Yajilin

Grey arrows count the shaded cells they point at; a single loop threads every cell that is neither.

What it is

A grid scattered with grey clue cells, each carrying a number and an arrow: that many shaded cells lie in that direction, all the way to the edge. Every remaining cell is either shaded — no two shaded cells touch orthogonally — or part of one closed loop through all the leftover cells.

How to play

Zero-arrows clear their whole ray, and a cleared cell must carry the loop. The loop’s mechanics do most of the work: a cell with two decided loop ends is finished, a dead-end must be shaded, and a shaded cell forces the loop around it. The arrows and the loop tighten each other — that interplay is the genre.

Purpose

The most-cited Nikoli genre the catalogue was missing, and the workspace’s first combined puzzle: shading and loop in one answer. It reuses masyu’s search architecture (edge decisions in row bands, union-find over cycles, proof-only pruning) with the clue logic swapped from circle shapes to ray counts.

History

Published by Nikoli as Yajirin (“arrow link”), from yajirushi (arrow) — a fusion of their own Yajisan-Kazusan counting clues with the loop genres.

This implementation

• Spec knobs: size (6–10), clues (share of cells printed as clues), difficulty, cell, line.
• Generation: solver-first. The clue cells are fixed, then the exhaustive search samples a valid configuration around them — loop and shading together, steered by a seeded branch preference. (Building the loop and the shading separately kept producing boards with slack: the rigidity of the genre comes from the loop threading between isolated shaded cells.) Arrows then report the truth about the shading, aimed at the most informative direction.
• Uniqueness by monotone repair: while a second answer exists, one shaded cell is converted into a clue cell and every count recomputed — each step keeps the sampled answer valid while strictly removing freedom, until the count of answers is exactly one (proven by exhaustive search) or the board is discarded.
• Guarantees: deterministic per seed; exactly one answer, loop and shading both; the shipped answer is the sampled configuration, checked outright. Difficulty is rated by clue density, the same basis as masyu, and the metadata names it.