The rules of Yajilin
Yajilin — ヤジリン — or Arrow Ring is a loop puzzle.
- Shade some empty cells black. Black cells never share an edge, though they may touch at corners.
- Draw one closed loop through the centre of every cell that is neither black nor an arrow. The loop turns only at right angles and never crosses or touches itself.
- An arrow counts the black cells in that direction, to the edge of the grid. Other arrow cells neither block that count nor add to it.
- Arrow cells are never black, and the loop cannot pass through them. Some black cells are counted by no arrow at all.
How to solve one
Fill in around a black cell
Black cells never share an edge, so the four cells touching a black cell are all on the loop.
Count what an arrow can hold
Black cells cannot touch, so a run of L undecided cells holds at most half of them, rounded up. If an arrow needs exactly that many, they can only sit in alternate cells.
A cell with nowhere to go is black
The loop enters and leaves every cell it visits. A cell with fewer than two open sides cannot be on the loop, so it is black.
One line in means two
A cell with a line into it is on the loop and needs a second line out. If only one other side is open, that line is forced.
Do not close the loop early
Joining two ends that already connect closes a ring. That is only allowed on the last move, when no cell is left outside it.
Count the colours
The grid is a chequerboard and a closed loop alternates between the two colours, so it visits the same number of each. A 9×9 has one more cell of one colour, so exactly one more of that colour stays off the loop.