Rules: Blacken some white cells and then draw a single closed loop (without intersections or crossings) through all remaining white cells. Blackened cells cannot share an edge with each other. Some cells are outlined and in gray and cannot be part of the loop. Numbered arrows in such cells indicate the total number of blackened cells that exist in that direction in the grid.
Answer String: Enter the length in cells of the horizontal loop segments from left to right in the marked rows, starting at the top. If the loop only has vertical segments in the marked row, enter 0. Separate each row’s entry with a comma. This example has the key “132,111,121,1221”.
(Brief) History of Yajilin: Yajilin was first published in 1999 by Nikoli in quarterly Communication 86; the original author was 猫山天歩 (Nekoyama Tenpo). The puzzle’s name comes from a combination of the Japanese word ‘yajirushi’, meaning arrow, and the English word ‘link’. As a loop puzzle, Yajilin arose from other “visit all cells” loop styles; the addition of unknown unvisited squares that must be determined gives it its unique character. At Grandmaster Puzzles, the rules for Yajilin have been slightly altered by allowing unused cells without arrow clues to allow greater diversity in puzzle design and themes.
History of this example: This Yajilin was written as an example by Thomas Snyder for his 2011 Double Decathlon competition where it went by the name “Almost Simple Loop” as it did not obey standard Yajilin rules as published at the time.
Sources for Yajilin Puzzles: Follow this link for classic Yajilin puzzles on this website and this link for variations on Yajilin puzzles. If you are new to this puzzle type, here are our easiest Yajilin Puzzles to get started on. More Yajilin puzzles can be found in The Art of Puzzles 2, in Yajilin by Murat Can Tonta and Prasanna Seshadri, and in our beginner-friendly book Logic Puzzles 101.
Design rules for contributors: A Grandmaster Yajilin will have a unique solution that can be reached by logic alone. Generally, a Grandmaster Yajilin should have an interesting visual theme or an interesting solution. Symmetry is encouraged, but no requirements of symmetry exist. Sizes from 10×10 and above are recommended (maximum aspect ratio of 2:1 if rectangular).