Proven Sudoku
How to read a sudoku grid
Solving guides use a shorthand for talking about squares and patterns. None of it is complicated, but all of it is assumed. This page explains every term the technique pages use.
Naming a square: r4c7
Rows are numbered 1 to 9 from the top. Columns are numbered 1 to 9 from the left. A square is named by its row and then its column, so r4c7 is the square in the fourth row, seventh column. It is read aloud as "row four, column seven".
The same shorthand names a whole row or column on its own. r4 is the entire fourth row. c7 is the entire seventh column. b3 is the third box, and boxes are numbered 1 to 9 left to right, top to bottom, so b1 is the top left box and b9 the bottom right.
House
A house is any row, any column, or any box: the nine squares that must contain the digits 1 to 9 exactly once between them. Most techniques are really statements about houses, which is why one word covers all three.
Candidate and pencil mark
A candidate is a digit that could still go in a square, given everything placed so far. The small digits you write into an empty square are your pencil marks, and they are the same thing. Almost every technique works by removing candidates rather than by placing digits: you narrow the possibilities until only one is left.
Given and placement
A given is a digit printed in the puzzle at the start. A placement is one you worked out. The difference matters for a small family of techniques that reason about how the puzzle was built, because those arguments are only valid about squares you deduced.
Elimination
An elimination is the removal of one candidate from one square, because it has been proved impossible. A technique that produces no eliminations has told you nothing, however impressive the pattern looks.
Bivalue and bilocation
A bivalue square has exactly two candidates left. A digit is bilocation in a house when it has exactly two squares left it could go in. Both are the raw material for the chain techniques, because two options means that ruling one out forces the other.
Conjugate pair, strong link, weak link
When a digit has only two possible squares in a house, those two squares form a conjugate pair, also called a strong link: exactly one of them is that digit, so if one is not, the other is.
A weak link is the softer statement: two squares that see each other cannot both hold the same digit, though both might be something else. Chains work by alternating strong and weak links.
Seeing
Two squares see each other when they share a row, a column, or a box, so they can never hold the same digit. When a page says a candidate can be removed from any square that sees two others, this is what it means.
Base sets and cover sets
The fish techniques are stated over two groups of houses. The base sets are the houses the digit is confined within. The cover sets are the houses that catch every one of those positions. When there are as many covers as bases, the covers are used up entirely, and the digit can be removed from the rest of them.
Fin
A fin is a leftover candidate that spoils an otherwise exact pattern. Rather than throwing the pattern away, the eliminations are narrowed to the squares that hold whether the fin is true or not.
One solution assumed
A properly set puzzle has exactly one solution. A family of techniques uses that as evidence: if a set of candidates would allow two different completions, that arrangement cannot be the real one. Those pages say so at the top, because the reasoning is only valid on a correctly built puzzle.