Basic Methods

Basic Sudoku Solving Methods

There are many Sudoku solving methods and solving one puzzle can often use several. Below are some basic and often used methods. A good introduction and reference for Sudoku methods can be found at Sudopedia.

# Hidden Singles

The first technique, called a Naked Single, is the last remaining candidate in a cell. There are two naked singles in the puzzle below, one in row 5 column 5, r5c5, and the other in r8c6. Naked singles are easy to spot because they are the only candidate in their cells.

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Since 9 is the only digit in r5c5, it must also be the only 9 in row 5, in column 5, and the middle box. Thus all other 9s in these houses can be eliminated. Selecting the 9 in r5c5 tells Xsudo to apply the logic, highlighting the Single in green and the eliminations in red. The red 9s can be removed from the puzzle and the green 9 can be assigned.

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# Hidden Singles

Hidden singles are more difficult to spot because they are the last digits in a row, column, or a box, which means they are mixed with other digits in their cell. Cross hatching can be used to find hidden singles like digit 6 in r7c7 (yellow cell below). Rows and columns are cross scanned for digit 6 to find a box where only one place remains to put a 6. The cross hatch prevents digit 6 in all but 2 cells in the last box and one of these cells already has a 7. Thus, digit 6 can be placed in the yellow cell. Digit 6 is one of two hidden singles in the puzzle. Can you see the other one?

Double clicking on digit 6 in r7c7 assigns it as logic and shows the Single in green and the candidates that it eliminates in red. The red candidates can be removed from the puzzle and the green single assigned to the solution.

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# Locked Candidates

Locked Candidates is a more complex move involving two or three candidates instead of one. Row 9 of the same puzzle has two 7s both of which are also in box 8 (light brown). The box has two additional 7s in row 8. One of the 7s in row 9 must belong to the puzzle's solution becasue they are the only 7s in their row, which also satisfies the box's requirement for a 7. Therefore, the red 7s in row 8 cannot be in the box and can be eliminated. In effect, the 7s in row 9 are locked in the box. Selecting the two 7s in row 9 reveals the logic and eliminations.

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# How To Find X-Wings (a fish!)

An X-Wing is a group of 4 candidates, or 2 pairs of candidates where:

· Each pair contains the only digits in a row or column, and

· The two pairs line up in the opposite direction, i.e., column or row.

X-Wings are not easy to spot but can be found using the candidate filter to highlight cells with a particular digit. The grid below shows the candidate filter for digit 8 where it's easy to see the two pairs in rows 2 and 7, which also line up in columns 5 and 8.

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# Confirming the X-Wing

Double clicking the X-Wing's 4 digits assigns them as logic and confirms the X-Wing, as shown below where the rows with pairs are highlighted gray and their candidates are linked (aligned) through the green columns. The logic of the X-wing goes like this. One of the 8s in each black row must belong to the solution (be true). Which ever two 8s are true, they must also be in the two green columns thus no other 8s can be elsewhere in the columns. Thus, all the red 8s can be removed.

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# Looking at Logic

Whenever logic is entered, Xsudo displays eliminations, assignments, and the logic that causes them. The logic for the X-Wing is shown below where solid red lines are truths and light green lines are links.

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# Looking at Logic in 3D

In three dimensions, the X-Wing looks like this. 3D is mostly useful for looking at connections but editing can also be done.

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# A Logical Way of Reasoning

One simple way of reasoning is based on truths and links, which can be seen by looking at the X-Wing diagram. In Sudoku, each row, column, and box must have exactly one of every digit thus we can reason that:

· Each black row must have exactly one true digit 8, thus two of the four (blue) eights must be true.

· The green links contain all blue 8s including which ever two are true.

· Since the green links contain the two true blue 8s, the other orange 8 can't be true and can be removed.

This same argument can be made anytime the number of links is the same as the number of truths. links contain all the 8s in the black sets and the number of links equals the number of black sets. As shown below, this is true for Singles (A), Locked Candidates (B), and the X-Wing (C). This simple idea is the basic idea behind a more general approach to Sudoku.