Andreas, this is ALOT of work for a medium post. Cudos!

The part of your argument that I have trouble understanding are two:

• 1- instead of giving a probabilistic answer why not check every row, then you know for certain. right?
• 2- more to the point, once bob verified all groups it seems he knows a permutation of the real answer? that IS information on the solution.

So I can tell I don’t really understand what is going on here…