>
> > So if the one R needs to visit the room again to catch up,
>
> To catch up? Catch up what?
To the condition that each one eventually visits any desired
number of times. I'm viewing the warden as actually trying to thwart
the strategy, with the one constraint being that condition.
...
> If the people are chosen randomly and go repeatedly to the room, then
> eventually
>
> > (We are trying for a guaranteed solution. A probabilistic one
> > is not good enough.)
>
> This is vague. Obviously, if the warden knew the strategy he could
> always thwart it if he wished. The warden must be assumed to be using
> a random-number generator to have any hope of having the problem be
> well-defined. And at random, eventually every R must see the B switch in
> the up and down position because X keeps getting chosen randomly to go
> in and flips B every time.
No. Contrast your solution with Alberto's, which is essentially
the one I found by googling. His will ALWAYS work, as long as all the
Rs
eventually visit twice and X (his M) keeps visiting.
Your solution is not guaranteed to terminate, but merely does
so with probability 1. (A clever warden could make things go on
forever.)
---David
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