Masyu: following the line
Once the first pearls are placed, the solve is a chain of small rules. Each one names a square or a pearl that has only one way left.
How it works
The hints on the Masyu page name these rules. Each one looks at a single square or pearl and the marks around it, and finds the only way the loop can go.
Two rules come from the loop itself. Every square has two lines or none, and there is only one loop. The rest come from the pearls: a white pearl goes straight, and a black pearl turns with two straight legs.
When nothing simple is left
Pick one open side and suppose the loop uses it. Follow these rules from there. If a square or a pearl breaks, the loop can’t use that side, so it is ×. The hints call this “Try both ways”. It is a proof by contradiction.
Worth memorizing
A square with two lines: its other sides are ×.
A dead end: a line with one way out takes it; an empty square with one open side is ×.
A line beside a white pearl runs straight through it.
A black pearl leg runs two squares straight, and the pearl never goes straight through.
A white pearl needs a turn right before it or right after it.
Never close the loop while a pearl or a line is left outside it.
Practice
0 of 3 rightThis black pearl’s leg goes left. Must the line carry on to column 1?
A line comes down into this white pearl. Must it leave downward?
The square at row 2, column 3 has two lines. Is its top side ×?