Standard Notation

First off

There are many people, who use many different notation techniques. Some use the notation presented on this page, some use dots instead of numbers, some use colors, some draw pink elephants onto the Sudoku grid. There is no right or wrong way, if it helps you finish your Sudoku (and you have fun doing it).

While there are many different notations out there, the (by far) most common one is the one described on this page: the Standard Notation.

What is notated

On the previous page "Candidates", we explained that there are (beside others) two commonly used candidate types: cell candidates and box candidates.

Cell candidates are, by far, the most important ones if you want to solve a Sudoku.

That is why the standard notation does only take cell candidates into consideration. We only deal with the question "For this cell, what numbers are possible?".

Standard Notation Advantages

The standard notation has the following advantages:

  • It is easy to use.
  • It offers clarity.
  • It is based on the human brain's ability to read patterns.
  • It is used by many people and computer programs.

How it is notated

You have already seen several examples of the standard notation on the previous page "Candidates".

Here is a very minimalistic example.

Each cell contains all possible numbers for that cell in a matrix-like notation. I.e. the 1 is always in the top left corner, the 3 is always in the top right corner, etc.

So each candidate has its fixed position within its cell.

Even when candidates are eliminated, the other candidates' positions stay the same.

Having fixed candidate positions is a big advantage, as our brains are very good at recognizing such patterns.

The most important thing

When you start writing down possible candidates, two things are extremely important:

  • consistency: don't switch notations like crazy. Stick to something. Switching will only get you confused and give you a hard time.
  • completeness: if you fill in candidates for a cell, be sure that all possible candidates are considered.

A completeness example:

The candidates 8 and 9 are entered in the cell, but a 7 is as likely there. So this cell's candidates are not complete.

If you ask anyone to help you with your Sudoku and they see something like this, they will start to doubt every single candidate you have entered and do it all over again.

Missing a candidate is one of the easiest ways to screw up your Sudoku, but also one of the easiest to prevent, if you keep it in mind.

Human vs. PC Solver

Human approach

Of course it is absolute overkill to start every Sudoku with all candidates notated like this, so it is best if you first start to enter possible candidates when

  • a cell is down to very few possible candidates (two or three) or
  • you are stuck and need to use more complicated techniques.

Too many candidates are more likely to confuse you than help you.

For a human solver, it is much more likely that a grid will look something like this.

Computer approach

There are, of course, also people who like filling in every possible candidate from the start. It is not efficient and yet it might be fun using a computer-like approach, because it is exactly how a computer solver might see and solve a Sudoku.

Take the Solver for example. It will first fill in all possible candidates like this.

Then, it will eliminate all candidates that are seen by givens.

This grid will be the result.

It will be the basis for all the different techniques that the Solver uses thereon after.

All those notated candidates might be confusing for someone who just started solving Sudokus, but it illustrates quite well how the computer does it.