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Sudoku techniques

The rule states that only one of each digit can be present in each row, column and 3x3 box.

There are 9 cells in a row. There are 9 digits to be placed. So, within each row, all cells must contain a different digit. The same applies to columns and boxes.

 

 

 

The Peers

Because a cell belongs to a row AND a column AND a box, there are always 20 other cells that share either a row, a column or a box with it. We call these the "peers" of the source cell.

When R5C7 contains a digit, it has an effect on all peers. None of those 20 cells can contain the digit that is placed in R5C7.

However, when the cell is empty, we scan the peers to determine what digits it cannot contain. Whatever remains can be placed in the cell. You will have to learn looking at the grid in both directions.

 

Candidates and houses terug naar boven

There are two terms that you need to learn before we start.

The "candidate" is a possible digit that can be placed in an empty cell. With the peers you can "eliminate" candidates. The aim is to eliminate enough candidates so that only one remains.

We will use the term "house" when refering to any group of 9 cells (row, column or box) that must all have different digits.

 

Naked Single terug naar boven

Eliminate the impossible digits by looking at the peers until there is a single candidate remaining.

R6C7 is empty. When you check the 20 peers, you will notice there is only one digit not used by any peer. It is digit number 6. This is the only "candidate" left for R6C7. It is called a "naked single".

This in turn will eliminate that digit as candidate in other peers.


 

 

 

 

Hidden Single terug naar boven

A hidden single exists when there is only one cell left in a house that allows a certain digit.

In this case, R5C5 is not a naked single, because there are seven remaining candidates 1, 2, 3, 4, 5, 7 and 9. When you look at C4 and C6, you can see that only R5C5 remains as a candidate for digit 2.

We call this a "hidden single", because the cell has multiple candidates (7 in the example), but hidden in this set is the last candidate for that digit in a house.

 

 

 

 

Locked Candidates terug naar boven

In stead of placing a digit, "Locked Candidates" helps you to eliminate candidates.

Digit 7 cannot be placed anywhere but in one of the 2 red cells

For the remaining cells of C2, digit 7 will be eliminated as a candidate.

After this, you need to check the grid to see if this elimination has revealed new Singles.

More examples

 

 

 

Locked Sets terug naar boven

It works by spotting sets of pairs (or triples, or even quads) within an house.

Let's start with the easiest to recognize: Naked pairs.

R5C1 and R6C1 both contain <18>, which means that they must be either <1> and <8>, or <8> and <1>. Either way around means that R4C1 cannot be an <8>. Similarly this applies to every other <1> and <8> in C1 and Block4, which can therefore be removed.

 

 


 

 

 

 

A locked set may contain any number of numbers, for example R6 contains <467> in three cells, so all remaining <4>, <6> & <7> can be removed from R6. We have a Naked Triple.

 

 

 

 

Another Naked Triple.

It may be a little confusing that not all 3 cells require all 3 digits as candidate.With any set size, 2 candidates is the minimum for each cell in the set. The maximum number of candidates is always the set size.

In this example, the 3 cells only allow digits 1, 4 and 9. Those digits are all needed to fill those 3 cells, so they cannot be used in any other cell in box 7. A total of 6 candidates can be eliminated from these cells, breaking the puzzle.

You can also have Naked Quads.

 

 

Hidden Sets terug naar boven

Hidden Sets are very similar to locked sets except that the numbers are hidden amongst others. So we are looking for N squares that contain N numbers. We have Hidden Pairs, Hidden Triples or Hidden Quads.

Here we have a Hidden Triple. Because 1.3 and 7 can only exist in three of the cells, that means they must be in those cells, leaving no room for any other. So you can remove the other candidates in those cells.

 

 

 

 

X-Wing terug naar boven

An X-Wing is a advanced technique which can eliminate certain candidates. X-Wings are when there are two lines, each having the same two positions for a number.

Both R1 & R9 contain two cells of <9>. So the <9> might be in R1C2 & R9C9 or R1C9 & R9C2. Although we don't know which way around <9> goes, we do know that all other <9> from C2 can be removed because the <9> is in either R1C2 or R9C2. Similarly, all other <9> from C9 can be removed.

 

 

 

 

 

Swordfish terug naar boven

A Swordfish is another technique which can eliminate certain candidates. We are looking for three rows (or columns) that contain up to three of a particular number in the same relative position.

We can see that C1, C4 & C6 contain up to three sets of <1> in the same relative position. So the <1> might be in R2C1, R9C1& R6C4 or R9C4, R2C6 & R6C6.

Although we don't know which way around <1> goes, we do know that all other <1> from R2 can be removed because the <1> is in either R2C1 or R2C6. Similarly, all other <1> from R6 and R9 can be removed.

 

 

Remote Pairs terug naar boven

Its name comes from a collection of locked pairs that are linked together remotely. The simplest way to picture them is to form a path through an even number of locked pairs The intersection of both ends of the path cannot contain either of the numbers in the locked pair. The path may consist of two, three or four hidden pairs (i.e. 4, 6 or 8 squares) and the intersection might be on a row, a column or in a 3x3 block.

2 can be eliminated as candidate in R5C6.

 

 

 

 

 

 

 

 

 

     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     

Peers for R5C7

 

 

 

 

 

 

 

 

 

     
     
     
     
     
     
     
1    
7    
     
     
  8 3
     
     
     
2 9  
    4
?    
     
     
     
     
     
     
5    
     
     

Naked Single

 

 

     
     
     
     
2    
     
     
     
     
     
     
     
  6  
  ?  
  8  
     
     
     
     
     
     
     
     
    2
     
     
     

Hidden Single

 

 

3   6
     
4   5
     
  7  
     
     
     
     
  *  
  *  
  *  
     
     
     
     
     
     
  *  
  *  
  *  
     
     
     
     
     
     

Locked Candidates

 

 

147
8 		147
8		 9
2 137 136
5 348 346
8
     
     
     
     
     
     
48 6 234
8
18 9 123
8
18 158 7
     
     
     
     
     
     
3 147
8 		148
146
79 		147 146
146
78
2 5
     
     
     
     
     
     

Locked Sets - Naked Pair

     
     
     
     
     
     
     
     
     
     
     
47 2 456
     
     
9 156 3
     
     
467 67 8
     
     

   
     
     
     
     
     
     

Locked Sets - Naked Triple

     
     
     
     
     
     
     
     
     
     
     
   
     
     
   
     
     
     
345
6 		17 146
7
49 2 8
345
79
19 14
     
     
     
     
     
     

Locked Sets - Naked Triple

 

 

     
     
     
     
     
     
     
     
     
     
456
9		 49 569
     
     
24 123
47 		123
7
     
     
256 127 8
     
     
     

   
     
     
     
     
     
     

Hidden Sets - Hidden Triple

 

 

    1
  *  
     
    3
     
  9  
6    
    *
     
9    
     
     
     
9    
     
     
     
  9  
  *  
  *  
    6
     
     
    2
    *
    *
4    

X-Wing

 

 

     
  * 4
9 2 6
4 7 9
* *  
     
6 2  
3 9 5
     
  3 1
     
* * 9
     
9 3 6
  *  
  6 9
     
2 8 3
  5  
4   8
  9 7
8 9 4
     
  5 2
7 1 6
9 5 2
* 3 *

Swordfish




     
     
     
     
    26
  26  
     
     
  26  
     
     
     
     
    29
     
     
  26  
     
     
     
     
     
     
     
     
     
     

Remote Pairs

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