The last Loop/Path puzzle is one of the “new” styles that debuted in the Breadth of America loop variety round, a Cross Border Parity Loop by Craig Kasper. (We expect this puzzle to be much harder for those who didn’t solve the three competition puzzles that preceded it.)

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or solve online (using our beta test of Penpa-Edit tools in linex mode where left click+drag draws lines and right click marks X’s; use tab to alternate to a shading mode to mark the loop states)

Author/Opus: This is the 9th puzzle from guest contributor Craig Kasper.

Rules: Draw a single, non-intersecting loop that has two states, which are white and black. The puzzle grid has heavily shaded borders, which define areas in the grid. Whenever the loop crosses a border (including borders inside an area), it changes state from white to black or from black to white. A black circled clue provides the number of cells in each area that the loop traverses in the black state, and a white circled clue provides the number of cells in each area that the loop traverses in the white state. Each “?” represents an unknown integer, zero or larger.

See also this example:

Estimated Difficulty: 2.5-3 stars

Solution: PDF for all Loop/Path playoff puzzles.

Note: Follow this link for other uncommon Loop/Path puzzles.

The next Loop/Path puzzle, reflecting an unusual grid geometry round, is this “Trophy” Slitherlink by Serkan Yürekli. Can you figure out how all the unusual parts of the grid will mark the 30th World Puzzle Championship.

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Author/Opus: This is the 415th puzzle from our managing editor Serkan Yürekli.

Rules: Variation of Slitherlink rules. Draw a single, non-intersecting loop on an irregular grid that can only follow the lines between the dots. Numbers inside a cell indicate how many of the edges of that cell are part of the loop.

Estimated Difficulty: 2 stars

Solution: PDF for all Loop/Path playoff puzzles.

Note: Follow this link for other classic Slitherlink. If you are new to this puzzle type, here are our easiest Slitherlink puzzles to get started on. More Slitherlink puzzles can be found in our books The Art of Puzzles and Slitherlink and Variations.

The 30th World Puzzle Championship had five “mini-playoffs” to determine the top solvers in five different genres. Today we’ll be releasing the Loop/Path puzzles starting with this Castle Wall puzzle by David Altizio with a theme involving many ascending series.

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or solve online (using our beta test of Penpa-Edit tools in linex mode where left click+drag draws lines and right click marks X’s)

Author/Opus: This is the 16th puzzle from guest contributor David Altizio.

Rules: Standard Castle Wall rules.

Estimated Difficulty: 2-2.5 stars

Solution: PDF for all Loop/Path playoff puzzles.

Note: Follow this link for more Castle Wall puzzles. If you are new to this puzzle type, here are our easiest Castle Wall puzzles to get started on. More Castle Wall puzzles can be found in these books in our e-store.

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or solve online (using our beta test of Penpa-Edit tools; in default linex mode: left-click+drag draws line, right click marks X on edge)

Theme: Odd vs. Even

Author/Opus: This is the 103rd puzzle from our contributing puzzlemaster Ashish Kumar.

Rules: Draw a single loop in the grid which may cross itself orthogonally, but otherwise does not touch or retrace itself. The clue numbers to the left/right of the rows indicate the number of squares visited by the nearest section of the loop that travels horizontally in the rows. The clue numbers to the top/bottom of the columns indicate the number of squares visited by the nearest section of the loop that travels vertically in the columns.

Also, see this example:

Difficulty: 2 stars

Time Standards (highlight to view): Grandmaster = 1:30, Master = 2:30, Expert = 5:00

Solution: PDF and solving video.

Note: Follow this link for other Round Trip puzzles. Some more Round Trip puzzles can be found in the book Loop Variety Collection by Ashish Kumar and Murat Can Tonta.

Since 2021, we have posted some extra difficult Sunday Stumpers, about once a month. These will be quite tough puzzles, but with a logical path to be found (and solution videos to help). This thirteenth Sunday Stumper of 2022 is an unusual Castle Wall puzzle by Stefan Liew where all the clues are on the “Outside”.

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or solve online (using our beta test of Penpa-Edit tools in linex mode where left click+drag draws lines and right click marks X’s)

Theme: Outside

Author/Opus: This is the 3rd puzzle from guest contributor Stefan Liew.

Rules: Standard Castle Wall rules.

Difficulty: 5 stars

Time Standards (highlight to view): Grandmaster = 11:00, Master = 22:30, Expert = 45:00

Solution: PDF and solving video.

Note: Follow this link for more Castle Wall puzzles. If you are new to this puzzle type, here are our easiest Castle Wall puzzles to get started on. More Castle Wall puzzles can be found in our beginner-friendly collection Intro to GMPuzzles as well as the larger collection Castle Wall, both by Serkan Yürekli.

This puzzle style was created by Erhard Notz for the 2019 World Puzzle Championship (innovations round). More Equality puzzles will be in our upcoming Loop Variety Collection 2.

