The balls are connected in pairs by lines. Every line makes a fixed number of turns, and all cells are used by the lines. Next to the puzzle a small figure indicates how many turns each line makes. We will solve a small puzzle of this type as example.
Three of the four corners of this puzzle are empty squares. Because every square of the puzzle has to be used, we can draw two line segments from each of them. From the upper left corner, we can not draw a line downwards, because then we connect two balls with a line that has no corners at all, so we draw a line segment to the right instead.
The line originating from the uppermost ball in the rightmost column already makes one turn. It has to make one other turn and then exactly run into another ball. This can be done in only one way, to the ball directly to the left of it.
The ball in the upper left could be connected with the ball directly below it, but then the other two balls can not be connected with just two turns while all squares are used. The lowest ball in the rightmost column can not be reached, so only the lowest ball in the third column remains. Now we can also connect the last two balls and the puzzle is finished.