Logic Masters Deutschland e.V.

Shade some cells according to the following rules :

• Black cells must no be orthogonally adjacent.
• Cells with numbers can be blackened.
• A number in a white field indicates the number of black fields in the corresponding direction.
• A number in a black field is irrelevant and does not necessarily indicate the correct number of black fields.
• All white cells must form a single orthogonally connected area. Example :
  

  Since I wasn't able to find numerous puzzles of this type nor a complete guide on how to solve them, here is a puzzle by Mokuani and how to solve it. (The real puzzle is at the bottom)

  

  First of all, consider the following : The 3 in the last column is an impossible value for the cells it is pointing. These "impossible" values should be tracked down as it's generally the first step to solve such puzzles.

  

  After marking the neighbouring cells as white, we get some white fields with numbers. As they are the strict maximum of black cells and can only be filled in one way, we can fill those in.

  

  Repeating the same procces should get you here.

  

  Let's take a look at another rule : "All white cells must form a single orthogonally connected area". At this point in the puzzle, even if we cannot go further with the numbers, we can rule out squares that would break this rule.

  

  Now, take a look at column 2. The last number is pointing at only 1 black square and withe cells. As such, it cannot be fulfilled and can be blackened.

  

  Following the rules aforementionned, we get to this point.

  

  Here is now a trick I call ladders. You can see that the 2s in column 6 will have to alternate between black and white. Here are the two possibilities :

  

  But using the first configuration will create two separate white fields :

  

  Thus only the second way of filling the black squares works. This is a very useful tip to avoid getting stuck when you believe there are multiple solutions. Let's write that down.

  

  Using the same "ladder" principle you can fill the last 6 black squares. You solved the puzzle !

  

  The following puzzle uses another 2 tricks for solving (one when starting), although they can be omitted by working through contradictions.

  

  You can use pvz.jp for solving it on your browser (left click for black, right for green).