Adjacency

• Adjacent Orthogonally or diagonally adjacent; share at least one common vertex; has a Chebyshev distance of 1
• Orthogonally adjacent, neighboring Share an edge (or two common vertices); has a Manhattan distance of 1
• Diagonally adjacent Share exactly one common vertex; has a Chebyshev distance of 1 but a Manhattan distance of 2

Connectivity

• Path A finite sequence of squares, where each square is orthogonally adjacent to the one before it and the one after it
• Non-touching path A path such that for every two adjacent squares, there is at most one square between them in the path’s sequence
• Polyomino, connected squares A set of squares S, in which there exists a path between any two squares in the set that is completely inside S (is a subset of S)

Common puzzle types
Some puzzles have essentially the same method of marking the answer, listed below. However, whenever there is any contradiction between this and the instructions in the puzzle, use the one in the puzzle. (One example is Ice Barn, where it is a path and not a loop, and that it may cross itself in certain places, but otherwise share the common traits of a loop puzzle.)

• Dynasty Shade in some cells on the grid black such that no black squares are orthogonally adjacent and all white squares are connected
• Latin Square Put an integer between 1 and n inclusive into each cell, where n is the size of the grid, such that each row and column contains exactly one instance of each number.
• Loop Draw a loop that passes some of the cells such that the loop never touches or crosses itself, the loop only turns on cell centers, and the loop only makes 90-degree turns.
• Snake Shade some squares black. Exactly two of the black squares have only one neighboring black square. All shaded squares must be on a non-touching path connecting these two black squares.
• Wall (Nurikabe-style) Shade in some cells on the grid black such that all black squares are connected and no 2×2 area is completely black.