### Yajilin (Castle Wall) by Thomas Snyder

See more discussion of the puzzles from the United States’ 2021 Puzzle Grand Prix on this post. Note there are some construction details and potential spoilers on that post so view it after you solve.

PDF

or solve online (using our beta test of Penpa-Edit tools using a composite mode where left click inside cell shades square, left click + drag draws line segment, right click inside cell adds dot, and right click on cell edge adds an x.)

Author/Opus: This is the 401st* puzzle from Thomas Snyder, aka Dr. Sudoku (*the 400th puzzle opus number is being held for an upcoming post).

Rules: Standard Yajilin 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.

Also, in addition to the usual gray clues, some clues are white and black and act similarly to Castle Wall clues. White clues must be inside the loop and black clues must be outside the loop. White and black clues indicate the sum of the lengths of loop segments in the indicated direction.

Difficulty: 2.5 stars (estimate based off competition points; timing standards not available from our usual testers)

Solution: PDF

• sj says:

I tried this several times but always got stuck on the bottom-left 1-uparrow-black-cell. The “solution” PDF doesn’t have any blackened cell in the “up” direction for this cell. Could someone please clarify?

• drsudoku says:

This puzzle is a combination of Yajilin AND Castle Wall. The black / white clue cells are Castle Wall clues. So a black square with a 1-up arrow indicates (1) the cell is outside of the loop and (2) the loop crosses a single edge in the vertical direction above the cell. Only the gray clues cells indicate Yajilin clues about shaded squares.

• sj says:

Thank you for the clarification. I missed that last part. Apologies.

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