Answer
The answer is as follows. 
Katrielle and the Millionaires' Conspiracy walkthrough
Puzzle Location: Grand entrance hall (The cat on the desk)
These ten cats need to be divided up into pairs, in accordance with the following rules:
1. There should be three pairs of cats of the same type - in other words, the same shape and colouring.
2. If a cat is wearing a ribbon, the other cat in the pair must also be wearing a ribbon.
Move the cats by sliding them to other cats' positions and swapping them over.
There are four cats wearing ribbons.
First sort these four cats into two pairs.
There needs to be three pairs of cats of the same type.
If there are four or more, it won't work.
Continuing on from hint two...
Now make another pair of the same type from the cats that are wearing ribbons.
There is also a pair who are not of the same type and neither is wearing a ribbon.
The answer is as follows.