Sudoku Glossary

Welcome to our Sudoku Glossary! In this comprehensive guide, you’ll find clear definitions and explanations for key Sudoku terms, techniques, and strategies. Whether you’re new to Sudoku or an experienced solver, this glossary will serve as a valuable resource as you sharpen your skills and deepen your understanding of the game.

What is a cell in Sudoku?

A cell in Sudoku refers to an individual square or box within the Sudoku grid. The standard Sudoku puzzle consists of a 9×9 grid, which is divided into 9 smaller 3×3 blocks (also known as boxes or regions). Each cell is the basic element of the Sudoku grid and can hold a number between 1 and 9. The objective of the Sudoku puzzle is to fill in every cell with a number, following the rules of the game:

1. Each row must contain the numbers 1 through 9, with no repetition.
2. Each column must contain the numbers 1 through 9, with no repetition.
3. Each of the nine 3×3 blocks must contain the numbers 1 through 9, with no repetition.

So, a cell in Sudoku is a single square within the grid that needs to be filled in with a number according to the rules of the game. There are 81 cells.

What is a row in Sudoku?

A row in Sudoku refers to a horizontal line of cells in the Sudoku grid. In a standard 9×9 Sudoku puzzle, there are 9 rows, each containing 9 cells.

What is a column in Sudoku?

A column in Sudoku refers to a vertical line of cells in the Sudoku grid. In a standard 9×9 Sudoku puzzle, there are 9 columns, each containing 9 cells.

What is a box in Sudoku?

A box in Sudoku, also known as a block or region, refers to one of the nine smaller 3×3 grids within the standard 9×9 Sudoku puzzle. The 9×9 grid is divided into nine equally sized 3×3 boxes, arranged in a 3×3 layout. Each box contains 9 cells.

So, a box in Sudoku is one of the nine smaller 3×3 grids within the larger 9×9 grid that needs to be filled in with numbers according to the rules of the game, ensuring that each number from 1 to 9 appears only once in each box.

What is a naked single in Sudoku?

A naked single, also known as a “lone number” or “singleton,” is a basic Sudoku solving technique. In this technique, a cell has only one possible candidate number left based on the numbers already filled in the row, column, and box (also known as a region or block) it belongs to.

To identify a naked single, you must examine the surrounding cells in the same row, column, and box to see which numbers are already present. The one number that is missing from the row, column, and box is the only possible candidate for the naked single cell.

Naked singles are often the first technique used when solving Sudoku puzzles, as they are relatively easy to spot and help reduce the number of possibilities in the grid.

What is a hidden single in Sudoku?

A hidden single in Sudoku is a cell that can only contain a specific number, not because it is the last remaining candidate for that cell, but because that number can’t be placed anywhere else within the same row, column, or box (region or block) it belongs to.

To identify a hidden single, you must look for a number that can only fit in one specific cell within a particular row, column, or box, even though that cell might have multiple remaining candidates. The reason it’s called a “hidden” single is that the unique placement of the number may not be immediately obvious, as it requires examining the constraints imposed by other filled numbers in the same row, column, and box.

Hidden singles are a fundamental technique in Sudoku and can help you progress in the puzzle by logically deducing where certain numbers must be placed, even if a cell still has multiple candidates.

What is a naked pair in Sudoku?

A naked pair in Sudoku is a technique used to eliminate candidate numbers in a row, column, or box (also known as a region or block). It occurs when two cells in the same row, column, or box have the exact same two candidate numbers and no others. These two numbers form an exclusive pair, meaning they must occupy those two cells.

The logic behind naked pairs is that since these two numbers can only be placed in those two specific cells, they cannot appear in any other cells within the same row, column, or box. As a result, you can safely eliminate these two numbers from the candidate lists of other cells in that row, column, or box.

Naked pairs are a more advanced Sudoku-solving technique than naked singles or hidden singles, and they can help you make progress in a puzzle by reducing the number of possibilities in the grid.

What is a hidden pair in Sudoku?

A hidden pair in Sudoku is an advanced solving technique that occurs when two cells in the same row, column, or box (also known as a region or block) exclusively share two candidate numbers, even if the cells have more than two candidates. These two numbers form a hidden pair, meaning they must be placed in those two cells within the row, column, or box.

