Is this euler 121? On Wed, Oct 19, 2011 at 6:24 PM, David Vaughan <[email protected] > wrote:
> Thanks, this was the method I had envisaged. I wasn't thinking about it in > the J way originally - this is something I'm trying to work on. > > On 19 Oct 2011, at 20:21, Marshall Lochbaum wrote: > > > Sorry--a few off-by-one errors. Here's code that gives you the correct > > result: > > p =. 4 :'(+/ */"1 >: y comb x) % (!>:x)' > > 4x p"0 i.>.-:4 > > 1r120 1r12 > > +/ 4x p"0 i.>.-:4 > > 11r120 > > > > Marshall > > > > On Wed, Oct 19, 2011 at 12:38 PM, David Vaughan < > > [email protected]> wrote: > > > >> Ignore the domain error thing that was just one of my usual careless > >> mistakes. > >> > >> But even so, the result is not right. > >> > >> (i.<.-:<:4) p 4 > >> 1r120 > >> (>:i.<.-:<:4) p 4 > >> 1r20 > >> > >> On 19 Oct 2011, at 17:03, Marshall Lochbaum wrote: > >> > >>> The number of ways to choose k red balls is the sum over all > combinations > >> of > >>> bags of the probability you draw a red ball from each of those bags, > >>> multiplied by the number of ways to choose the red balls, which is 1. > So, > >> I > >>> suggest you find one of the various comb verbs running around, and then > >>> something like > >>> (+/ */"1 k comb n) % (!>:n) > >>> will give you that probability. Then make this into a verb dependent on > >> k, > >>> apply it with rank zero to (i.<.-:<:n), and add those results up. > >>> > >>> Marshall > >>> > >>> On Wed, Oct 19, 2011 at 11:09 AM, David Vaughan < > >>> [email protected]> wrote: > >>> > >>>> That was untested - hence errors. > >>>> > >>>> If r and b are two choices, and you start with a bag containing r,b > and > >>>> after each turn where you take one item from the bag you add another > r. > >> The > >>>> goal is to find the probability of choosing more b's than r's. As I > >> probably > >>>> haven't explained well, here's an example: > >>>> > >>>> b,r - take b, return it and add another r > >>>> b,r,r - take r, return it and add another r > >>>> b,r,r,r - take b, return it. > >>>> > >>>> In this case there were 3 turns, and 2 b's were chosen vs 1 r, so that > >> is a > >>>> success. The probability of taking more b's than r's is the > probability > >> of > >>>> taking 3 b's = %24 plus the probability of taking 2 b's and 1 r = > >> 24%~1+2+3 > >>>> which gives 7r24. Though I'm not actually sure my idea for the general > >> case > >>>> is totally correct. > >>>> > >>>> On 19 Oct 2011, at 15:48, Marshall Lochbaum wrote: > >>>> > >>>>> The correct way is to compute all the terms in the expression and > then > >>>>> multiply them together. Something like > >>>>> n* > *&.>/ >:@i.&.> n->:i.k > >>>>> However, the expressions you gave will return length errors, since > >>>> (>:i.n-2) > >>>>> is patently not the same length as (>:i.n-1). What exactly are you > >> trying > >>>> to > >>>>> compute? > >>>>> > >>>>> Marshall > >>>>> > >>>>> On Wed, Oct 19, 2011 at 10:39 AM, David Vaughan < > >>>>> [email protected]> wrote: > >>>>> > >>>>>> I couldn't really think of an appropriate title for this. My issue > is > >>>> that > >>>>>> I want to compute an expression that has a different number of terms > >>>>>> depending on y. > >>>>>> > >>>>>> +/(>:i.n-1)*n NB. for all n, y >: n > 1 > >>>>>> +/(>:i.n-2)*(>:i.n-1)*n NB. for all n, y >: n > 2 > >>>>>> > >>>>>> and so on, so that: > >>>>>> > >>>>>> lim =. <:<.y%2 > >>>>>> > >>>>>> and we carry on the style of expression above until we are doing it > >> for > >>>> all > >>>>>> n, y >: n > lim. > >>>>>> > >>>>>> So in the case for y=.5, lim=.1 and we only do the first of the > lines > >>>>>> above. For y=.7, we would do the second one as well. For y=.9 we > would > >>>> do > >>>>>> the same as the second but with a (>:i.n-3) multiplied with it all > as > >>>> well. > >>>>>> I guess/hope there is some way of achieving this with power? > >>>>>> > ---------------------------------------------------------------------- > >>>>>> 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 > >> > >> ---------------------------------------------------------------------- > >> 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 > -- Of course I can ride in the carpool lane, officer. Jesus is my constant companion. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
