Polygraph

First appeared on 8th 24-Hour Puzzle Championship (2007).[1] The author of the puzzle was Serkan Yürekli (Turkey).

Draw a single closed loop along the grid lines. The numbers that are outside the loop indicate the number of cell sides used by the loop. The numbers that are inside the loop indicate the number of the cell sides unused by the loop.

(Rules and example from WPC 2018 IB)

In the original puzzle by Serkan, the roles of inside and outside clues were the other way around. Commonly presented as an inside/outside Slitherlink variant, this puzzle is actually closer to shading puzzles (consider inside/outside patterns around clues).

Sheep and Wolves

The version only with sheep first appeared in 2008 US Nationals. Wolves were first added in a puzzle in 2009 US Nationals. Both of those puzzles were written by Dave Tuller (USA).

Draw a single, non-intersecting loop that only consists of horizontal and vertical line segments between the dots. A number inside a cell indicates how many of the edges of that cell are part of the loop.

Cells marked with “W” (for “wolf”) must be outside the loop; cells marked with “S” (for “sheep”) must be inside the loop.

(Rules and example from PGP IB)

Filled Loop

First appeared on LMD portal in 2009. The author of the puzzle was Richard Stolk (Netherlands).

Draw a single closed loop along the grid lines. The loop does not cross or touch itself. Numbers in the grid indicate how many sides of some cells are used by the loop.

Every cell in the loop must form part of one of the given set of pentominoes so that adjacent pentominoes touch each other at exactly one border segment. There are no points where three or more pentominoes meet. Pentominoes may be rotated and mirrored. No pentomino is used more than once.

(Rules and example (using FILNPT) from WPC 2014 IB)

First appeared on LMD portal in 2013. The author of the puzzle was Christian Halberstadt (Germany). Grid is Hexagonal by default because of parity.

Draw a closed loop along the dotted lines that uses each grid point at most once. A person walks along the loop, alternating between their left and right foot, always one edge per step. The numbers indicate how many steps on the edges of the respective cells that a person makes with their right foot.

(Rules and example from WPC 2019 IB)

First appeared on 2013 Puzzle Marathon. The author of the puzzle was Jakub Hrazdira (Czech Rep.)

Draw a single, non-intersecting loop that only consists of horizontal and vertical segments between the dots. A number inside a cell indicates how many of the edges of that cell are part of the loop.

However, exactly one number in each row and each column is wrong (the value of that number doesn’t correspond with the number of square edges used by the loop). Moreover, each square with the wrong number should be crossed by the loop diagonally.

(Rules and example from 2013 Puzzle Marathon IB)

First appeared on WPC 2016/Round 11 under the name of "Fences Switch". (Here, the puzzle is renamed in accordance with the name of this article.) The puzzle was written by Matej Uher (Slovakia).

Draw a single, non-intersecting loop that only consists of horizontal and vertical segments between the dots. A number inside a cell indicates how many of the edges of that cell are part of the loop.

However, the clues are not in their correct positions. Every number in the grid must be paired with and switch its position with exactly one of its orthogonal neighbours. Solvers must determine the pairing.

(Example from WPC 2016 IB. Pairing in the solution grid is just for illustrative purposes.)