Sudoku Basics: Naked Pairs & Singles
Nothing beats the feeling of playing and solving your first easy Sudoku puzzle. And once you’ve completed one, you want to test out more of your Sudoku skills and play on another grid. It's like getting an itch to use new software on your phone and tapping that app icon as soon as possible.
While all these skills are helpful and can help you slowly solve a grid, they have their limitations and lack efficient elimination power within the game. If you want to be able to solve medium Sudoku puzzles or one of higher difficulty, it's time to dip into the last end of the basics.
That’s why in today’s Sudoku game article, we’ll learn about naked pairs and singles— powerful elimination tools that work hand-to-hand with pencil marking. Continue reading for more Sudoku tips!
Prerequisite to Using Naked Pairs & Singles
Before we define naked pairs and singles (or as some Sudoku players around the world call it, a twin or just a pair), you must know what pencil marking in Sudoku is. To briefly sum up, pencil marks in a Sudoku game are digit candidates that are possibly correct for that particular. It could be that both 1 and 4 are the answer to a cell, so you put in temporary notations of 1 and 4 in that particular cell.
They are called pencil marks as the original game was created on sheets of paper and these digits can be erased anytime based on your solving process and preferences.
What Are Naked Pairs & Singles?
To make use of naked pairs and singles, it’s ideal that you fill in the whole grid (or at least a significant portion of it) with pencil marks. A lot of people use the Snyder notation technique while playing on most puzzles to make this process faster, but we’ll be using basic pencil marking today.
Naked pairs are a pair of two-digit pencil marks that belong in the same row, column or box. Here’s an example so you can easily identify it in a Sudoku grid:
Now, shift your focus to box 8. You can see that cells r8c5 and r8c6 have the same two-digit notation, a 4 and 5. This is the first naked pair we’ll be using.
Fully understanding how to use naked pairs and singles in Sudoku relies on knowing what peer cells are. Peer cells are cells that are connected via the same row, column or box. Let’s pick out this number 5 in cell r4c4. The peer cells for this cell are the whole of box 5, the entire row 4 and the entire column 4.
Now, is the 1 in cell r9c4 a peer cell to the 5? Yes, it is! Is the 3 in r4c9 peers with the 5? It also is. Knowing these peer cells is integral in the elimination process involved with using naked pairs and singles.
Using Naked Pairs & Singles
Let’s return to our identified naked pair in our sample Sudoku grid. So our pair has a 4 and a 5, and are both in the same single row in box 8. We’ll use the naked pair to begin the elimination process, but how does it work?
Naked pairs work by eliminating every other candidate within their peer cells, and it plays under the logic of Sudoku itself since numbers can’t be repeated in any row, column or box. By identifying a pair of candidates for a specific area of the grid, we can significantly reduce the number of candidates to eliminate as we continue to solve.
Using our naked pair, we can eliminate all the other 4s and 5s that are peer cells with the naked pair. Let’s start within the box. There is a 4 in cell r8c4 and 5s in cells r7c6 and r9c6. We can now remove them and reduce the number of candidates in this box.
And after removing the 4 in cell r8c4, we’re left with just one candidate digit, a 9. This is what we call a naked single. Why is it called a naked single? Because it is one digit that has no other number to hide behind and is the only number that can go in that specific cell. A naked single usually counts as the answer you can use to fill in the cell (unless there were errors in the pencil marking process). So now, we fill in cell r8c4 with an answer of 9.
Now that we’ve removed the 4s and 5s in the box, let’s eliminate those in the same row as our naked pair. Now that we’ve removed several more digits in row 8, we’re left with more naked singles, with an 8 in cell r8c7 and a 7 in r8c9. With these answers, we can also eliminate the candidate 9 in r8c1, which then leaves us with a naked single of 2.
Congratulations! You’ve just learned how to use a naked pair for more efficient elimination and create naked singles for answering and further elimination!
Basic Rhythm to Try in Free Sudoku Puzzles
To give you an idea, try using this rhythm every time you see a naked pair in your Sudoku game:
1. Identify the naked pair
2. Clear out the box they’re in
3. Clear out the row or column they’re in
4. Identify naked singles
5. Eliminate notes using the answer from a naked single
Rinse and repeat until you get into the flow of solving your Sudoku puzzle! Since we didn’t use Snyder notation in our sample Sudoku grid, you can see that there are cells with even three candidates. Elimination can potentially thin them out and even create more naked pairs to work with.
To become more proficient in using this technique, try it out on an easy Sudoku puzzle here at our site first or finish off the sample grid we used above. To give you a hint, there’s another naked pair in box 8 you can start with if you’re going to finish the sample Sudoku puzzle we provided.
Have fun and continue your journey to becoming a capable Sudoku player!