Sudoku: Naked Candidates Reduction Method Clarified

In Sudoku ‘naked’ candidates may be present in pairs, triples or quads. The candidates are ‘naked’ if they are alone, i.e. not ‘hidden’ among other candidates in the squares. If ‘naked’ candidates are present those numbers must necessarily be in those squares. Therefore, those candidates can be removed the other squares within the group. In the squares with ‘naked’ candidates we do not yet know where each of the numbers should be placed, only that they collectively should be in those squares. Later in the solving process the unique position of each number will become clear. Let us go through the method for pairs, triples and quads and give some examples.

Sudoku Naked Pairs

If two squares in a group (row, column or block) have the same pair of candidate numbers and only these, then these candidates make up a ‘naked’ pair. The two numbers are linked to those two squares. Therefore, those candidate numbers can be removed from the other squares within the group.

This board shows a 'naked' pair (2 and 9, shown in blue) in column B in squares B4 and B8. These candidates are 'naked' because no other candidates are present in those squares. The numbers are therefore linked to those squares. The candidates, which can be removed from the other squares (2 from B2, B3, B6 and B9 and 9 from B2 and B9), are shown in red.
In the small picture you can see the final solution for this part of the board. In column B number 9 should be in square B4 and number 2 in square B8.

Sudoku Naked Triples

If in three squares within a group the candidates are limited to three numbers, those candidates make up ‘naked’ triples. All three candidate numbers need not be present in all three squares, but those numbers are linked to the three squares. Therefore those three candidate numbers can be removed from the other squares within the group.

This board shows 'naked' triples (3, 4, and 6, shown in blue) in block P in squares A8, B8 and C8. These candidates are 'naked' because no other candidates are present in those squares. The numbers are therefore linked to those squares. The candidates, which can be removed from the other squares (3, 4 og 6 from square A7, 3 and 6 from square B7, 4 and 6 from square C7 and 3, 4 and 6 from square A9), are shown in red.
In the small picture you can see the final solution for this part of the board. In block P number 6 should be in square A8, number 3 in square B8 and 4 in square C8.

Sudoku Naked Quads

If in four squares within a group the candidates are limited to four numbers those candidates make up ‘naked’ quads. All four candidate numbers need not be present in all four squares, but those numbers are linked to the four squares. Therefore those four candidate numbers can be removed from the other squares within the group.
This board shows 'naked' quads (2, 5, 7 and 9, shown in blue) in row 2 in squares D2, E2, F2 and H2. These candidates are called 'naked' because no other candidates are present in those squares. The candidates, which can be removed from the other squares (5 and 9 from squares A2 and G2), are shown in red.
In the small picture you can see the final solution for this part of the board. In row 2 number 7 should be in square D2, number 9 in square E2, number 2 in square F2 and number 5 in square H2.

This method of finding ‘naked’ candidates in Sudoku can be used repeatedly for candidate reduction. Thereby the solution of the Sudoku puzzle may be easier to find. Shortly we will go through other effective methods of candidate reduction.