Puzzle Madness
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Nurikabe-An example

Here we will work our way through a Nurikabe example, please make sure you are familiar with and understand the rules first!
This is our starting grid. The very first thing we do is isolate all the squares with '1' in them, since we know these walls only have one square in them, all the square next to them must be black.
The other thing we can do straight away here is we can put in black squares to seperate any numbers next to each other diagonally, since we know two walls can't touch in this way.
The next thing we can do is look at the wall in the top-right with a '2' in it. We know this wall must contain two squares, and it can only expand upwards, so the square above it must be white. This wall is now complete, and we can now surround it with black squares.
We can now look at square A in this puzzle. If this square was white, it would cut off the square above it from the rest of the black squares, so square A must also be black.
Similarly, square A here must also be black, otherwise the square to it's right (and the one above that) would be cut off from the rest of the black squares.
One of the rules of Nurikabe is that you can't have a 2*2 square of black squares. To stop this from occuring, squares B and C must be white.
This completes this wall, so we can surround this wall with black squares.
This only leaves one direction for our '4' wall to expand, and that is to the left.
We now look at square D, this must be black, otherwise we're again going to have two seperate black sections isolated from each other.
Now look at square E. There isn't a wall that can reach this square (they are all too far away), so this square must be black.
To avoid seperating our two black sections, square F must also be black. Square F could be white by itself, but for square F to be white, square G would also have to be white, and that would break our rules.
To avoid having a 2*2 set of black squares, square G must be white.
We can now decide that squares H, I, and J must be black to connect the black squares above them to the rest of the black squares. We don't know exactly yet how they're going to connect, but we do know that for them to connect at all, these three squares must be black.
This means that our wall with 4 squares in it can only expand down to square K.
This completes our 4-wall, and means we can surround this wall with black squares.
The 2-wall in the bottom-left must expand upwards to stop us having a 2*2 set of black squares above it, so we can finish that section of the Nurikabe puzzle now.
There's only one way for our 3-wall to expand, and that is in to squares L and M, so these must be white.
This wall is now finished and we can surround it with black squares.
For the two seperate black sections to be joined, square N must be black.
This only leaves one way for us to finish the puzzle!
Finished!
This Nurikabe puzzle is actually one of our Daily Nurikabe puzzles, want to play now?
This is an example 7*7 grid, you can get much bigger grids than this, but generally the bigger the grid, the harder the puzzle is going to be. You're still applying the same set of rules, but it can get very complicated!