The most elegant way to generate permutations in SQL server

Question

Given a the following table:

Index | Element
---------------
  1   |    A
  2   |    B
  3   |    C
  4   |    D

We want to generate all th

Answer 1

Just using SQL, without any code, you could do it if you can crowbar yourself another column into the table. Clearly you need to have one joined table for each of the values to be permuted.

with llb as (
  select 'A' as col,1 as cnt union 
  select 'B' as col,3 as cnt union 
  select 'C' as col,9 as cnt union 
  select 'D' as col,27 as cnt
) 
select a1.col,a2.col,a3.col,a4.col
from llb a1
cross join llb a2
cross join llb a3
cross join llb a4
where a1.cnt + a2.cnt + a3.cnt + a4.cnt = 40