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Quad Bulge Series Vol. 2: Naked Fitness

The "naked single" solving technique also known as "singleton" or "lone number" is one of the simplest Sudoku solving techniques. Using this technique the candidate values of an empty cell are determined by examining the values of filled cells in the row, column and box to which the cell belongs. If the empty cell has just one single candidate value then this must be the value of the cell. In the example below, if you examine the values of the filled cells in the same row, column and box as the highlighted cell you can see that the highlighted cell has only a single candidate value since all other possible candidate values are already used. To illustrate this more clearly the same example with candidate values in empty cells is shown below, as you can see the highlighted cell has a single candidate value. The "naked pair" solving technique is an intermediate solving technique.

Each individual cell in the naked triple does not have to contain all three candidates however. In fact it is perfectly legal for each individual cell to have only two of the three candidates. The highlighted cells in the example below show a naked triple containing the candidate values 2,4,7 in the centre box.

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These candidate values can be removed from all other unsolved cells in the box. This reveals a naked pair containing the candidate values 3,5 in the central row of the same box.

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Reducing the candidate lists of other unsolved cells in the same row reveals a naked single in that row. The "naked quad" solving technique is similar to the naked triple solving technique described above. In a naked quad, four cells in a row, column or box contain some combination of the same four candidates only.

The highlighted cells in the example below show a naked quad containing the candidate values 1,7,8,9. This reveals a naked pair containing the candidate values 2,6 in the bottom row of the same box.

The "naked quint" is the final solving technique in the naked subset series and is similar to the naked triple solving technique described above.

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In a naked quint, five cells in a row, column or box contain some combination of the same five candidates only. The highlighted cells in the example below show a naked quint containing the candidate values 1,2,3,6,8. These candidate values can be removed from all other unsolved cells in the row.

Naked Quad. The "naked quad" solving technique is similar to the naked triple solving technique described above. In a naked quad, four cells in a row, column or box contain some combination of the same four candidates only. The highlighted cells in the example below show a naked quad containing the candidate values (1,7,8,9). 'Naked' in this context refers to all the remaining possible candidates on a cell which are going to be used in a strategy. The simplest such situation is a Naked Single - or the last remaining candidate on a cell. Naked Quad A Naked Quad occurs when exactly four digits are candidates in four cells of a house. You can eliminate these digits from the other cells in this house. In the sudoku diagram below, in the third row, only the four digits 3, 4, 6 and 8 can be placed in the R3C1, R3C2, R3C3 and R3C9 cells.

This reveals a naked pair containing the candidate values 5,7 in same row. Sudoku Solver.

Naked Quad

Naked Subsets. Hidden Subsets.

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Play puzzle number Go. Naked triples are harder to spot.

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Sometimes, all three numbers in a naked triple appear in all three squares of the triple. However, sometimes the numbers of the triple don't all appear in all three squares, as in the example below. The squares that have 7, 8, and 9 in red form a naked triple.

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Notice that if a square other than one of the naked triple squares were set to 7, for example, then the three naked triple squares would only have 8 and 9 as their candidates.

The square that has 7, 8, and 9 in it would have both 8 and 9 as its remaining candidates, but each of the other two naked triple squares would be set to 8 and 9, respectively.

Naked Pairs, Naked Triples, Naked Quads Strategy

This would be invalid, because the square with 8 and 9 as its candidates would no longer have any valid options. The following interactive puzzle can be solved using nothing but the naked triples strategy. Naked quads are rare, but they can occur. They can be difficult to find, however, unless you specifically look for them.

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In the example above, the numbers in red form a naked quad. The four squares that contain the red numbers only contain numbers 2, 4, 8, and 9. That means that those four squares MUST contain those four numbers. Because of that, you can eliminate the 4 as shown crossed out in red.

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The following interactive puzzle can be solved using nothing but the naked quads strategy. Try solving the following interactive puzzle. It can be solved using only the Naked Pairs, Triples, and Quads strategy.

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