# A puzzle for Pythonistas

Alan James Salmoni alan_salmoni at yahoo.com
Fri Jan 31 13:59:17 CET 2003

```Hi folks,

This is just a little puzzle to test your brains on - well, I should
come clean really, so what I need to do is work out a way to get all
the interactions from 2 or more variables for SalStat a small
statistics package, but to be honest, I am rather stuck on this bit.

The problem is defined like this: I have a list of unique integers,
and the list is of arbitrary length, though 2 elements is the minimum.
Using each integer only once, what are the possible combinations of 2
or more elements that can be derived from this list. I know how to
work out how many combinations there are: ((2**len(list))-1-len(list))
which is quite simple.

To illustrate:

If list = [1,2,3], then there are 4 possible combination: 1-2, 1-3,
2-3, and 1-2-3.
If list = [1,2,3,4] then there are 11 possible combinations: 1-2, 1-3,
1-4, 2-3, 2-4, 3-4, 1-2-3, 1-2-4, 1-3-4, 2-3-4, and 1-2-3-4.

All my ideas so far rely on brute force, and I was wondering if anyone
could think of an elegant and pythonic way of achieving the required
result.

I have a nasty feeling that the code may be complex, so feel free to
tell me to s0d off if you want! :)

Alan James Salmoni
SalStat Statistics
http://salstat.sunsite.dk

```

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