Q. What is the name of the high school in Glee?

Naked Singles

How to Solve Sudoku

The only option left!

Sudoku - Naked Single Candidates
Finding Naked Singles is simple using candidates!

Naked singles appear in every sudoku puzzle you solve and is where a cell has only one possible option left. Eight of the numbers from 1 - 9 already appear elsewhere in a house that cell belongs to, or all other candidates have been eliminated from that cell through more advanced techniques such as pointing and claiming.

Spotting naked singles when using candidates is very simple... it's the only number left in the box! If you are playing without using candidates though, which is typical for easy puzzles (especially with pencil and paper), then you will tend to locate all the hidden singles first and only look for naked singles when you have exhausted all the hidden singles, as they are more difficult to spot.

There is no single solution path that you have to take and whether you focus on hidden or naked singles will be determined by your preference and use of candidates. Sometimes, the same puzzle (like this one) can be solved by using entirely hidden singles, or by using entirely naked singles! However, there will be times when you will be forced to find a hidden or naked single to make progress.

Sudoku - Naked Single Box
Naked Single in Row 5 Col 8

The difficulty with finding naked singles, without candidates, is in forming a memory map of which numbers already occur in one of the three houses (row, column, box). You can't simply scan one house, or use a cross-hatching method to reveal them like you can with hidden singles. Essentially you have to check each cell and remember how many distinct numbers that cell can "see", and what options are still possible for that cell and if it's only one, it's a naked single!

By picking a cell and working methodically through the numbers from 1 - 9, you can count the number of options still available as you go. As soon as you find two numbers that could possibly be in that cell (or in other words, two numbers the cell can't "see" in any of the three connected houses) you know it isn't a naked single and can stop checking that cell.

Choosing which cells to check is difficult, but you know that the total number of digits in each of the cell's three houses must be at least 8 to have a chance of seeing the 8 distinct numbers required.

You can expect numbers to be repeated across the three different houses (but not within of course) and you only need to eliminate each number once, but there is no point testing a cell for a naked single where there are only 3 digits in the same row, 2 digits in the column and 2 digits in the same box for example, as that is only 7 possible numbers that can be eliminated from 9, so there must be at least 2 possibilities left. If a digit is in the same row (or column) but also in the same box then it only counts once as it is part of two overlapping houses to that cell. By looking for cells with digit counts of eight or higher in the three houses combined you are more likely to find a naked single.

Sudoku - Naked Single Box
Naked Single in Row 1 Col 2

In this example you can see that the cell r1c2 (row 1 column 2) has the numbers 1, 3, 4, 5, 6, 7, 8 and 9 in at least one of the three houses it is part of and means that this cell can only be the number 2 as it is the only number is cannot "see".

There are 9 intersecting digits in total. The numbers 6, 3, 9, 8, 5 appear in the same row. The numbers 1, 7 appear in the same column. And the numbers 6, 3, 1, 9, 7, 4 appear in the same box. The number 9 is found twice, once in the row and once in the box, while the numbers 1 and 7 are in both the cell's box and column.

Sudoku - Naked Single Box
Naked Single in Row 3 Col 7

The r3c7 cell can "see" 12 digits, 8 of which are distinct. The only number it can't "see" in any of the three houses is 3, so that must be the only number than can go in that cell!

The number 9 appears independently in the cell's row, column and box, for a total of 3 times. The numbers 5 and 7 appear twice each - in a box and column, and a row and column relationship. Each other number appears once in either the row, column or box the cell is part of.

The number of times a cell can "see" a particular number is not important, other than to realise any one of these eliminates it from being a candidate for that cell. The important thing is to establish that it can see 8 distinct numbers leaving only one option for that cell.

When you add the candidates to the puzzle you can see immediately where the naked singles are! You may find that you want to use candidates, or want to fill in all the "easy" singles first before resorting to using candidates to save time by not having to write so many in.

All techniques, other than full house, hidden single and naked single, don't actually tell you what number goes in a cell, only what number doesn't go in a cell! This is known as a process of elimination and in doing so you reduce the puzzle down to hidden and naked singles. But when you can't solve a puzzle using just these two techniques and get stuck, this is the point where you will want to start thinking about using candidates to keep track of any eliminations!

Hidden Singles

Play online sudoku now or check out our 300 Sudoku Puzzles: Easy to Extreme book! Or start off with 150 Easy Sudoku Puzzles.

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