Solution to Puzzle Number 10

I meant to post this yesterday, but I ended up getting delayed due to some unknown blogging error that would not let me upload images. Here is the solution to Puzzle Number 10: Tetris Shape Reconstruction. In the puzzle, I asked if there existed a unique colour assignment linking each of the given colours to one of the Tetris shapes for the following image:

To be entirely honest, I had originally intended there to be a solution. However, after posting the image I realised there was not, and the puzzle therefore ended up a little sneakier than I had originally intended. Robert and Scott both successfully spotted my sneakiness, while Paul fell for my (unintended) trap and successfully mapped all the shapes without realising that red could not be mapped to only the J or L shape. Sarah had intended to answer the puzzle, but I accidentally spoiled the answer for her before she even had a chance to give it a go.

One can quickly see that Green = I and Orange = T due to the isolated shapes in the bottom left. Likewise, it is clear that Purple = O and the blue at the top means Blue = J. Since I has already been mapped, one can rest assured that Yellow = Z, which leaves only two shapes and two colours. Cyan = S is a valid mapping, but Red needs to be both J and L in order to create the left-most red area. Due to the inconsistent chirality of the red shape, there is no possible mapping to the Tetris shapes.