From: Ken Bloom <kbloom@...>
Date: 2007-04-09T03:40:07+09:00
Subject: Re: [QUIZ] Getting to 100 (#119)

On Mon, 09 Apr 2007 01:39:19 +0900, Christian Neukirchen wrote:

> =begin
>> The quiz, then, is to solve this problem without thinking, instead
>> letting the computer think for you.
> 
> I did not intent to seriously submit this solution, but it can be
> helpful as an example of how to use Ruby to solve a problem quickly
> without thinking too much or locating Knuth on the bookshelve. Writing
> this code took maybe ten minutes and happened step-by-step with checking
> the immediate results.
> 
> Since there are only 168 solutions (254 if you allow a sign before the
> first digit), brute-forcing is the simplest thing one can do. Additional
> operations can be added by changing the base and mapping the digits onto
> further operations.  (Different digit order is not that easy to
> implement and maybe be futile to do with brute-forcing.) =end
> 
> (00000000..'22222222'.to_i(3)).map { |x| x.to_s(3).rjust(8, "0").
>                                                    tr('012', '-+ ') }.
>   find_all { |x| x.count("-") == 2 and x.count("+") == 1 }.

A less ram-intensive version of this would swap the map and find_all 
calls as follows:

(00000000..'22222222'.to_i(3)).
  find_all { |x| x.to_s(3).count("0") == 2 and
		 x.to_s(3).count("1") == 1 }.
  map { |x| x.to_s(3).tr('012', '-+ ').rjust(8," ")}.

(It doesn't keep maintain references to the bad combinations of 
operators, allowing the GC to reclaim them earlier.)

> map { |x|
>     t = "1" + x.split(//).zip((2..9).to_a).join.delete(" ") [eval(t), t]
>   }.sort.each { |s, x|
>     puts "*****************" if s == 100
>     puts "#{x}: #{s}"
>     puts "*****************" if s == 100
>   }
> 
> __END__
> 
> 2#787<p4>lilith:~/mess/current$ ruby quiz119.rb |grep -C4 100$
> 123-456-7+89: -251
> 123+45-67-89: 12
> 123-45+67-89: 56
> *****************
> 123-45-67+89: 100
> *****************
> 12+345-67-89: 201
> 1-234+567-89: 245
> 1-23-456+789: 311
>

I like this answer a lot. Think you could generalize it to the extra 
credit?

-- 
Ken Bloom. PhD candidate. Linguistic Cognition Laboratory.
Department of Computer Science. Illinois Institute of Technology.
http://www.iit.edu/~kbloom1/