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: Digit Series

Author/Opus: This is the 224th puzzle from Thomas Snyder, aka Dr. Sudoku.

Rules: (Standard Balance Loop rules.) Draw a single, non-intersecting loop that passes through all circled cells. All white circles must have equal segment lengths on both sides of the circle before turning. All black circles must have unequal segment lengths on both sides of the circle before turning. Numbers indicate the sum of the segment lengths on both sides of the circle.
Also, see this example:

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 “11,311”.

Time Standards (highlight to view): Grandmaster = 4:00, Master = 8:00, Expert = 16:00

Solution: PDF

Note: Follow this link for other Balance Loops.

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: Antisymmetry

Author/Opus: This is the 71st puzzle from our contributing puzzlemaster Prasanna Seshadri.

Rules: (Standard Balance Loop rules.) Draw a single, non-intersecting loop that passes through all circled cells. All white circles must have equal segment lengths on both sides of the circle before turning. All black circles must have unequal segment lengths on both sides of the circle before turning. Numbers indicate the sum of the segment lengths on both sides of the circle.
Also, see this example:

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 “11,311”.

Time Standards (highlight to view): Grandmaster = 7:00, Master = 12:30, Expert = 25:00

Solution: PDF

Note: Follow this link for other less common Loop variations.

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: Big X

Author/Opus: This is the 70th puzzle from our contributing puzzlemaster Prasanna Seshadri.

Rules: (Standard Balance Loop rules.) Draw a single, non-intersecting loop that passes through all circled cells. All white circles must have equal segment lengths on both sides of the circle before turning. All black circles must have unequal segment lengths on both sides of the circle before turning. Numbers indicate the sum of the segment lengths on both sides of the circle.
Also, see this example:

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 “11,311”.

Time Standards (highlight to view): Grandmaster = 8:30, Master = 10:30, Expert = 21:00

Solution: PDF; a solution video is available here.

Note: Follow this link for other less common Loop variations.

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: Squares

Author/Opus: This is the 69th puzzle from our contributing puzzlemaster Prasanna Seshadri.

Rules: (Standard Balance Loop rules.) Draw a single, non-intersecting loop that passes through all circled cells. All white circles must have equal segment lengths on both sides of the circle before turning. All black circles must have unequal segment lengths on both sides of the circle before turning. Numbers indicate the sum of the segment lengths on both sides of the circle.
Also, see this example:

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 “11,311”.

Time Standards (highlight to view): Grandmaster = 3:30, Master = 5:45, Expert = 11:30

Solution: PDF

Note: Follow this link for other less common Loop variations.

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: Clue Symmetry and Logic

Author/Opus: This is the 68th puzzle from our contributing puzzlemaster Prasanna Seshadri.

Rules: (Standard Balance Loop rules.) Draw a single, non-intersecting loop that passes through all circled cells. All white circles must have equal segment lengths on both sides of the circle before turning. All black circles must have unequal segment lengths on both sides of the circle before turning. Numbers indicate the sum of the segment lengths on both sides of the circle.
Also, see this example:

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 “11,311”.

Time Standards (highlight to view): Grandmaster = 3:00, Master = 4:00, Expert = 8:00

Solution: PDF

Note: Follow this link for other less common Loop variations.

Here are our best Loop/Path puzzles of 2020, in chronological order, selected from the 26 web posts in this category based on FAVE votes, web comments, and tester comments. All of these puzzles are gathered in this PDF file.

A lot of our early puzzles as we were relaunching the website got a good number of FAVE votes. And we seemed to start out strong with this first regular post: an antisymmetric no-numbers Balance Loop by Murat Can Tonta.

Murat had another favorite puzzle with this “Parallel Universes” Slitherlink with an interesting logical path around the grid.

Serkan Yürekli put a little uncertainty into this Slitherlink variation with several missing numbers that must fulfill Sudoku-like constraints. The logical challenge got a lot of favorable comments.

Serkan delighted us again in September with a visually beautiful Snake (Cipher) puzzle that announces itself on the outside of the grid.

Our final best Loop/Path puzzle of 2020 comes from this November post from Tom Collyer, who focused on some less common patterns to give us a really challenging Slitherlink.

(View image directly for larger form.)

PDF

or solve online (using our beta test of Penpa-Edit tools in yajilin mode where left click shades squares, left click+drag draws lines and right click marks X’s; note that the default puzzle info is too long — even for an url shortener — so copy and paste all the text in this file into the “Load” option in the upper-right of the penpa-edit interface to access.)

Theme: Clue Symmetry and Logic (for TheSubro)

Author/Opus: This is the 158th puzzle from our contributing puzzlemaster Serkan Yürekli.