The logic behind hidden pairs is that since these two numbers can only be placed in those two specific cells, all other candidate numbers in those cells can be eliminated. The two numbers that form the hidden pair are then the only candidates left for those two cells.

Hidden pairs can be more difficult to spot compared to naked pairs because the cells containing the hidden pair may have other candidate numbers as well. However, recognizing hidden pairs can significantly help you make progress in a Sudoku puzzle by narrowing down possibilities and simplifying the grid.

What is a locked candidate in Sudoku?

A locked candidate, also known as a “pointing pair” or “box-line reduction,” is an intermediate Sudoku-solving technique that helps eliminate candidate numbers from a row, column, or box (region or block). This technique occurs when a specific number can only be placed in a specific row or column within a box, effectively “locking” it into those cells.

The logic behind locked candidates is that since a particular number can only be placed in a certain row or column within a box, it cannot appear anywhere else in that row or column outside the box. This allows you to eliminate that number from the candidate lists of other cells in the same row or column that are not part of the box in question.

To identify locked candidates, look for a number that is restricted to a single row or column within a box. Once you find such a number, you can safely eliminate it as a candidate from other cells in that row or column outside the box.

Using the locked candidate technique can help you progress in a Sudoku puzzle by reducing the number of possibilities in the grid and making it easier to spot other techniques like naked singles or hidden singles.

What is an X-Wing in Sudoku?

An X-Wing is an advanced Sudoku-solving technique that helps eliminate candidate numbers in rows and columns. It occurs when there are two parallel rows (or columns) in which a specific candidate number appears exactly twice, and the appearances of the candidate align with each other in the corresponding columns (or rows).

The X-Wing technique is based on the fact that if one of the aligned candidate numbers is the correct number in one row, then the other candidate number in the same column must be the correct number in the other row, forming a diagonal pattern like an “X.” Since the candidate numbers in these aligned cells must be the correct numbers in their respective rows, the same number can be eliminated as a candidate from other cells in the intersecting columns (or rows, if you found the X-Wing in columns).

To identify an X-Wing, look for two rows (or columns) where a specific candidate number appears only twice and aligns with the same columns (or rows). Once you find an X-Wing, you can eliminate that candidate number from the other cells in the intersecting columns (or rows).

The X-Wing technique can significantly help you make progress in a Sudoku puzzle by narrowing down possibilities and simplifying the grid, making it easier to apply other solving techniques.

What is a swordfish in Sudoku?

A swordfish is a more complex Sudoku-solving technique that helps eliminate candidate numbers in rows and columns. It occurs when there are three parallel rows (or columns) in which a specific candidate number appears two or three times, and the appearances of the candidate form a rectangular pattern across three corresponding columns (or rows).

The swordfish technique is an extension of the X-Wing technique and relies on a similar logic. When a swordfish pattern is present, it means that the specific candidate number must appear in one of the pattern-forming cells in each row (or column), so it can be eliminated as a candidate from other cells in the intersecting columns (or rows).

To identify a swordfish, look for three rows (or columns) where a specific candidate number appears two or three times and aligns with the same three columns (or rows) in a rectangular pattern. Once you find a swordfish, you can eliminate that candidate number from the other cells in the intersecting columns (or rows).

The swordfish technique can be challenging to spot but can significantly help you make progress in a Sudoku puzzle by narrowing down possibilities and simplifying the grid, making it easier to apply other solving techniques.

What is a jellyfish in Sudoku?

A jellyfish is an even more advanced Sudoku-solving technique that helps eliminate candidate numbers in rows and columns. It occurs when there are four parallel rows (or columns) in which a specific candidate number appears two, three, or four times, and the appearances of the candidate form a rectangular pattern across four corresponding columns (or rows).

The jellyfish technique is an extension of the X-Wing and swordfish techniques and relies on similar logic. When a jellyfish pattern is present, it means that the specific candidate number must appear in one of the pattern-forming cells in each row (or column), so it can be eliminated as a candidate from other cells in the intersecting columns (or rows).

To identify a jellyfish, look for four rows (or columns) where a specific candidate number appears two, three, or four times and aligns with the same four columns (or rows) in a rectangular pattern. Once you find a jellyfish, you can eliminate that candidate number from the other cells in the intersecting columns (or rows).

