Step 2 of 5
No branches, no traps
The path is one line. A cell with its links is closed, and a loop is never allowed.
The rule of thumb: The path is one line: no cell gets three links, and no cut can wall off cells the line can’t come back for.
Two quiet rules hold the whole puzzle together. First, no cell gets a third link: once a cell has both of its links, every other edge around it is out. Second, no loops: an edge that would join the two ends of the same stretch of path closes a circle, and the answer is one line, so that edge is out too.
Both rules work as eliminations, and eliminations are what make the joins from step 1 possible. Cross off the edges a finished cell can not use and its neighbors suddenly have fewer ways out. Cross off the edge that would close a loop and the stretch has to keep going somewhere else.
The first two practice boards lean on one rule each, and the third needs both together.
Where to look: Cells that just got their second link, and any stretch of path whose two ends sit side by side. Ask what each end can no longer do.
Worked example
A real position from a board that needs No branches, no traps. Purple ring: what the reasoning rests on. Grey line: links already known. Dashed: the edges in question. Green line: a link it proves. Red cross: an edge it rules out.
Branches and loops handled. Next: the four cells that decide themselves before you draw anything. Step 3: Corners commit →