How did you get on trying to tile the floor, any luck?
Secure data store B71 Floor Plan (STRAP)
I will be more than a little surprised if you managed it. Click on the triangle below to see why!
Solution
The solution is a lovely invariant. Colour the grid diagonally with three colours according to row + column modulo 3. Every horizontal or vertical 1×3 panel necessarily covers exactly one square of each colour. A complete tiling with eleven panels would therefore have to cover 11 squares of each colour.
Before the plinths are removed, the 6×6 board contains 12 squares of each colour. Our three plinths occupy two squares of one colour and one of another, leaving colour totals of
10 yellow; 11 red; 12 blue
Those cannot possibly be covered by eleven panels each using one of every colour.
So the floor cannot be tiled, despite both the total area and the panel count working perfectly.