The jellyfish technique can be quite challenging to spot and apply but can significantly help you make progress in a Sudoku puzzle by narrowing down possibilities and simplifying the grid, making it easier to apply other solving techniques.

What is a skyscraper in Sudoku?

A skyscraper is an advanced Sudoku-solving technique that involves finding a specific pattern of candidate numbers in rows and columns to eliminate other candidates. The technique is named “skyscraper” because the pattern resembles two tall buildings connected by a bridge.

The skyscraper technique is based on the concept of “strong links” and “weak links” between candidate numbers in a Sudoku grid. A strong link exists between two candidate numbers when one of them must be the correct number in a row, column, or box. A weak link exists when there is a possibility that one of the candidates is the correct number, but it is not certain.

In the skyscraper technique, you look for two parallel rows (or columns) in which a specific candidate number appears exactly twice, creating two strong links. These strong links are connected by two weak links in the corresponding columns (or rows). When you find such a pattern, you can eliminate the candidate number from the cells that “see” both ends of the weak links.

To identify a skyscraper, look for a specific candidate number that forms the pattern described above. Once you find a skyscraper, you can eliminate that candidate number from the other cells in the grid that see both ends of the weak links.

The skyscraper technique can significantly help you make progress in a Sudoku puzzle by narrowing down possibilities and simplifying the grid, making it easier to apply other solving techniques.

What is a two-string kite in Sudoku?

A two-string kite is an advanced Sudoku-solving technique that involves finding a specific pattern of candidate numbers in rows and columns to eliminate other candidates. The technique is called a “two-string kite” because the pattern resembles a kite shape with two strings.

The two-string kite technique is based on the concept of “strong links” and “weak links” between candidate numbers in a Sudoku grid. A strong link exists between two candidate numbers when one of them must be the correct number in a row, column, or box. A weak link exists when there is a possibility that one of the candidates is the correct number, but it is not certain.

In the two-string kite technique, you look for a specific candidate number that forms a kite shape across two rows and two columns. The pattern consists of one strong link in a row (or column) and two weak links connecting the strong link to two other candidate numbers in the corresponding columns (or rows). When you find such a pattern, you can eliminate the candidate number from the cells that “see” both ends of the weak links.

To identify a two-string kite, look for a specific candidate number that forms the pattern described above. Once you find a two-string kite, you can eliminate that candidate number from the other cells in the grid that see both ends of the weak links.

The two-string kite technique can significantly help you make progress in a Sudoku puzzle by narrowing down possibilities and simplifying the grid, making it easier to apply other solving techniques.

What is a triple in Sudoku?

A “triple” in Sudoku refers to a situation where three cells within a row, column, or block (also called a box or region) contain a unique set of three candidate numbers, and none of these cells can contain any other numbers. This scenario is also called a “naked triple” or “triple set.”

The presence of a triple can be used as a solving technique in Sudoku, as it allows you to eliminate those three candidate numbers from other cells in the same row, column, or block. By removing these candidates, you can often make progress in solving the puzzle and uncovering additional numbers.

What is a quad in Sudoku?

A “quad” in Sudoku, also known as a “naked quad” or “quad set,” refers to a situation where four cells within a row, column, or block (also called a box or region) contain a unique set of four candidate numbers, and none of these cells can contain any other numbers.

The presence of a quad can be used as a solving technique in Sudoku, as it allows you to eliminate those four candidate numbers from other cells in the same row, column, or block. By removing these candidates, you can often make progress in solving the puzzle and uncovering additional numbers.

What is a unique rectangle in Sudoku?

A “unique rectangle” in Sudoku is a solving technique used to prevent multiple solutions in a puzzle. This technique is based on the principle that a valid Sudoku puzzle must have a unique solution. Unique rectangles occur when there are two diagonally opposite corners of a rectangle that share the same two candidates, and the other two corners also share the same two candidates. These four cells are also located in two different rows, two different columns, and two different blocks.

The unique rectangle technique can be applied when there are additional candidates in one or more of the four cells, making it possible to eliminate those extra candidates to ensure a single solution.

What is a BUG in Sudoku?

A “BUG” in Sudoku stands for “Bivalue Universal Grave.” It is a term used to describe a particular configuration in a Sudoku grid, which arises when every remaining unfilled cell has only two candidates (bivalue cells) except for one cell that has three candidates. In this configuration, there is a risk of creating multiple solutions or none at all, violating the requirement that a valid Sudoku puzzle must have a unique solution.

