This is a Trichain puzzle. The rules of Trichain are as follows:
- Numbers must be white, and match the size of their white islands.
- Each white island can only contain at most one number. Some white islands may have no numbers.
- Black squares must be part of L-trominoes.
- Black L-trominoes cannot be adjacent horizontally or vertically, but all of them must be connected diagonally. In other words, one standing on a black square must be able to visit any other black square via Chess King's moves, stepping on black squares only.
Here is an example Trichain puzzle, and its solution:
Here is the real Trichain. Go for it!