Takeya Saikachi presents us with a new loop genre in which you need to discover the rules by solving the example first.

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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: Triplets

Author/Opus: This is the 40th puzzle from our contributing puzzlemaster Takeya Saikachi.

Rules: To solve the main puzzle, you must first discover the genre’s rules by solving the example puzzle.

Example: solve online

Difficulty: 3.5 stars

Time Standards (highlight to view): Grandmaster = 4:35, Master = 7:15, Expert = 14:30

Hints: 1. This is a loop puzzle style that involves visiting all cells, forming a single closed loop. But what do the number clues do?
2. When thinking the right way, each number clue will have two uses.
3. Looking at individual clues may not be enough.
4. Pair all the clues together (as passed through by the loop) and consider any special properties you find.
5. This puzzle draws inspiration from a region division puzzle with a four-letter name (rot13 = NENS) that also pairs clues together.

Solution: PDF and solving animation.

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

Note 2: Comments on the blog are great! For a more interactive discussion, please also consider using our week-0-discussion thread on the GMPuzzles Discord. If you are not yet part of this Discord community, use this link.

Grant Fikes created his Numberlink art with a lyre, just like ancient people did.

(view directly for a larger image)

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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: Lyre

Author/Opus: This is the 425th puzzle from our contributing puzzlemaster Grant Fikes.

Rules: Connect each pair of identical numbers with a path passing through edge-adjacent cells. No cell may be used on more than one path.

Difficulty: 2.5 stars

Time Standards (highlight to view): Grandmaster = 1:15, Master = 3:40, Expert = 7:20

Solution: PDF and solving animation.

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

Note 2: Comments on the blog are great! For a more interactive discussion, please also consider using our Season 2 Preview Week Discussion post on the GMPuzzles Discord. Not a member of the Discord? Click this link for basic access and check subscriber instructions for role-related access.

Serkan Yürekli constructed a gate whose walls reach out to both opposite corners.

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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: Gate

Author/Opus: This is the 421st puzzle from our managing editor Serkan Yürekli.

Rules: Connect each pair of identical numbers with a path passing through edge-adjacent cells. No cell may be used on more than one path.

Difficulty: 1 star

Time Standards (highlight to view): Grandmaster = 0:20, Master = 0:30, Expert = 1:00

Solution: PDF and solving animation.

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

Note 2: Comments on the blog are great! For a more interactive discussion, please also consider using our Season 2 Preview Week Discussion post on the GMPuzzles Discord. Not a member of the Discord? Click this link for basic access and check subscriber instructions for role-related access.

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.

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.

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: 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.

This style, whose name means “Triangular Numbers” in English and has also been called “Four Directions Loop” elsewhere, was originally created by the Indian team that organized the 2017 World Puzzle Championship as part of an instructionless team round. More Mukkonn Enn will be in our upcoming Loop Variety Collection 2.

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: Sequences

Author/Opus: This is the 386th puzzle from our managing editor Serkan Yürekli.

Rules: Draw a single, non-intersecting loop that passes through the center of all cells, including clue cells; the loop may either go straight through or turn at each clue. Each clue cell is divided into four sections; if a number is present in a section and the loop travels in that direction, then the number represents the length of the straight loop segment in that direction, measured from the clue cell to the cell where the loop turns. If the loop does not travel in that direction, then the number means nothing.

Also see this example:

Difficulty: 1 star

Time Standards (highlight to view): Grandmaster = 0:45, Master = 1:00, Expert = 2:00

Solution: PDF and solving video.

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