To resolve a BUG, you need to identify a cell that shares a candidate number with the cell that has three candidates, and then eliminate that number as a candidate from the cell with three candidates. This action will restore uniqueness to the puzzle and allow you to proceed with solving it.

What is a forcing chain in Sudoku?

A forcing chain in Sudoku is an advanced solving technique that involves identifying a series of connected cells with only two candidates (bivalue cells) in a way that forces a specific outcome. The concept behind forcing chains is that if you hypothetically assign a value to a specific cell, it will have a chain reaction on other cells, eventually leading to a certain result. The chain can either lead to a contradiction, confirming that the initial assumption was incorrect, or it can reveal information about the correct placement of numbers in the puzzle.

Forcing chains can be used in various forms, such as simple forcing chains, XY-chains, and remote pairs. They all rely on the principle of making logical deductions based on the consequences of a hypothetical assignment.

To illustrate a simple forcing chain, consider a bivalue cell with candidates {1, 2}:

1. Hypothetically assign the value 1 to the cell.
2. This assignment forces other cells to take specific values due to the rules of Sudoku.
3. Follow the chain of forced assignments.
4. If the chain results in a contradiction, then the initial assumption (assigning 1 to the cell) is incorrect, and the cell must contain the other candidate (in this case, 2).
5. If the chain reveals information about the correct placement of numbers without contradiction, you can use that information to make progress in solving the puzzle.

Forcing chains can be an effective technique for solving difficult Sudoku puzzles, but they often require a deep understanding of the puzzle’s structure and logical thinking to apply correctly.

What is a colouring in Sudoku?

Colouring in Sudoku is an advanced solving technique that involves assigning different colours to candidate numbers within connected cells to identify patterns that can help eliminate candidates and make progress in solving the puzzle. This technique is particularly useful when dealing with bivalue cells (cells that have only two candidates) and finding conjugate pairs.

In colouring, you usually start by selecting a specific candidate number that appears in multiple bivalue cells. Then, you assign two different colours (commonly referred to as Colour A and Colour B) to this candidate in different cells, following these rules:

1. If two cells with the same candidate are in the same row, column, or block, and they cannot both contain the candidate (due to Sudoku rules), they must have opposite colours.
2. If two cells can “see” each other (i.e., they are in the same row, column, or block) and both contain the candidate, they should be assigned the same colour.

After the colouring process, you can make deductions based on the resulting colour patterns:

1. If the same candidate number with the same colour appears in a row, column, or block more than once, it creates a contradiction. In this case, all candidates with the opposite colour must be correct.
2. If the same candidate number with the same colour appears in a cell along with another candidate that has the same colour, you can eliminate the other candidate, as it cannot be the correct solution.

Colouring can be a powerful technique to solve difficult Sudoku puzzles, but it requires careful observation and logical thinking to be applied effectively.

What is a pattern overlay in Sudoku?

Pattern Overlay, also known as Pattern Overlay Method (POM) or Template Overlay, is an advanced solving technique in Sudoku that involves overlaying different possible patterns of a specific candidate number onto the grid to identify commonalities and eliminate other candidates. This technique is particularly useful for solving very difficult Sudoku puzzles.

The Pattern Overlay process can be divided into the following steps:

1. Choose a specific candidate number (e.g., the number 5) that appears in multiple unsolved cells throughout the grid.
2. Identify all possible patterns or placements of this candidate number that obey the rules of Sudoku. A pattern is a set of positions for the chosen number in each row, column, and block.
3. Overlay these patterns onto the Sudoku grid, one at a time.
4. Look for cells where the chosen number appears in all possible patterns. If a cell contains the chosen number in every pattern, it means that the chosen number must be placed in that cell, regardless of which pattern is correct. In such cases, you can eliminate other candidates from that cell.

Pattern Overlay can be a very powerful technique, but it’s also quite complex and time-consuming. It requires a deep understanding of the Sudoku puzzle’s structure and often involves analysing many possible patterns to make progress in solving the puzzle. Because of its complexity, Pattern Overlay is typically used as a last resort when simpler techniques have been exhausted.

What is a bifurcation in Sudoku?

