Sudoku HowTo

# Naked Candidates

When a cell contains only the candidates that are being considered, and the candidates are not hidden or covered by a clutter of additional values they are referred to as Naked Candidates.

A Naked Single is a cell that contains only one candidate.

A Naked Single becomes the solution for that cell.
A Naked Pair is two cells in the same unit that contain the same two candidates, and only those two candidates.

When there are two cells in the same unit (row, column or box) and each cell contains only the same two candidates, those two candidates have to be placed in the two cells. If either of the two candidates are placed in any other cell in that unit then there will only be one value left to fill two cells.

A Naked Pair doesn't determine which candidate eventually goes into each cell but it does mean the two values cannot be placed in any other cells in the same unit.

In the Naked Pair example in Figure 1 the blue cells in box 2 are a Naked Pair with the candidates 1 and 6.

The values 1 and 6 have to be placed in the blue cells in box 2. If either the 1 or the 6 was to be placed in any other cell in box 2 then there would only be one value left and two cells to fill. The 1 and 6 can be removed from all other cells in box 2.

The example puzzle has multiple Naked Set instances that can be seen by starting it in the Helper.
A Naked Triplet is three cells in the same unit that contain a combination of only three candidates. Not all three candidates have to be in all three cells but the total number of candidates in the three cells can only be three.

Just like with the Naked Pair, this pattern does not determine which of the three candidates will go into each of the three cells but it does mean the three candidates cannot be in any other cells in the unit.

In the Naked Triplet example in Figure 2 the three blue cells in row 5 only contain candidates 2, 7 and 8.

The values 2, 7 and 8 have to end up in the three blue cells. If either the 2, 7 or 8 is placed in any other cells in row 5 then there would only be two values left to fill three cells. The 2, 7 and 8 can be removed from all other cells in row 5.

The example puzzle has multiple Naked Set instance that can be seen by starting it in the Helper.
A Naked Quad is four cells in a unit that contain some combination of a total of four candidates. Just like the Naked Triplet not all four candidates need to be in all four cells but the total number of candidates in the four cells can only be four.

Once again, this does not determine which of the four values will finally go into each of the four cells, but it does mean the four values cannot be in any other cells in the unit.

In the Naked Quad example in Figure 3 the blue cells in column 7 only contain the candidates 2, 6, 7 and 9.

The values 2, 6, 7 and 9 have to be in the blue cells in column 7. If either of these values is placed in any other cell in column 7 there would only be three values left to fill four cells. The 2, 6, 7 and 9 can be removed from all other cells in column 7.

You may also notice that the candidates removed in this example could have been identified by seeing the Hidden Pair of 1 and 5 in column 7. It is often the case that a Naked Set and a Hidden Set exist in the same container.
9 July 2014
by John
RE: Comments and feedback for nakedCandidates

Thanks for pointing this out. Its all fixed now.
4 July 2013
by r ross
RE: Comments and feedback for nakedCandidates

some thing is wrong in figure 2 you talk about row 6 but the colored cells are in row 5

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