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What is notated
As opposed to Standard Notation, where we only notate cell candidates, with Cell&Box Notation we notate
- cell candidates, as well as
- box candidates (Snyder Notation).
As a reminder: for box candidates we ask "For this number, what cells are possible (within the 3x3 box)"
For more on candidates, see this page.
Snyder Notation
Notation of box candidates is also called Snyder Notation, which is named after Thomas Snyder, a renowned puzzle solver and handcrafter. Since we already talked about cell candidate notation on the previous page, this page will focus on the box candidate part.
While certainly not being the first person to notate box candidates, Thomas Snyder was the one showing the world several times at championships just how efficient that technique alone is. It has been since promoted by several YouTube channels, among others the biggest Sudoku YouTube channel Cracking the Cryptic.
Snyder Notation has its advantages primarily in speed solving, after all, Thomas Snyder has won several Sudoku championship titles. The use and notation of box candidates helps to quickly see and eliminate candidates via pairs and triples.
So it is helpful when it comes to lower level solving techniques (mostly up to "Locked Candidate" or fishes like the "X-Wing"), and might increase your solving speed there.
The limitations of box candidates are with Sudokus that are much harder than the Sudokus you will find at speed solving competitions. For the more complicated solving techniques you need to also be able to notate cell candidates.
That is why the sudoku.coach app uses the Cell&Box Notation (using cell candidates as well as box candidates).
How it is notated
As opposed to Standard Notation, with Cell&Box notation, we will put all cell candidates into the center of the cell.
The box candidates are at the corners of the cell.
See how the fixed 3s prevent a 3 from being anywhere except those two cells (within the 3x3 box)? Same with the 9.
The cell candidates being in the middle and the box candidates being in the corners makes sure that you can clearly distinguish between the two, which is very important.
Where notating box candidate (Snyder Notation) helps you
Here is a very basic example. See how the given 7s block most cells in the bottom left box?
We will pencil mark those two cells where a 7 is possible.
Since we know that one of those two cells is going to be a 7, we can eliminate all 7s in the line that goes in direction of the candidates.
In combination with all 7s in the upper half of the Sudoku grid, we now know where the 7 must go in the top left box.
It does not matter which one of those two cells will contain a 7 in the end. The rest of the column cannot contain another 7 either way.
But is it really that helpful?
Now you might say that you could have seen that without notating the box candidates, which can of course be true, but that is true for all candidates. Candidates are just candidates, whether they are on paper or simply in your head. The point of notation on paper is simply that you don't risk to forget that info.
Imagine the Sudoku grid being like this instead. (The two 7s in the top half are missing.)
Here, we can still enter the two candidates. And they will be a reminder for the rest of the solving process that this column cannot contain another 7.
If the two fixed 7s in the top half reveal themselves later, you can immediately see that since the column is blocked, the 7 can only go in the top left cell.
The other advantage
The other advantage (besides quickly seeing what candidate is blocked in what row or column) is the following:
If there are only two cells in a box that can be a certain candidate, and one of those two cells is taken by another number, you immediately know that the other cell must then hold the candidate.
Example: If this is the position...
... and one of the cells is taken by another number...
... the other cell must be a 7. Easy as that.
In general: having the grid full of cells that contain only two candidates (be it cell or box candidates) can lead to very satisfying solving chains, where you can basically turn off your brain for a couple of seconds, and fill in solution after solution without thinking.
Balancing it out
Don't do this!
Pencil marks can be very useful for solving a Sudoku faster, but as with cell candidates, don't overdo it.
Marking six box candidates like in this example accomplishes nothing. Quite the opposite: it slows you down and only makes more clutter.
The most useful situations are, when the number can only be in two or three cells in a row or column.
Candidates distributed over more than one line (row or column) are only useful if they interact with another box like in this example: