Yajilin

Yajilin is a type of logic puzzle

Logic puzzle

A logic puzzle is a puzzle deriving from the mathematics field of deduction.-History:The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the author of Alice's Adventures in Wonderland...

 published by Nikoli

Nikoli

Nikoli Co., Ltd. is a Japanese publisher that specializes in games and, especially, logic puzzles. Nikoli is also the nickname of a quarterly magazine issued by the company...

. It has been published in English under the name Arrow Ring, such as in the 2005 U.S. qualifier for the World Puzzle Championship.

Rules

Yajilin is played on a rectangular grid of squares. At the beginning, cells are either indicative (containing a number and an arrow pointing "up", "down", "left," or "right") or empty. Black cells, an additional cell type, may be discovered during the solving process.

The goal is to draw a single continuous non-intersecting loop that passes through each cell that is neither black nor indicative. The loop must "enter" each cell from the centre of one of its four sides and "exit" from a different side; all turns are 90 degree

Degree (angle)

A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...

s.

For each indicative cell, its number indicates the count of the black cells that lie in that row or column in the direction of its arrow. Indicative cells can never be black, and do not count as a black cell for the purpose of satisfying other indicative cells, although the loop cannot pass through them.

On a solved board,

• Every non-indicative cell is either black or contains a segment of the loop.
• Every indicative cell is accurate. For example, if an indicative cell has an arrow that points to the left and the number '3', there must be exactly 3 black cells to the left of that indicative cell in the same row.
• Black cells do not touch each other orthogonally
  Orthogonality
  Orthogonality occurs when two things can vary independently, they are uncorrelated, or they are perpendicular.-Mathematics:In mathematics, two vectors are orthogonal if they are perpendicular, i.e., they form a right angle...
  
   (they do not share a side).

There may be black cells that are not accounted for by the indicative cells.

History

Yajilin is an original puzzle of Nikoli; it first appeared in Puzzle Communication Nikoli #86 (June 1999). The name is Japanese

Japanese language

is a language spoken by over 130 million people in Japan and in Japanese emigrant communities. It is a member of the Japonic language family, which has a number of proposed relationships with other languages, none of which has gained wide acceptance among historical linguists .Japanese is an...

, in which it is a contraction of ヤジルシ (yajirushi, directing arrow) and リンク (rinku, the English word 'link').