You need the random draw to pick a prisoner who hasn't been, and then for the random draw to pick the designated "counter" prisoner.
On Tue, Sep 11, 2012 at 7:52 AM, Skip Cave <[email protected]> wrote: > Jordan > > I think 1e6 is much too high. The problem seems to be equivalent to drawing > from a bag of 100 uniquely-numbered balls (0-99) with replacement. Then the > question is: how many draws on average does it take to see every number? > > A quick modelling of this process: > > $~.?100$100 NB. how many unique balls in 100 random draws, with > replacement ? > 65 > $~.?100$100 NB. Try a couple more times. > 63 > $~.?100$100 > 62 > $~.?300$100 NB. Try 300 draws with replacement. > 94 > $~.?300$100 > 99 > $~.?300$100 > 92 > $~.?500$100 NB. Try 500 draws with replacement. > 98 > $~.?500$100 > 100 > $~.?500$100 > 97 > $~.?500$100 > 100 > $~.?700$100 NB. Try 700 draws with replacement. > 100 > $~.?700$100 > 100 > $~.?700$100 > 100 > > So it looks like making somewhere around 500 random draws on average, will > let the drawer see all 100 numbers. So it will typically be a couple of > years before the prisoners can be sure of their fate. > > Skip > > > On Mon, Sep 10, 2012 at 10:32 PM, Jordan Tirrell <[email protected] > >wrote: > > > 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? > > > > > > -- > Skip Cave > Cave Consulting LLC > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
