The general goal is to draw a line (sometimes a loop) around the grid
Has some overlap with Partitioning Puzzles since the line can partition the grid into two sections. However, this category specifically pertains to performing the partition by drawing a loop
Goal: Draw a single continuous non-intersecting loop.
Constraint: The loop visits all cells with circles.
Constraint: Loop segments extending orthogonally (up to turning points) from a white circle are of equal length.
Constraint: Loop segments extending orthogonally (up to turning points) from a black circle are of unequal length.
Constraint: If a circle contains a number, the number indicates the sum of the lengths of the loop segments on both sides of the circle before turning.
Goal: Draw a single continuous loop along the lines of the grid.
Constraint: All numbers on the grid are contained inside.
Constraint: Each number indicates the total number of cells visible in any orthogonal direction before a line in the loop is reached.
Variant: Inside/Outside - numbers can be anywhere. In both cases the number indicates how many cells can be seen orthogonally from that cell including the cell itself.
Goal: Draw a single continuous non-intersecting loop that properly passes through all circled cells.
Constraint: The loop enters each cell it passes through from the center and exits on a different side. In a rectangular grid, all turns are 90 degrees.
Constraint: White circles must be travelled straight through, but the loop must turn in the previous or next cell in its path.
Constraint: Black cells must be turned upon, but the loop must travel straight through the next and previous cells in its path.
Variant: Gray circles which MAY either be white or black. The solver must deduce their color.
Variant: Allowing wrap arounds from the edges of the board.
Variant: The board is divided into regions. The loop must turn in each region at least once.
Goal: Draw a single continuous non-intersecting loop that passes through all dots at the centers of the cells.
Constraint: Dots must be travelled straight through.
Constraint: Segments of a straight line going out the dot must be equal That is, the length of the straight line segment going in equals the length of the straight line segment going out.
Constraint: The loop must cross the borders of each region exactly twice.
Constraint: In a region, the loop must visit either all cells with black cells or all cells with white circles.
Constraint: Alternate between region types when following the loop. That is, if the current region has all X colored cells visited, then the next region visited must have all Y colored cells visited.
Goal: Draw a single, continuous, non-intersecting loop.
Constraint: Some cells are black. Not all black cells are given
Constraint: Some cells are indicative consisting of a number and an arrow pointing in an orthogonal direction. The number tells you the count of the black cells that lie in that row or column in the direction of the arrow.
Constraint: Indicative cells are never black and do not count as black cells for the purposes of satisfying other indicative cells.
Constraint: Not all black cells may be accounted for by an indicative cell
Constraint: The loop may not pass through indicative cells
Constraint: The loop may not pass through black cells.
Constraint: The loop must pass through all non-indicative, non-black cells.
Constraint: Loops must enter each cell from the center of one of the four sides and exit from a different side. All turns are orthogonal (90 degrees).
Variant: Regional - Shade some cells and draw a single non-intersecting loops through all white cells.
Numbers in regions indicate the number of black cells in the region.
Regions with no number can contain any number of black cells.