How to read R1C2, and why the notation matters

The short version

There are only two conventions you need, and they are both counting.

Cells are Row + Column. R1C1 is the top-left corner, R9C9 is the bottom-right. R4C7 is fourth row down, seventh column across.

Boxes are the three-by-three blocks. This site names them by position — top-left, centre, bottom-right — rather than numbering them, because different books number them differently and a name does not need a decoder ring.

Everything else is a consequence of those two.

Why the name matters

A technique you cannot name is a technique you cannot check.

Consider the sentence "the 4 can only go in the eighth row, fourth or eighth column". It is accurate and nearly useless. Now: "in column 4 the 4 has two homes, R8C4 and R9C4". You can put a finger on both cells, verify the claim, and disagree with it if it is wrong.

That is the whole argument for notation. It converts reasoning into something checkable, which is the only kind of reasoning worth trusting on a sudoku board.

Reading a cell name

Two digits, one letter each, in that order.

Which box a cell belongs to is arithmetic, not memory: rows 1-3 are the top band, rows 4-6 the middle, rows 7-9 the bottom. Columns work the same way left to right. R8C2 sits in the bottom band and the left stack, so it is in the bottom-left box.

Writing candidates so they stay readable

The mistake almost everyone makes is writing candidates in whatever order they arrive: a 3, then squeeze in a 7 above it, then a 1 in the margin.

Instead, reserve nine fixed positions in every cell — the same layout everywhere, in reading order:

`` 1 2 3 4 5 6 7 8 9 ``

A 7 is always in the bottom-left slot. A 2 always top-middle. After a few puzzles you stop reading the digits and start reading positions, which is far faster, and a missing digit becomes a visible hole rather than something you have to check by reciting the list.

This is not a personality preference. It is the difference between a candidate grid you can scan in one glance and a candidate grid you have to decode cell by cell.

Describing a move out loud

Once cells have names, a move becomes a single sentence, and the sentence is testable.

• A placement: "R2C6 is 5."
• An elimination: "remove 4 from R8C2, R8C3 and R9C3."
• A pattern: "in columns 4 and 8, the 4 has two homes each, and they line up in rows 8 and 9."

That last sentence is how every technique article on this site is written, and it is not decoration. If a pattern cannot be stated in that form, the pattern is probably not there — vague intuition dressed up as a shape is the most common way solvers talk themselves into a wrong elimination.

When to write candidates down

Not immediately. A full candidate grid is expensive: eighty-one cells times up to nine digits is a lot of pencil work, and on an easy puzzle you will fill the board before you need any of it.

The workable threshold is: start writing when scanning stops producing results. While hidden singles are still falling out of the board, candidates are overhead. Once you have swept every digit and found nothing, the board has stopped being readable at a glance, and that is the moment the grid earns its cost.

There is a middle setting worth knowing: write candidates only for digits that are nearly finished, or only in the two or three boxes that look congested. Partial marking is not a compromise — it is usually the right amount of information, and it keeps the board legible.

When to pencil-mark, in more detail.

Where to use it

Use it in your own head, not just on paper. The habit of naming a cell before reasoning about it catches errors earlier, because a claim you cannot point at is a claim you probably have not verified.

The next four techniques — naked pairs, hidden pairs, pointing and claiming — are all stated in this notation. Reading them without it is possible. Checking them without it is not.