Archive for the ‘Other Loop/Path’ Category:

Numberlink by Grant Fikes

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

Numberlink by Grant Fikes

(view directly for a larger image)

PDF

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.

Numberlink by Serkan Yürekli

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

Numberlink by Serkan Yürekli

PDF

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.

WPC Loop/Path Mini-Playoff 3/3: Cross Border Parity Loop by Craig Kasper

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.)

Cross Border Parity Loop by Craig Kasper

PDF

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:

Cross Border Parity Loop by Craig Kasper

Estimated Difficulty: 2.5-3 stars

Solution: PDF for all Loop/Path playoff puzzles.

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

Equality by Murat Can Tonta

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.

Equality by Murat Can Tonta

PDF

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:

Equality Example by Serkan Yürekli

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.

Country Road by Martin Ender

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

Country Road by Martin Ender

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:

Country Road by Serkan Yürekli

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.

Line of Sight by Ashish Kumar

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

Line of Sight by Ashish Kumar

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:

Line of Sight Example by Serkan Yürekli

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.

Geradeweg by Prasanna Seshadri

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.

Geradeweg by Prasanna Seshadri

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:

Geradeweg Example by Serkan Yürekli

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.

Rail Pool by Martin Ender

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.

Rail Pool by Martin Ender

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:

Rail Pool Example by Serkan Yürekli

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.

Mukkonn Enn by Serkan Yürekli

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.

Mukkonn Enn by Serkan Yürekli

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:

Mukkonn Enn Example by Serkan Yürekli

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.

Nanro Loop by Bryce Herdt

Nanro by Bryce Herdt

PDF

or solve online (using our beta test of Penpa-Edit tools; use the tab key to alternate between shading, number entry, and composite loop drawing modes)

Theme: Parquet

Author/Opus: This is the 23rd puzzle from guest contributor Bryce Herdt.

Rules: Variation of Nanro rules. Label some cells with numbers to form a single non-intersecting loop; no 2×2 group of cells may be fully labeled, but the loop may touch itself orthogonally or diagonally. The region boundaries divide the loop into segments, and each region must have at least one segment. Numbers denote the length in cells of each segment within a region; all numbers in a region must be the same. When two numbers from different segments are orthogonally adjacent, the numbers must be different. (Consequently, segments in the same region must not share an edge.)

Also see this example:

Nanro Loop Example by Serkan Yürekli

Difficulty: 4 stars

Time Standards (highlight to view): Grandmaster = 6:15, Master = 9:15, Expert = 18:30

Solution: PDF and solving video.

Note: Follow this link for Nanro puzzles on this website and this link for variations on Nanro puzzles. If you are new to this puzzle type, here are our easiest Nanro Puzzles to get started on. More Nanro puzzles can be found in A Number o’ Nanro by Prasanna Seshadri.