Bifurcation in Sudoku, also known as “trial and error” or “guessing,” is a solving technique that involves making an assumption about the value of a cell and then attempting to solve the puzzle based on that assumption. If the assumption leads to a contradiction or breaks the rules of Sudoku, it can be concluded that the assumption was incorrect, and the other candidate value for the cell must be the correct one.

Bifurcation can be an effective technique for solving difficult Sudoku puzzles, but it is generally considered a last resort when other logical solving techniques have been exhausted. It is not favoured by many Sudoku enthusiasts because it deviates from the logical and deductive nature of the game.

To apply bifurcation, follow these steps:

1. Choose an unsolved cell with the least number of candidates, preferably a bivalue cell (a cell with only two candidates).
2. Make an assumption by assigning one of the candidates as the value of the cell.
3. Continue solving the puzzle using other techniques based on this assumption.
4. If the assumption leads to a contradiction or breaks the rules of Sudoku, backtrack, and try the other candidate value for the cell.

Bifurcation can help you break through challenging parts of a Sudoku puzzle, but it’s important to remember that it should be used only when other logical techniques have been exhausted.

What is a Y-Wing in Sudoku?

A Y-Wing is an advanced solving technique in Sudoku that involves three cells forming a specific pattern, resembling the shape of the letter “Y.” Each of these cells has only two candidates (bivalue cells). The Y-Wing technique can be used to eliminate candidates in other cells and make progress in solving the puzzle.

The Y-Wing consists of three cells with the following properties:

1. The “pivot” cell, which connects to the other two cells (called “wings” or “pincers”). The pivot cell shares a row, column, or block with each of the wings.
2. Two “wing” cells that do not share a row, column, or block with each other but are connected to the pivot cell.

The pivot cell and the two wing cells each share one common candidate. The pivot cell contains candidates A and B, while the wing cells contain candidates B and C, with B being the common candidate between all three cells.

To apply the Y-Wing technique, follow these steps:

1. Identify a Y-Wing pattern in the Sudoku grid.
2. Find cells that can “see” (share a row, column, or block) both wing cells.
3. If any of these cells contain candidate B, you can eliminate it as a possibility.

The logic behind the Y-Wing technique is that if the pivot cell contains candidate B, neither wing cell can contain candidate B. If the pivot cell contains candidate A, one of the wing cells must contain candidate B. In either case, candidate B cannot appear in any cell that can see both wing cells.

The Y-Wing technique can be a powerful tool for solving more difficult Sudoku puzzles, but it requires a keen eye for spotting patterns and good understanding of the puzzle’s structure.

What is a Y-Cycle in Sudoku?

A Y-Cycle in Sudoku is a variation of the XY-Chain technique, which is an advanced solving method involving a sequence of connected bivalue cells (cells with only two candidates). In a Y-Cycle, the chain forms a loop, connecting back to the starting cell. As a result, it creates a cycle of alternating candidate pairs, with each connected cell sharing one common candidate.

Y-Cycles can be used to eliminate candidates in other cells and make progress in solving the puzzle. The process of identifying and applying a Y-Cycle is as follows:

1. Identify a sequence of bivalue cells connected in such a way that the chain forms a loop and connects back to the starting cell. The connections between cells can occur within a row, column, or block (box).
2. Ensure that each connected cell shares one common candidate with the previous and the next cell in the chain, creating an alternating pattern of candidate pairs.
3. Locate cells that can “see” (share a row, column, or block) two or more cells of the Y-Cycle containing the same candidate.
4. If the same candidate is found in any of these cells, you can eliminate it as a possibility.

The logic behind the Y-Cycle technique is that if a candidate is removed from one cell in the cycle, it will create a chain reaction that forces the other candidate to be true in the connected cells, ultimately eliminating the possibility of the candidate in the cells that can see two or more cells of the Y-Cycle containing the same candidate.

Y-Cycles can be a powerful technique for solving more difficult Sudoku puzzles, but they require a good understanding of the puzzle’s structure, keen observational skills, and logical thinking to be applied effectively.

What is a palindrome in Sudoku?

A palindrome in Sudoku refers to a specific variant of the puzzle in which certain cells must contain the same digits in a symmetrical pattern. In other words, the digits must read the same forwards and backwards when considering the palindrome pattern.

