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
