I have 9 humanoid robots and each one has 9 parts. The 9 parts are:
3) Shoulders (counts as a pair)
4) Legs (counts as a pair)
5) Hand 1
6) Hand 1 duplicate (unattached)
7) Hand 2
8) Hand 2 duplicate (unattached)
1) Each robot's parts can be interchanged.
2) All parts can only connect to their designated areas as shown in the diagram. Meaning, the HEAD can only connect to the top of the BODY, the SHOULDERS can only connect to the upper BODY, the LEGS can only connect to the lower BODY, the BACK PACK can only connect to the back of the BODY, and HAND 1 and HAND 2 can only connect to either left or right SHOULDER.
3) Aside from each robot's spare duplicate hands, no other two parts are the same.
4) The HEAD, SHOULDERS, LEGS, and BACK PACK can only connect to the BODY. They cannot connect to other parts i.e. HEAD to HEAD, SHOULDERS to LEGS, etc.
5) HAND 1 and HAND 2 can only connect to the SHOULDERS. Each hand can connect to either to left shoulder or right.
6) The robot must always have all 7 parts intact. A robot cannot be incomplete
7) The robot can have two different HAND 1's or two different HAND 2's equipped.
8) Since each robot has a duplicate HAND 1 and HAND 2, the robot can have two same HAND 1's or two same HAND 2's.
9) In case a robot has two identical HANDS equipped i.e. two green hands or two purple hands or two other identical hands from another robot, interchanging them does not count as another combination.
10) Shoulders cannot be switched to the left or right.
PROBLEM: How do I solve for all possible combinations?