Yajilin Rules: How to Play, Strategies and Variations

What is Yajilin?

Yajilin is a two-part logic puzzle. Some cells in the grid hold a clue: a number with an arrow pointing up, down, left or right. Your job is to shade some of the empty cells black, following what the clues say, and then draw a single closed loop that passes through every cell that is neither shaded nor a clue.

The two halves feed each other constantly. Shaded cells block the loop, so where you shade decides where the loop can go. And because the loop must reach every remaining cell without dead ends, the loop tells you where shading is impossible. Neither half can be solved on its own.

If you already know Masyu or Slitherlink, the loop will feel familiar. The difference is that Yajilin's loop must visit every available cell, which makes it far more demanding, and the shading adds a layer of counting that the other loop puzzles do not have.

A short history

Yajilin is an original puzzle of the Japanese publisher Nikoli, the company behind the modern form of Sudoku. According to Nikoli, it first appeared in Puzzle Communication Nikoli Vol. 86 in June 1999.

The name comes from yajirushi, the Japanese word for arrow, a nod to the arrow clues that make the puzzle unique. In English it has also been published under the name Arrow Ring.

Yajilin has become a favorite of competitive solvers because it packs so much reasoning into a small grid. You can read more in Wikipedia's Yajilin article.

The core rules

A standard Yajilin follows five rules. The first three describe the shading, the last two describe the loop.

1. 1Clues count shaded cellsA number with an arrow tells you exactly how many shaded cells lie in that direction, counting all the way to the edge of the grid in that row or column.
2. 2Shaded cells never touchNo two shaded cells may share a side. Touching diagonally at a corner is allowed.
3. 3Clue cells stay clearClue cells are never shaded and do not count toward other clues. Extra shaded cells that no arrow points at are allowed.
4. 4Loop through everything elseDraw one closed loop that passes through every cell that is not shaded and not a clue. No such cell may be left empty.
5. 5One simple loopThe loop runs horizontally and vertically through cell centers. It never crosses itself, branches or visits a cell twice.

Put together, every non-clue cell ends up in one of two states: shaded, or on the loop. That simple either-or is the engine of the whole puzzle.

A solved example

Here is a 6×6 Yajilin with just three clues. It has exactly one solution. Rows are counted from the top and columns from the left.

Begin with the 1↑ in row 4, column 1. Suppose the cell directly above it were shaded. Then the corner could not be shaded (it would make the count 2), so the 1← in the top row would need its shaded cell in row 1, column 3. The corner cell, the cell beside it and the cell below it would then each have just two exits, forcing a closed 2×2 loop in the top-left corner. That breaks the one-loop rule, so the cell above the clue is on the loop. It has only two open neighbors, so the loop runs through both, which puts row 2, column 1 on the loop too. The 1↑ must therefore shade the top-left corner, and that single cell satisfies the 1← as well. Finally, the 2→ needs two non-touching shaded cells among the four to its right. Of the three possible pairs, only columns 3 and 6 let every remaining cell join one loop.

How to play: a step-by-step method

Yajilin rewards a steady routine. Work through these steps in order and loop back whenever you get stuck.

1. Read every clue and mark easy counts. A 0 means every cell in that direction is on the loop. A clue that needs as many shaded cells as can possibly fit forces an alternating pattern.
2. Mark loop cells with a small dot. Every cell you know is not shaded must be on the loop, so a dot is a quick way to record that.
3. Draw the loop around each shaded cell. The unshaded neighbors of a shaded cell are all loop cells, and they often have so few exits that their path is forced.
4. Fix cells with only two exits. A loop cell surrounded by shaded cells, clues or the edge on two sides must use its other two sides. A corner loop cell always turns.
5. Shade cells that would be dead ends. If a cell could only ever connect in one direction, it cannot be on the loop, so it must be shaded.
6. Keep the loop in one piece. Never close off a small loop while other cells still need visiting. Use this to rule out tempting connections.

Strategies experienced solvers use

These patterns turn up in almost every Yajilin. Spotting them quickly is what separates a long struggle from a clean solve.

Strong Yajilin solving means moving back and forth between counting and path-drawing: the arrows place shaded cells, and the loop's need to visit everything places the rest. For practice, LogicPuzzles.io has Yajilin arrow-loop puzzles with a daily 8×8 grid and unlimited 6×6, 8×8 and 10×10 boards.

Variations and related puzzles

Standard Yajilin is the version you will see in almost every collection, but its two halves link it to several other classics.

• Grid size and clue density. Small 6×6 grids are a gentle introduction. Larger boards with few clues are among the hardest loop puzzles regularly published.
• Masyu. Also a one-loop puzzle, but the loop passes through pearls instead of covering every cell. It makes a gentler first step into loop logic.
• Slitherlink. Draws its loop along the grid lines around numbered cells rather than through cell centers.
• Hitori and Heyawake. Two Nikoli shading puzzles that share Yajilin's rule that shaded cells may never touch along a side, combined with a requirement that all unshaded cells stay connected.
• Nurikabe. Another shading puzzle where numbers control which cells stay white. Our Nurikabe guide covers it.

Common mistakes

The most common mistake is leaving a cell empty. In Yajilin, every non-clue cell is either shaded or on the loop. A cell that is neither means the solution is not finished, or not correct.

Second, solvers often count the wrong cells. An arrow counts all the way to the edge of the grid, not just the next few cells, and it ignores any clue cells along the way.

Third, it is easy to shade two touching cells when working from two different clues at once. Always check the four neighbors of a new shaded cell.

Finally, beginners sometimes assume every shaded cell needs a clue. Unclued shading is allowed, and on harder grids it is often required to make the loop work.

Why Yajilin is an advanced puzzle

Most pencil puzzles ask you to manage one kind of logic. Yajilin asks for two at once: local counting from the arrows and global path logic from the loop. Clues are usually sparse, so many deductions come from the loop alone, and the loop cannot be finished until the shading is right.

If Yajilin feels like a big jump, build up to it. Masyu teaches loop logic with friendly pearl clues, and Nurikabe teaches shading with connectivity. Once both feel natural, Yajilin becomes one of the most satisfying puzzles to solve.

Frequently asked questions