Festina lente, sed festina.
> -----Oorspronkelijk bericht-----
> Van: Programming <programming-boun...@forums.jsoftware.com>
> Namens 'Mike Day' via Programming
> Verzonden: zondag 27 oktober 2019 17:50
> Aan: programm...@jsoftware.com
> Onderwerp: Re: [Jprogramming] Quora problem
>
> Thanks. I haven’t got time for a considered reply right now. Might get round
> to it tomorrow afternoon.
>
> Cheers,
>
> Mike
>
> Sent from my iPad
>
> > On 27 Oct 2019, at 12:01, R.E. Boss <r.e.b...@outlook.com> wrote:
> >
> > I don't think your S3 is overkill, actually it simplifies the
> > prefixes-suffixes
> machinery.
> >
> > ;<@(2018 (#-1+I.)@e.~ (-~{:))\ 6%~ (* (>: * >:@+:)) i.>.%:2018
> > 12
> >
> > /:~;(3 : '<@(y |:@(](#~,: (#-1+I.)@])e.~) (-~{:))\ 6%~ (* (>:*
> > >:@+:)) i.>.%:>./y')2019+i:50
> > 1969 11
> > 1985 2
> > 2010 5
> > 2018 12
> > 2025 1
> > 2030 3
> > 2030 4
> > 2051 7
> > 2054 13
> >
> >
> > R.E. Boss
> >
> >
> >> -----Oorspronkelijk bericht-----
> >> Van: Programming <programming-boun...@forums.jsoftware.com>
> >> Namens 'Mike Day' via Programming
> >> Verzonden: donderdag 24 oktober 2019 11:08
> >> Aan: programm...@jsoftware.com
> >> Onderwerp: Re: [Jprogramming] Quora problem
> >>
> >> (I see RE Boss has just posted, while I was drafting - sorry if it's
> >> the
> >> same!)
> >>
> >> I thought to exploit the property that
> >> S3(n) = sum i^2, i <: n, is n(n+1)(2n+1)%6 but solving S(n) - S(m) =
> >> 2018 isn't that easy!
> >> Anyway, we could define
> >> S3 =: 6 <.@%~ (* (>: * >:@+:)) but as we need a string of
> >> squares it's overkill.
> >> Either way, it's useful to be able to identify the indices of ones
> >> in a boolean
> >> matrix:
> >> ixbin =: $#.inv I.@,
> >>
> >> So we get, accprding to taste:
> >>
> >> -/"1 ixbin 2018 = -/~ +/\ *: i. >: 20
> >> 12
> >> -/"1 ixbin 2018 = -/~ S3 i. 20 NB. not as efficient as it looks!
> >> 12
> >>
> >>
> >> ts'-/"1 ixbin 2018 = -/~ S3 i. 20'
> >> 1.53e_5 8768
> >> ts'-/"1 ixbin 2018 = -/~ +/\ *: i. >: 20'
> >> 8.7e_6 9856
> >>
> >> MIke
> >>
> >>
> >>
> >>
> >>> On 24/10/2019 07:36, Skip Cave wrote:
> >>> I occasionally try to solve Quora math problems to polish my J skills.
> >>> Here's a problem that
> >>>
> >>> * "The integer 2018 can be written uniquely as the sum of
> >>> consecutive squared integers. How many squares does the sum
> >>> contain?"*
> >>>
> >>> a=.2^~i.100
> >>>
> >>> NB. Find how many consecutive squared integers it takes to sum to
> >>> 2018. Try each length until I get a hit.
> >>>
> >>> +/2018=+/"1]5,\a
> >>>
> >>> 0
> >>>
> >>> +/2018=+/"1]6,\a
> >>>
> >>> 0
> >>>
> >>> +/2018=+/"1]7,\a
> >>>
> >>> 0
> >>>
> >>> +/2018=+/"1]8,\a
> >>>
> >>> 0
> >>>
> >>> +/2018=+/"1]9,\a
> >>>
> >>> 0
> >>>
> >>> +/2018=+/"1]10,\a
> >>>
> >>> 0
> >>>
> >>> +/2018=+/"1]11,\a
> >>>
> >>> 0
> >>>
> >>> +/2018=+/"1]12,\a
> >>>
> >>> 1 NB. A hit!
> >>>
> >>> +/2018=+/"1]13,\a
> >>>
> >>> 0
> >>>
> >>>
> >>> So the answer is 12
> >>>
> >>> List them:
> >>>
> >>> b#~2018=+/"1 b=.12,\a
> >>>
> >>> 49 64 81 100 121 144 169 196 225 256 289 324
> >>>
> >>>
> >>> Is there a way to do this search without explicit looping?
> >>>
> >>>
> >>> Skip
> >>>
> >>>
> >>> Skip Cave
> >>> Cave Consulting LLC
> >>> --------------------------------------------------------------------
> >>> --
> >>> For information about J forums see
> >> http://www.jsoftware.com/forums.htm
> >>
> >>
> >>
> >> --
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