[vox-tech] [OT] Binary Representation Challenge

[Micah J. Cowan]

On Tue, Sep 20, 2005 at 12:02:26PM -0700, Alex Mandel wrote:
> I realize this might be not be a challenge for some of you.
> --
> I need to make a list of all possible permutations given 9 options and 
> that you can choose any number of options at once.
> I've figured out using nCr statistics that this is 511 choices, but now 
> I need to represent them in 2^9 binary code: 000000001, 000000010 etc
> 
> Anyone got a quick way? I thought about writing a python code or 
> something but then I got confused just thinking about the algorthim.
> 
> Now the best would be if you had an idea that I could implement with my 
> limited toolset: R, OpenOffice, Python, and I guess I could add a 
> package to Cygwin if necessary.

Perhaps its simpler than you think?

If all you need is the different permutations of two-choice options, all
of which can be selected in any combination, then this is exactly the
same as counting in binary.

Or is it actually printing the representation of the binary that is
posing a problem?

FWIW, Knuth has recently published a couple of fascicles from Volume IV
of TAOCP; both of them dealing with "Generating all Tuples and
Permutations". I was stumped by how much there is to know about such a
seemingly simple subject.

-Micah