The answer from hexomino is valid, but here is my attempt of solving this puzzle without backtracking.
For this solution, a misaki cell is considered as neither black or white.
I use two additional rules (which is derivable from those 6 rules):
- There is no sequence of black or misaki cells connected by edges or sides so that it either forms a loop or connects from side to side. (Because if it's all black, it effectively breaks a white cell network into two, and for every misaki cells, every possible placement of white cell near that misaki cells results in connecting the former cell and the latter cell with black cells)
- A black cells cannot have 3 black cells as the corner neighborhood unless it shares a side with a misaki cell, as it ensures 2x2 black cells.
- This configuration is impossible: (With _ is white and # is black or the edge of the level)
Alternatively, you can leave out the last 2 rules but it has to be replaced with short backtracking.
Here is my solution:
The first step is similar to hexomino's solution, with stopping numbered misaki cells from expanding to a direction that has either has not enough cells or forces the numbered misaki cell to read more cells than what the number says.
The misaki cell with is labelled with number 5 is forced to go down, so we expand there.
Look at the red cells
This violates additional rule #3, so we color it back
I also expanded the white cells when there is only one way to expand the white cells network
Look at the red lines
Those red lines are almost connected except for one cyan cell. These lines have to be broken as per additional rule #1
There is one extra white cell added just below the three white cells to avoid making the white cell above that added cell becoming a dead end. (Only misaki cells can be a dead end)
If we want to extend the cell with label "5", we see that it's impossible to extend north or east, so we extend it west.
The result is this:
This is similar to step 4, so no explanation is needed.
However, the next state changes drastically as the white expansion rule works most productively here.
Look at the two red cells, the topmost one violates the additional rule #2 if it's colored black, so it has to be white. The lower one violates the additional rule #3 if it's colored white, so it has to be black.
Note since white cells are not allowed to be a deadend except for misaki cells, we have to do expansion on it.
Probably you know this from playing other puzzle games like lights up. Basically, according to white expansion rule, at least one of the yellow cells has to be white. However, according to the misaki rule, there is only one white cell among the yellow and the red cells, so the red cells can't possibly be white, so we color it black
And an expansion rule as usual.
The last step is a straightforward additional rule #1 application.
After some expansion rule, the puzzle is finished.