In a Palindrome Sudoku, the puzzle usually contains a set of grayed-out cells or marked lines that indicate the location of the palindrome. The constraints of a regular Sudoku still apply, meaning each row, column, and 3×3 box must contain the numbers 1 through 9 exactly once. Additionally, the palindrome constraint must be fulfilled to solve the puzzle correctly.

The palindrome constraint can help provide additional information to solve the puzzle, as filling in one cell within the palindrome pattern will also determine the value of the symmetrically opposite cell.

It’s important to note that the term “palindrome” in Sudoku is not a solving technique but a variant that introduces an additional constraint to the standard puzzle.

What is a hidden triple in Sudoku?

A hidden triple in Sudoku is an advanced solving technique that involves identifying a group of three cells within a row, column, or block (box) that contain a unique set of three candidate numbers, even though the cells themselves might have more than three candidates in total. The hidden triple is called “hidden” because these three candidates do not appear in any other cells in the same row, column, or block, but they may be accompanied by other candidates in the involved cells.

The presence of a hidden triple can be used to eliminate other candidates from those three cells, simplifying the puzzle and allowing for further progress in solving it.

What is a pointing pair in Sudoku?

A pointing pair in Sudoku is a basic solving technique that involves two cells within a 3×3 block (box) that share the same candidate number and are located in the same row or column. The pointing pair is called “pointing” because the candidate numbers in these two cells essentially “point” outside the box, indicating that the candidate number cannot appear in any other cell in the same row or column outside the box.

The pointing pair technique can be used to eliminate the specific candidate number from other cells in the same row or column outside the 3×3 block.

The pointing pair technique is an effective method for simplifying candidate lists and making progress in solving Sudoku puzzles, and it relies on careful observation of the candidate numbers in each block.

What is a box/line reduction in Sudoku?

A box/line reduction, also known as an intersection removal or line-box interaction, is a basic solving technique in Sudoku that focuses on the interaction between rows/columns and the 3×3 blocks (boxes). The technique can be used to eliminate specific candidate numbers from cells within a row or column based on their presence in a 3×3 block or vice versa.

The box/line reduction technique works in two scenarios:

1. If a candidate number appears in a single row or column within a 3×3 block, you can eliminate that candidate from the rest of the cells in the same row or column outside the block.
2. If a candidate number appears only in a specific 3×3 block along a row or column, you can eliminate that candidate from the rest of the cells in the block.

The box/line reduction technique is an effective method for simplifying candidate lists and making progress in solving Sudoku puzzles, and it relies on careful observation of the candidate numbers in each row, column, and block.

What is a single digit candidate in Sudoku?

A single-digit candidate in Sudoku, often referred to as a “naked single” or “lone number,” is a basic solving technique that involves identifying a cell with only one possible candidate number. This occurs when all other numbers from 1 through 9 have been placed in the same row, column, or 3×3 block (box), leaving only one possible number for the cell.

When you identify a single-digit candidate or a naked single, you can confidently place the number in the cell, as it is the only valid option based on the Sudoku rules.

Identifying single-digit candidates or naked singles is one of the most straightforward solving techniques in Sudoku and is essential for solving puzzles of all difficulty levels.

What is a fish pattern in Sudoku?

A fish pattern in Sudoku is a term used to describe a family of advanced solving techniques that involve rows and columns in a specific pattern. These techniques are used to eliminate candidates from other cells in the grid. Fish patterns can be found in different sizes, and they are generally named after the number of rows and columns involved in the pattern.

The most common fish patterns are:

1. X-Wing (2×2 fish): This technique involves two rows and two columns, where a specific candidate number appears only twice in each of the rows and is aligned with the same columns. Similarly, the candidate number appears only twice in the involved columns and is aligned with the same rows. With this pattern, you can eliminate the candidate number from other cells within the involved rows and columns.
2. Swordfish (3×3 fish): This technique involves three rows and three columns, where a specific candidate number appears two or three times in each row and is aligned with the same columns. Similarly, the candidate number appears two or three times in each of the involved columns and is aligned with the same rows. With this pattern, you can eliminate the candidate number from other cells within the involved rows and columns.
3. Jellyfish (4×4 fish): This technique involves four rows and four columns, where a specific candidate number appears two, three, or four times in each row and is aligned with the same columns. Similarly, the candidate number appears two, three, or four times in each of the involved columns and is aligned with the same rows. With this pattern, you can eliminate the candidate number from other cells within the involved rows and columns.

