I got 6 7850's, and I tried to put them all on one mobo using unpowered riser cables.  I'm running Xubuntu 12.04, cgminer 3.0.0, Catalyst 12.08.  The motherboard is a GIGABYTE FM2 AMD A85X with 3 PCI-E x1 slots and 3 PCI-E x16 slots.  I'll provide links.

http://www.newegg.com/Product/Product.aspx?Item=N82E16813128566
http://www.newegg.com/Product/Product.aspx?Item=N82E16814202004

Here are my results

0  (x1)  Yes
1  (x16) Yes
2  (x1)  No
3  (x1)  Does not even show up
4  (x16) Yes
5  (x16) Yes

So I disconnected the #2 and #3 cards, and this is what happened

0  (x1)  Yes
1  (x16) Yes
2  (x16) No
3  (x16) No

So I have no idea what I'm doing wrong.  I was using 2 750w power supplies.  If there is some trick to making this work, I would really like to know, but for the time being I'm going back to using 3 cards per board. 

Thoughts and comments, are very much appreciated.