybody is a perfect logician.
Tue Sep 06, 2016 7:01 pm  by jatekchhateja@

During the strategy time, they assign a leader. Only the leader can ever answer the question as yes, everybody else will say no, always.

Now, everytime a prisoner(other than the leader) goes into the room, he'll switch on the light provided he hasn't done so once already.
If the light is on, he'll simply come back and wait for the next turn. If he has switched on the light once in the past, then he'll again walk back without altering the state of the light.

Everytime the leader goes into the room, he'll switch the light off if it's on, or else come back without doing anything.

Once the leader switches off the light 99 times, everybody would have visited the room with the lamp/light at least once.

PS: This is based on the assumption that the light is initially known to be off. If the initial state of the light Is unknown, the solution will be slightly different, but the logic will be same. Give this a try too.
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