Solutions, Sieves, Spaces, Sets, and Symbols -- or More Words to Confuse You

Okay, more definitions for the terms I mean to use as I go along.  Mind  you, I expect I'll goof now and then.  There's nothing like reading a whole lot of conflicting vocabularies to leave you with too many synonyms.

Solution -- kind of obvious, I hope -- I mean the filled in grid you should have by the end of the puzzle.

Sieve -- not so obvious.  The pattern of the givens at the beginning of a sudoku puzzle. Think of it as an overlay with holes in it that lets you see only certain parts of the solution.  If the right sieve has been applied to the right solution, the game will have a unique outcome.

Symbol -- in a standard sudoku the symbols we use are the nine digits other than zero.  The symbols could be anything -- chairs, bananas, sushi rolls, asterisks, etc., but digits are comfortable to use because most of us can write them without confusing them, and they have a sequence which, while not applicable to the puzzle, makes it easier to assess which ones might be missing or in use.  For clarity's sake, as I go along, I will try to always use a digit (4) to indicate a symbol and a word (four) to indicate a quantity.

Space --  there are a lot of ways to describe the eighty-one cells/positions/boxes/squares/locations in a standard nine by nine sudoku puzzle, but I try to use "spaces" most of the time.  After all, you could draw them as circles, and as long as they were arranged in that familiar pattern it would make no difference whatsoever.

Set -- there are twenty-seven sets in a standard puzzle.  Each set has one occurrence of each of the nine symbols used.  Two kinds of sets are long -- the columns and the rows.  One kind of set is squat -- the squares.  (In variations of sudoku, columns and rows are usually unchanged, but the third sort of set could very different.) That squat set is given all kinds of names, but for now we'll call them squares instead of boxes/nonets/etc., because I want to be able to use the mnemonic "PAIRS IN SQUARES".

There's actually one more word I want to introduce.

Array -- An array is the collection of nine spaces in which a certain symbol appears in the solution.  (Mathematically, yes, it's another kind of set, but for our purposes sets will always have assorted symbols, and arrays will only have one.)  There are nine arrays in a puzzle, which interlock in such a way that each array has a representative in every column, row, and square.

More vocabulary tomorrow.