Star Slitherlink is a puzzle original of this blog to the best of my knowledge, based of nikoli’s Slitherlink.
Besides the usual Slitherlink that a cell can be either empty or contain a number, a cell can now contain a star or a cross. A numbered cell or a crossed cell doesn’t contain any star.
First, the loop never crosses itself, and no, the loop doesn’t branch. Not even touching itself at a point. A number tells how many loop segments (or blackened edges) are around that cell.
Next, each row and column contains a number of stars, determined by the puzzle. Stars may not be placed on a cell that contains a number of a cross, and the loop must contain all the stars.
Form a loop that satisfies all the above conditions.
Note that if the loop is identical but the stars are placed differently, it’s a different solution (and you should notify me of such).
Walkthrough for the example
First, get the most obvious thing first; R3C1 must be a star by its column.
See R1C2. The top is blank by R1C1, and the left is blank; otherwise, the loop will go to R1C1’s left, breaking the 0. So the bottom and the right sides must be passed for the 2 to be satisfied. This makes the left part go down (the only way).
To complete the 3, the lower part must go around the 3 down, then right, then up. This makes R4C2 not in the loop, so it can’t contain a star. This makes R4C3 to be a star, and thus must be within the loop…but we will deal with this later. Now, continuing the lower part, it must go right (otherwise it hits the loop), then down and right so that the star is within the loop. And oh, R2C2 is obviously a star, the only spot left.
Now, the upper part. It must go right (only way), then up (avoid 0), then right (only way), then right (to contain star), then down (only way), then down again (avoid 0), then down again (otherwise it’s stuck between 0 and 1), then down again (avoid 1), then right…and we have a loop.