I got an expected number of rounds around 1e6. It seems a bit high but I think it might be right. So if they want to be 100% they'll die of natural causes while waiting.
I wasn't on the forums 5 years ago but its certainly a good problem. On Mon, Sep 10, 2012 at 6:06 PM, Roger Hui <[email protected]>wrote: > V. good. > > A related question for the 100 Prisoners problem, is the expected > number of rounds before the prisoners go free, if each prisoner has > the same chance of being picked in each round. > > Did you solve the 88 Hats problem when it was posed here 5 years ago? > > > > On 9/10/12, Jordan Tirrell <[email protected]> wrote: > > 99 of the prisoners switch the light if and only if it is currently off > and > > they have not turned it on in a prior round. > > > > The one other prisoner turns the light bulb off every time time he finds > it > > on (otherwise leaves it off). He asserts the claim after he has turned it > > off 99 times. > > > > > > > > On Mon, Sep 10, 2012 at 11:55 AM, Roger Hui > > <[email protected]>wrote: > > > >> 100 prisoners are in solitary cells, unable to see, speak or communicate > >> in > >> any way from those solitary cells with each other. There's a central > >> living > >> room with one light bulb; the bulb is initially off. No prisoner can see > >> the light bulb from his own cell. Everyday, the warden picks a prisoner > >> at > >> random, and that prisoner goes to the central living room. While there, > >> the > >> prisoner can toggle the bulb if he wishes. Also, the prisoner has the > >> option of asserting the claim that all 100 prisoners have been to the > >> living room. If this assertion is false (that is, some prisoners still > >> haven't been to the living room), all 100 prisoners will be shot for > >> their > >> stupidity. However, if it is indeed true, all prisoners are set free. > >> Thus, > >> the assertion should only be made if the prisoner is 100% certain of its > >> validity. > >> > >> Before the random picking begins, the prisoners are allowed to get > >> together > >> to discuss a plan. So -- what plan should they agree on, so that > >> eventually, someone will make a correct assertion? > >> ____________________ > >> > >> Posed to me by Arthur Whitney at Iverson > >> College<https://sites.google.com/site/iversoncollege/>. > >> This puzzle resembles the 88 > >> Hats<http://www.jsoftware.com/papers/88hats.htm>puzzle but is (IMO) > >> easier. > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
