Alternate Corners is part of the Loop Puzzle genre. Alternate Corners has an unclear origin. It goes under many names : Every Second Turn, Roundabouts, Intermediate Bend, and others that are similar. My best guess is that it was an entry in a puzzle contest at some point and it caught on.
With most loop puzzles, it’s usually a good idea to evaluate the border first. Since the loop must pass through every cell, all corners must have a bend, whether or not they contain a circle. In addition, all circles along the edge must have a line pointing toward the center of the grid, because every one of them is a corner.
Lines Between Circles
There are two basic things to watch for. First, look around your grid for bends outside of circles. Initially, this will probably be in a corner that doesn’t contain a circle. because a line only bends one time between circles, the ends must travel straight until the next circle they touch.
Next, look for a line approaching a cluster of circles that are close together. Has it turned yet? If not, then you know that it must do so before reaching a circle.
Forced Exits
Every line you place acts as a wall for adjacent cells. Eventually, those walls will close off two sides of a cell. Because our loop has to travel through every cell, that means the remaining two sides must be exit points for that cell. Sometimes that means the cell contains a straight line, and sometimes it means a new corner. So when a cell only has two exit points remaining, you can safely draw in the line to fit.
Double-Bends, Loops, and Branches
As you solve, pay attention to potential illegal placements. Remember, a line may only turn one time between circles, and the line of the loop may not create any separate loop or branch. That is, a cell will never have more than 2 exit points. If it helps, place a small X on cell borders where you can’t place a valid line.
Solving the Puzzle
As you can see, Alternate Corners is one of the more simple loop puzzles. Basically, as long as you avoid creating loops, branches, or double-bends, it’s pretty straightforward. After you get the hang of it, you’ll be ready to try a more difficult loop puzzle, such as Masyu. Now, let’s solve the 10×10 example puzzle.
Create a single closed loop which passes through all the circles, but not necessarily all the cells, without crossing itself or branching. Black and white circles have different rules about how the line of the loop passes through them.