Alberto Monteiro wrote:
>
> Chose one Prisoner, M, that will count something. The
> other prisioners are P2, P3, ... P23 (n = 23?)
>
> Each prisoner P_n must switch A from 1 to 0, but
> he must do it just _twice_.. After that, and when he
> finds A in 0, he will only switch B
>
> Prisoner M will switch A from 0 to 1 whenever possible
> [else he will switch B], and count how many times he
> does it. When he would do it the (2n)-th time, he will
> announce that everybody has entered the room.
>
Good, but I think you're slightly off on the count.
There are n-1 prisoners other than M. So once they have
all been in the room twice, M will come and see 2(n-1) 0's
for switch A from them. M might also have seen one more
0 if M were in the room first and switch A started that
way. So M should announce on seeing the (2n-2)th 0. That
is guaranteed to happen, and can't happen if one of the
P_i has never been in the room.
---David
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