Learn Sudoku - Single Candidate

This article assumes you know the basics of Sudoku. If you need a quick introduction to the game, check out the Introduction to Sudoku.

All of the red words in this article are dynamic. Click on them to get helpful clues!

Single Candidate is the sister technique of Single Position. Being one of the fundamental scanning skills needed to complete a puzzle, the earlier you master this, the earlier you can move on to more advanced skills.

So what is it? Simple! It is looking for an empty cell that has only one candidate (thus the name Single Candidate!) You might be thinking right now: "But isn't that what Single Position is?" Well, they are similar, but not the same. With Single Position you are looking for the only empty cell inside of a unit (i.e., row, column, or block) that can hold a particular symbol. Single Candidate is kind of the reverse of this. Instead of focusing on a particular unit (such as a row or column), you will focus on just one empty cell and figure out all of the candidate symbols for that cell. If there is only one candidate then you have found a Single Candidate and may fill it in!

Sound simple? Well, that's because it is! But if you are still scratching your head, don't worry. I'll give some examples to help make the concept more clear. Then I'll give some tips to help you master this technique.

But even if you completely understand, don't skip this article! The technique may be easy to understand, but it should not be underestimated. You will need a firm grasp of this technique before moving onto more advanced techniques. To help you to understand why this technique (and also the Single Position technique) is so important, let me say that all of the advanced techniques simply help narrow down the possibilities (candidates) of empty cells. But it is only with the Single Candidate and Single Position techniques that you can fill in the puzzle. In other words, they are the foundation upon which you will build all of your other skills.

Alright, let's look at an example. In the puzzle to the left I have highlighted an empty cell that can be filled in using the Single Candidate technique. If you are feeling motivated, take a moment to see if you can fill in the cell on your own. Simply go through each possible symbol (1 through 9) and see if that symbol is a candidate for the highlighted cell. If there is only one candidate then you can fill it in.

Don't worry if you can't see right away what the answer is. We'll walk through solving this together.

The first step in looking for all of the candidates of an empty cell is to take note of what row, column, and block that cell is a part of. Click here to highlight them. Next, we just need to remember that no symbol can appear in the same row, column, or block more than once. By keeping this in mind we can walk through each symbol (1 through 9) and see if it is already in the empty cell's row, column, or block. If so then we move on to the next symbol. If it is not already in that cell's row, column, or block then that symbol is said to be a candidate for that empty cell. If there is only one candidate for an empty cell then we can go ahead and fill it in.

Let's now walk through all of the possible symbols, 1 through 9, and take note of which ones are a candidate for the highlighted empty cell. Naturally we'll start with 1. Try to find any 1's that share the same row, column, or block as the highlighted empty cell and click here to check your answer. Now we now that 1 is not a candidate for the empty cell. Let's move onto the number 2. Click here to highlight all of the 2's that are related to the empty cell. Likewise check for 3's, 4's, 5's, 6's, 7's, 8's, and 9's. So the answer is 6. Why? Because that is the only candidate! We can now fill it in.

You may be thinking to yourself right now "That's a lot of work just for one cell! Do I have to do this for every cell in the puzzle?!" You are right, that can be quite a bit of work just for one cell. (Don't worry, you will get much faster!) But here's a tip to help you find out which cells to try this technique on first: Look for single candidates in places where the row, column, and block are almost filled in. This makes lots of sense when you think about it. If a row only has one cell filled in then all of the other cells in that row will have a lot of candidates. On the other hand if a row only has one empty cell left, then there is only one candidate for that cell! So always start in places that have as many cells already filled in as possible.

By this point you should be able to describe what the difference is between Single Position and Single Candidate. They are both quite basic, but are indispensable.

Scanning for single candidates can be slow and tedious. You will quickly realize how important it is to keep track of what you have already figured out. After you calculate all of the candidates of an empty cell, try to remember them so that you won't have to walk through the same steps later in the puzzle. Is this difficult? Yes, especially at first. But the more puzzles you solve the easier this will become. The brain is an amazing thing. The more you perform a series of thoughts in your mind, the brain actually makes physical changes to itself to optimize those thoughts. This is why human number crunchers can do arithmetic in their head so quickly. They have performed the calculations so many times that their brains have actually hard-coded the calculations. The neurons actually rearrange themselves! After solving only 4 or 5 puzzles you will see that you are much faster at the basic techniques and you will be able to remember previous cell's candidates much better.

Getting better at scanning for single candidates will not only help you solve puzzles faster, but will help with the more advanced techniques. This is a good time to stop reading and practice what you have learned by solving some easy puzzles.

When you feel ready, move onto the article about pencil marks.