Rules: This puzzle combines four loop varieties commonly featured at GMPuzzles: Balance Loop (upper left), Yajilin (upper right), Castle Wall (lower left), and Masyu (lower right).

Draw a single, non-intersecting loop throughout all four quadrants. The loop may enter and exit the different quadrants as many times as needed.

The standard rules for each puzzle type are true for each quadrant, with these additional considerations:

Balance Loop: Use the entire length of segments (including parts of the segments that extend into an adjacent quadrant) when determining the balanced/unbalanced status of a circle clue.

Yajilin: The arrow clues refer only to shaded cells within the Yajilin quadrant. The loop must occupy all cells adjacent to a shaded cell, even in an adjacent quadrant.

Castle Wall: Number clues only apply within the grid and DO NOT include any line segments that cross the bold border with another grid or any segments in other quadrants. (Another way to say this is that the Castle Wall clues refer to the number of thin lines crossed in the lower-left quadrant only.)

Masyu: Normal rules apply for white and black circles, but the path satisfying these rules can extend into an adjacent quadrant. (For example, a white circle can be passed through crossing a quadrant edge, provided it turns immediately on one side of the circle whether the turn is in the Masyu quadrant or in another quadrant.)

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.

Solution: PDF

Time Standards (highlight to view): Grandmaster = 18:00, Master = 35:00, Expert = 1:10:00

Here are our best Loop/Path puzzles of 2015.

The first best “Loop” puzzle is a hybrid with object placement and featured twelve pentomino shaped loops. Serkan Yürekli wrote this favorited Slitherlink (Pentomino) puzzle.

Prasanna Seshadri introduced a new puzzle style this year in the form of Balance Loop; this particular puzzle was one of the best of 2015.

Prasanna included Balance Loop as part of his quite special Birthday Loop mix. Alongside his 100th puzzle spectacular, Prasanna definitely made a lot of great combo/other puzzles this year.

(View image directly for larger form.)

The best 2015 Loop/Path puzzle came from our newest contributing puzzlemaster. With just two clues, Murat Can Tonta’s Snake Egg still yielded an elegant and surprising challenge.

(Note: This puzzle is at a Saturday+ difficulty, and is being posted today to mark the occasion of Prasanna’s birthday. Our regular “easy” puzzles will run on Tuesday and Wednesday this week.)

(View image directly for larger form.)

PDF

or solve online (using our beta test of Penpa-Edit tools in yajilin mode where left click shades squares, left click+drag draws lines and right click marks X’s; note that the default puzzle info is too long — even for an url shortener — so copy and paste all the text in this file into the “Load” option in the upper-right of the penpa-edit interface to access.)

Theme: 24 on 03/02/15

Author/Opus: This is the 73rd puzzle from our contributing puzzlemaster Prasanna Seshadri.

Rules: This puzzle combines four loop varieties commonly featured at GMPuzzles: Balance Loop (upper left), Yajilin (upper right), Castle Wall (lower left), and Masyu (lower right).

Draw a single, non-intersecting loop throughout all four quadrants. The loop may enter and exit the different quadrants as many times as needed.

The standard rules for each puzzle type are true for each quadrant, with these additional considerations:

Balance Loop: Use the entire length of segments (including parts of the segments that extend into an adjacent quadrant) when determining the balanced/unbalanced status of a circle clue.

Yajilin: The arrow clues refer only to shaded cells within the Yajilin quadrant. The loop must occupy all cells adjacent to a shaded cell, even in an adjacent quadrant.

Castle Wall: Number clues can see beyond the CW quadrant ONLY IF the line segment begins from a cell within the CW quadrant. (For example, if a segment starts in the rightmost column of the CW quadrant and goes three cells further to the right into the Masyu quadrant before turning, this segment would contribute 3 to the count of segments for that row.)

Masyu: Normal rules apply for white and black circles, but the path satisfying these rules can extend into an adjacent quadrant. (For example, a white circle can be passed through crossing a quadrant edge, provided it turns immediately on one side of the circle whether the turn is in the Masyu quadrant or in another quadrant.)

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.

Time Standards (highlight to view): Grandmaster = 30:00, Master = 55:00, Expert = 1:50:00

Solution: PDF

Our recent week of Balance Loop puzzles is gathered together in this PDF and the solutions are in this PDF. More Balance Loop puzzles (that are only in these books and not on our website) can be found in our e-store at this link.

The daily solution videos, this week from Prasanna, are on the posts and linked below:

Astute observers may have noticed that Japanese Sums was recently added to our Number Placement puzzle list on the main blog roster. We’ve also fully digitized the Penpa backlog for it. This upcoming week will feature this “new” puzzle to the website, as well as a Sunday Stumper next week. Japanese Sums will also be one of the six puzzle styles in Grandmaster Puzzles Quarterly 4 which will be released later today, so watch for more information on that.