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TOP > Techniques > Naked Pairs/Triples/Quads

Solving Techniques 2
Naked Pairs/Triples/Quads

When a pair like [1,2] [1,2] exists, this technique allows for the elimination of [1,2] as candidates from other cells.

Naked Pairs

The candidates for the center box are [2,6 and 7]. However, since there is already a 7 in row F, at F9, a pair of [2,6][2,6] arises. Hence, [2 or 6] can't be entered at D5, confirming that a 7 is in this cell.

In the example below, too, a [2,3] pair arises between G1 and I1, in the lower left box. Hence, a 2 or 3 can't be in the other cells of this box. Therefore, a [6] goes in I2 and at the same time a [1] is confirmed for H2.


Naked Triples

Lets examine row F. Between F1[1,2], F4[1,2,6], and F5[2,6] a triple of 1, 2, 6 arises. In these cells, a 1, 2 or 6 will be entered, eliminating the possibility of having these numbers in other cells in the same row. Hence, an [8] at F2 is confirmed.

{3,3,3} of [1,2,3][1,2,3][1,2,3] ,
{3,3,2} of [1,2,3][1,2,3][1,2],
{3,2,2} of [1,2,3][1,2][2,3],
and {2,2,2} of [1,2][2,3][1,3],

are all types of triples that will work out.

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Naked Quads

The same can be applied to patterns of 4.

Naked Pairs/Triples/Quads is also a basic problem solving technique for Sudoku.

The fewer the hints, the more candidates there will be for the cells, and there will be many naked patterns that will arise. Pairs are easy, but triples and quads occur not just with the same three or four numbers, but also work when there are not enough numbers, so they are trickier to find. Once you start looking for these patterns, the problems will become much easier to solve.

Names of cells in Sudoku

A1A2A3A4A5A6A7A8A9
B1B2B3B4B5B6B7B8B9
C1C2C3C4C5C6C7C8C9
D1D2D3D4D5D6D7D8D9
E1E2E3E4E5E6E7E8E9
F1F2F3F4F5F6F7F8F9
G1G2G3G4G5G6G7G8G9
H1H2H3H4H5H6H7H8H9
I1I2I3I4I5I6I7I8I9

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