Re^4: Multiple Combinatorics

[aartist]

Yes: if Group B (1..6) is subset of Group A(0..7) and Pick(B)=2 is equal to Pick(A)=2 then we apply 'b): pick nothing from larger group';

In this case, we still have picked 2 values from larger group automatically, which holds the initial condition. Only thing that '0' and '7' won't be picked at all in any resultset. ( from the given data).

[BrowserUk]

The only way to deal with this efficiently is to reduce the input sets to non-overlapping sets prior to permuting them.

To do that, you need to lay out the rules for overlapping sets. You'd need to define how to deal with:

1. One set completely overlaps another;
   1. the overlap is less than the number to be picked from the smaller group.
   2. The overlap is less than the number to be picked from the larger group.
   3. The overlap is equal to the number to picked from the smaller group.
   4. ...
2. There is only a partial overlap between the groups:
   1. The overlap is smaller than the number to be picked ....
   2. ...

Whence you've defined how all the possibilities should be resolved into distinct groups, the rest should be relatively easy.

I'm still bugged by your lack of explanation of what the purpose of this is?