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or solve online (using our beta test of Penpa-Edit tools; use tab to shift between the default linex mode where left click+drag draws lines and right click marks X’s and a shading mode to help mark cells.)

Theme: Quadrants

Author/Opus: This is the 236th puzzle from our contributing puzzlemaster Murat Can Tonta.

Rules: Draw a single, non-intersecting loop in the grid that passes through some of the white cells. Each bold region must be visited at least twice by the loop. Each visit to the same region must pass through the same number of cells. If a number clue is given in a region, that number indicates the number of cells not used by the loop in that region. The loop cannot pass through gray cells, and gray cells cannot be counted as part of any bold region.

Also see this example:

Difficulty: 4 stars

Time Standards (highlight to view): Grandmaster = 5:45, Master = 9:30, Expert = 19:00

Solution: PDF and solving video.

Note: Follow this link for other Loop/Path puzzles. More Equality puzzles are in the book Loop Variety Collection 2.

This puzzle style, originally published by Nikoli, was part of our first Loop Variety Collection.

PDF

or solve online (using our beta test of Penpa-Edit tools; in default lineox mode: left-click+drag draws line, clicking one time in a cell marks a circle and a second time marks an X)

Theme: 2 Many 2×2’s

Author/Opus: This is the 2nd puzzle from guest contributor Martin Ender.

Rules: Draw a single, non-intersecting loop in the grid that enters and exits each bold region exactly once. If a number clue is given in a region, that number indicates the exact number of cells used by the loop in the region. Unused cells cannot be orthogonally adjacent across different regions.

Also, see this example:

Difficulty: 3.5 stars

Time Standards (highlight to view): Grandmaster = 5:15, Master = 8:15, Expert = 16:30

Solution: PDF and solving video.

Note: Follow this link for other Loop/Path puzzles. More Country Road puzzles can be found in the Loop Variety Collection by Ashish Kumar and Murat Can Tonta.

This puzzle style was created by Naoki Inaba, and will be in our upcoming Loop Variety Collection 2.

PDF

or solve online (using our beta test of Penpa-Edit tools in default edgex mode where left-click+drag draws line and right click marks X’s)

Theme: Pairs

Author/Opus: This is the 102nd puzzle from our contributing puzzlemaster Ashish Kumar.

Rules: Draw a single, non-intersecting loop that only consists of horizontal and vertical segments between the dots. The clues in the grid indicate the length of the straight line segment first seen in the direction of the arrow.

Also see this example:

Difficulty: 3 stars

Time Standards (highlight to view): Grandmaster = 4:15, Master = 5:30, Expert = 11:00

Solution: PDF and solving video.

Note: Follow this link for other Loop/Path puzzles. More Line of Sight puzzles are in the book Loop Variety Collection 2.

This puzzle style was created by Robert Vollmert (Geradeweg roughly means “Straight Path” in English). More Geradeweg will be in our upcoming Loop Variety Collection 2.

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or solve online (using our beta test of Penpa-Edit tools in default linex mode where left-click+drag draws line and right click marks X’s)

Theme: Knight Matrix

Author/Opus: This is the 248th puzzle from our contributing puzzlemaster Prasanna Seshadri.

Rules: Draw a single, non-intersecting loop that passes through all cells with circles; the loop may either go straight through or turn at each circle. If the loop goes straight through a circle, the number on that circle indicates the length of the straight segment. If the loop turns at a circle, the number on that circle indicates the length of both loop segments extending from that circle.

Also see this example:

Difficulty: 2.5 stars

Time Standards (highlight to view): Grandmaster = 2:30, Master = 4:30, Expert = 9:00

Solution: PDF and solving video.

Note: Follow this link for other Loop/Path puzzles. More Geradeweg puzzles are in the book Loop Variety Collection 2.

This puzzle style was created by Martin Ender (first example here), and was one of the “new generation” of puzzles at the 2022 World Puzzle Championship. While it won’t be in our upcoming Loop Variety Collection 2, we are planning to have some more Rail Pool in GMPuzzles projects in the future.

PDF

or solve online (using our beta test of Penpa-Edit tools in default linex mode where left-click+drag draws line and right click marks X’s)

Theme: Tetris

Author/Opus: This is the 1st puzzle from guest contributor Martin Ender.

Rules: Draw a single, non-intersecting loop that passes through the centers of all cells, including clue cells. Clues represent all of the different lengths of the straight line segments that pass through all cells within the region, either partially or fully contained by that region. Each number within a region must be represented by at least one line segment. Each “?” represents a positive integer; if a clue cell has more than one “?”, all numbers and “?”s in that clue must be different from each other.

Also see this example:

Difficulty: 2.5 stars

Time Standards (highlight to view): Grandmaster = 1:30, Master = 2:45, Expert = 5:30

Solution: PDF and solving video.

Note: Follow this link for other Loop/Path puzzles.