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Re: Strings and numbers

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WJ wrote:

> Steve Graham wrote:
> 
> > 
> > http://programmingpraxis.com/2015/07/21/a-number-puzzle/#comments
> 
> 
> 
> >  Find a 10-digit number, with all digits unique, such that the first n
> >  digits of the number are divisible by n. For instance, in the 3-digit
> >  number 345, the 1-digit prefix, 3, is divisible by 1, the 2-digit
> >  prefix, 34, is divisible by 2, and the 3-digit prefix, 345, is
> >  divisible by 3.
> 
> Gauche Scheme:
> 
> (define (next divisor integer digits)
>   (filter-map
>     (lambda (d)
>       (let1 new-int (+ (* 10 integer) d)
>         (and (zero? (mod new-int divisor))
>              (list new-int (delete d digits)))))
>     digits))
> 
> 
> ;; Recursion.
> (let go ((divisor 1) (candidates (list (list 0 (iota 10)))))
>   (if (> divisor 10)
>     (caar candidates)
>     (go (+ divisor 1)
>         (append-map
>           (lambda (x) (apply next divisor x))
>           candidates))))
> 
> 3816547290

Ruby:

def next_digit( divisor, digits_so_far )
  number_so_far = digits_so_far.join.to_i * 10
  ((0..9).to_a - digits_so_far).select{|d|
    ((number_so_far + d).modulo divisor).zero? }.
    map{|d| digits_so_far + [d]}
end

candidates = [[]]
1.upto(10){|divisor|
  candidates = candidates.map{|digit_list|
    next_digit( divisor, digit_list) }.flatten(1) }
candidates

 ===>
[[3, 8, 1, 6, 5, 4, 7, 2, 9, 0]]

-- 
[Y]ou can never fix a decaying empire; the empire can only fall when the time
comes.  You cannot fix the empire by sending good and honest men to the capital,
because the simple logic of the system corrupts everyone along the way.
www.kolumbus.fi/aquilon/america-middle-class-and-the-end-of-growth.htm

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Strings and numbers Steve Graham <solitary.wanderer52@gmail.com> - 2015-08-03 13:24 -0700
  Re: Strings and numbers Julian Fondren <julian.fondren@gmail.com> - 2015-08-03 13:51 -0700
    Re: Strings and numbers "Rod Pemberton" <boo@fasdfrewar.cdm> - 2015-08-03 17:38 -0400
    Re: Strings and numbers Steve Graham <solitary.wanderer52@gmail.com> - 2015-08-03 14:44 -0700
  Re: Strings and numbers Paul Rubin <no.email@nospam.invalid> - 2015-08-03 20:59 -0700
    Re: Strings and numbers Steve Graham <solitary.wanderer52@gmail.com> - 2015-08-04 12:19 -0700
      Re: Strings and numbers "WJ" <w_a_x_man@yahoo.com> - 2015-08-07 09:29 +0000
        Re: Strings and numbers "WJ" <w_a_x_man@yahoo.com> - 2015-09-04 15:14 +0000
          Re: Strings and numbers "WJ" <w_a_x_man@yahoo.com> - 2015-09-07 19:34 +0000
            Re: Strings and numbers Julian Fondren <julian.fondren@gmail.com> - 2015-09-08 11:48 -0700
            Re: Strings and numbers Paul Rubin <no.email@nospam.invalid> - 2015-09-09 00:41 -0700
              Re: Strings and numbers Richard Todd <richard.wesley.todd@gmail.com> - 2015-09-10 00:32 -0700
                Re: Strings and numbers Richard Todd <richard.wesley.todd@gmail.com> - 2015-09-10 10:29 -0700
                Re: Strings and numbers Paul Rubin <no.email@nospam.invalid> - 2015-09-10 17:22 -0700
                Re: Strings and numbers Richard Todd <richard.wesley.todd@gmail.com> - 2015-09-10 21:34 -0700
                Re: Strings and numbers humptydumpty <ouatubi@gmail.com> - 2015-09-11 02:16 -0700
                Re: Strings and numbers humptydumpty <ouatubi@gmail.com> - 2015-09-11 07:33 -0700
                Re: Strings and numbers Paul Rubin <no.email@nospam.invalid> - 2015-09-13 00:12 -0700
                Re: Strings and numbers humptydumpty <ouatubi@gmail.com> - 2015-09-13 02:09 -0700
                Re: Strings and numbers Paul Rubin <no.email@nospam.invalid> - 2015-09-11 15:53 -0700
                Re: Strings and numbers Andrew Haley <andrew29@littlepinkcloud.invalid> - 2015-12-18 16:02 -0600
            Re: Strings and numbers "WJ" <w_a_x_man@yahoo.com> - 2015-09-12 23:38 +0000
              Re: Strings and numbers "WJ" <w_a_x_man@yahoo.com> - 2015-09-13 19:41 +0000
            Re: Strings and numbers "WJ" <w_a_x_man@yahoo.com> - 2015-11-29 18:09 +0000

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