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-   -   Ruby solve classic math problem: make 56 from four 4s (http://www.velocityreviews.com/forums/t862281-ruby-solve-classic-math-problem-make-56-from-four-4s.html)

Kelly Jones 03-31-2010 09:11 PM

Ruby solve classic math problem: make 56 from four 4s
 
A classic math problem asks "using only four 4s and any
mathematical operation, come up with the number
56". "4!+4!+4+4" is one of probably several answers [1].

I want to write a ruby program that solves the
generalization: "given X number of the digit Y and a
set of permitted mathematical operations/functions, can
you come up with the number Z?"

Has anyone already done this?

[1] http://mathforum.org/ruth/four4s.puzzle.html

--
We're just a Bunch Of Regular Guys, a collective group that's trying
to understand and assimilate technology. We feel that resistance to
new ideas and technology is unwise and ultimately futile.


Michael Fellinger 04-01-2010 11:49 AM

Re: Ruby solve classic math problem: make 56 from four 4s
 
On Thu, Apr 1, 2010 at 6:11 AM, Kelly Jones <kelly.terry.jones@gmail.com> wrote:
> A classic math problem asks "using only four 4s and any
> mathematical operation, come up with the number
> 56". "4!+4!+4+4" is one of probably several answers [1].
>
> I want to write a ruby program that solves the
> generalization: "given X number of the digit Y and a
> set of permitted mathematical operations/functions, can
> you come up with the number Z?"
>
> Has anyone already done this?
>
> [1] http://mathforum.org/ruth/four4s.puzzle.html


The first thing that came to mind was http://www.rubyquiz.com/quiz60.html
Not exactly what you want, but still good reading :)

> --
> We're just a Bunch Of Regular Guys, a collective group that's trying
> to understand and assimilate technology. We feel that resistance to
> new ideas and technology is unwise and ultimately futile.



--
Michael Fellinger
CTO, The Rubyists, LLC


Robert Klemme 04-01-2010 12:56 PM

Re: Ruby solve classic math problem: make 56 from four 4s
 
2010/3/31 Kelly Jones <kelly.terry.jones@gmail.com>:
> A classic math problem asks "using only four 4s and any
> mathematical operation, come up with the number
> 56". "4!+4!+4+4" is one of probably several answers [1].
>
> I want to write a ruby program that solves the
> generalization: "given X number of the digit Y and a
> set of permitted mathematical operations/functions, can
> you come up with the number Z?"


As long as you do not limit the number of unary operations that
program is not guaranteed to terminate - especially if there is no
solution for given X, Y and Z. Am I missing something?

It should be interesting to see what solution strategy you are picking.

Kind regards

robert

--
remember.guy do |as, often| as.you_can - without end
http://blog.rubybestpractices.com/


Brian Candler 04-01-2010 02:12 PM

Re: Ruby solve classic math problem: make 56 from four 4s
 
Michael Fellinger wrote:
> The first thing that came to mind was
> http://www.rubyquiz.com/quiz60.html
> Not exactly what you want, but still good reading :)


Even closer is this one:
http://www.rubyquiz.com/quiz7.html
--
Posted via http://www.ruby-forum.com/.


Kelly Jones 04-01-2010 05:31 PM

Re: Ruby solve classic math problem: make 56 from four 4s
 
On 4/1/10, Robert Klemme <shortcutter@googlemail.com> wrote:
> 2010/3/31 Kelly Jones <kelly.terry.jones@gmail.com>:
>> A classic math problem asks "using only four 4s and any
>> mathematical operation, come up with the number
>> 56". "4!+4!+4+4" is one of probably several answers [1].
>>
>> I want to write a ruby program that solves the
>> generalization: "given X number of the digit Y and a
>> set of permitted mathematical operations/functions, can
>> you come up with the number Z?"

>
> As long as you do not limit the number of unary operations that
> program is not guaranteed to terminate - especially if there is no
> solution for given X, Y and Z. Am I missing something?
>
> It should be interesting to see what solution strategy you are picking.


Thanks, and thanks to everyone else who replied.

You're right: I hadn't thought of this.

If I start with 4 and allow sqrt, I get sqrt(4),
sqrt(sqrt(4)), sqrt(sqrt(sqrt(4))) and so on. Of
course, these aren't integers after the first sqrt, but
they could theoretically combine with other 4
combinations later to form an integer.

I incorrectly thought one iteration of a unary operator would suffice.

I originally got interested in this problem because I
thought factorial was a cheat. Some of the solutions on
http://mathforum.org/ruth/four4s.puzzle.html use the
gamma function, integer 4th root, etc. Where do you
draw the line? If you allow constant functions (eg,
f(x) = 56), the solution is trivial.

My new goal is to solve the simpler problem, very
similar to http://www.rubyquiz.com/quiz7.html (thanks,
Brian!).

Given X copies of the digit Y and the 5 mathematical
operators plus, minus, multiply, divide, and exponent,
along with concatenation and decimals (see below), can
you construct the number Z?

My approach for 5 copies of the digit 7 (example):

% With one 7, you have {7, 0.7} (the latter because we
allow decimals-- but not 0.07)

% With two 7s, we union two sets:

% {77, 7.7, .77} (from decimals and concatenation)

% Apply + - * / ^ to every ordered pair of elements
in the resultset for one 7 (including "pairs" like
{7,7}). Not showing the results, but you get the
idea.

% We then recurse. For n 7s, we union:

% {777...[n times], 777...[n-1 times].7, 777...[n-2 times].77, etc}

% Applying + - * / ^ to every ordered pair of the
resultset for n-1.

It might still be interesting to create a website that does this.

--
We're just a Bunch Of Regular Guys, a collective group that's trying
to understand and assimilate technology. We feel that resistance to
new ideas and technology is unwise and ultimately futile.



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