Terminology

I haven't been able to find a standard terminology for talking about Sudoku puzzle solving, so I've developed one of my own which I use throughout this wiki (and the code for Sūsen). Here goes:

• Puzzles, Squares, and Geometries. A puzzle is a grid of fillable spaces called squares (or sometimes cells). The shape of the grid is determined by the geometry of the puzzle, which also determines the puzzle's value constraints: rules about allowed values and their placement in a solution. For example, the standard Sudoku geometry requires that a puzzle grid be an n by n square whose side length n is itself a perfect square (say m times m), and its value constraints are:

  • Squares can contain only the values 1 through n.
  • Each row must contain each allowed value exactly once.
  • Each column must contain each allowed value exactly once.
  • Each of the n non-overlapping m by m sub-regions of the grid must contain each allowed value exactly once.

• Solvability and Solutions. If all of a puzzle's squares are filled and all its geometric value constraints are met, the puzzle is said to be solved, and the filled-in values are called a solution for the puzzle. A puzzle with empty squares is said to be unsolved. If an unsolved puzzle has one or more solutions consistent with its current values, each of those solutions is called a possible solution for the puzzle, and the puzzle is said to be solvable, otherwise it is said to be unsolvable. If a solvable puzzle has only one possible solution, the puzzle is said to be fully specified (aka well formed), otherwise it is under-specified.