Fish patterns can be powerful techniques for solving more challenging Sudoku puzzles, but they require keen observation and a good understanding of the puzzle’s structure. While these techniques can be complex, finding and utilizing them can greatly simplify the grid and help make progress in solving the puzzle.

What is an empty rectangle in Sudoku?

An empty rectangle in Sudoku is an advanced solving technique that involves a specific configuration of candidate numbers within a 3×3 block (box). The term “empty rectangle” refers to the absence of a specific candidate number in either two rows or two columns within the block, creating a rectangular-shaped empty space.

The empty rectangle technique can be used to eliminate candidates in other cells within the grid. To apply the empty rectangle technique, follow these steps:

1. Identify a 3×3 block with an empty rectangle pattern for a specific candidate number.
2. Locate a “pivot” cell in the remaining row or column of the block (depending on the empty rectangle’s orientation) that contains the candidate number.
3. Identify cells in the grid that “see” both the pivot cell and one of the cells in the empty rectangle (share a row, column, or block).
4. If any of these cells contain the specific candidate number, you can eliminate it as a possibility.

The logic behind the empty rectangle technique is based on the fact that the candidate number must appear in one of the two remaining cells of the empty rectangle (in the row or column that is not empty). Consequently, any cell that sees both the pivot cell and one of these remaining cells cannot contain the candidate number.

The empty rectangle technique can be a helpful tool for solving more difficult Sudoku puzzles, but it requires careful observation and a good understanding of the puzzle’s structure.

What is a Franken X-Wing in Sudoku?

A Franken X-Wing in Sudoku is a variation of the X-Wing technique, which is an advanced solving method involving two rows and two columns. In a standard X-Wing, a specific candidate number appears only twice in each of the involved rows and is aligned with the same columns, or vice versa. With this pattern, you can eliminate the candidate number from other cells within the involved rows and columns.

The Franken X-Wing is a more complex variation that combines aspects of the X-Wing pattern and the fish patterns in Sudoku. In a Franken X-Wing, one of the rows or columns involved in the pattern belongs to a single 3×3 block (box), while the other row or column spans across multiple blocks.

The logic behind the Franken X-Wing is similar to that of a standard X-Wing. When a specific candidate number appears in this pattern, it implies that the number must appear in one of the cells in the row or column that is constrained within a single block. Consequently, you can eliminate the candidate number from other cells within the involved rows and columns outside the block.

To apply the Franken X-Wing technique, follow these steps:

1. Identify a Franken X-Wing pattern in the Sudoku grid.
2. Eliminate the specific candidate number from other cells within the involved rows and columns outside the block.

The Franken X-Wing technique can be helpful for solving more difficult Sudoku puzzles, but it requires keen observation and a good understanding of the puzzle’s structure to be applied effectively.

What is a double ALS in Sudoku?

A double ALS (Almost Locked Set) in Sudoku is an advanced solving technique involving two Almost Locked Sets in the grid. An Almost Locked Set is a group of cells containing a set of candidate numbers where the number of candidates is one more than the number of cells. In other words, if you were to remove one candidate from the set, it would become a locked set, and each number would have a unique place within the group of cells.

The double ALS technique is used to eliminate candidates from other cells by finding a connection between two Almost Locked Sets. The connection is typically in the form of a shared candidate number, referred to as the “restricted common” (RC).

To apply the double ALS technique, follow these steps:

1. Identify two Almost Locked Sets that share a restricted common candidate.
2. Determine if there is another candidate number (called “X”) that appears in both Almost Locked Sets.
3. Identify cells in the grid that can “see” (share a row, column, or block) cells from both Almost Locked Sets containing the candidate number X.
4. Eliminate candidate X from those cells.

The logic behind the double ALS technique is that, due to the restricted common candidate, one of the Almost Locked Sets must be a true locked set. Therefore, any cells that can see cells from both Almost Locked Sets containing candidate X cannot contain candidate X themselves.

The double ALS technique can be a powerful tool for solving more difficult Sudoku puzzles, but it requires careful observation and a good understanding of the puzzle’s structure.

What is a colouring wrap in Sudoku?

A colouring wrap in Sudoku is a term used to describe a situation that arises when using the colouring technique. The colouring technique is an advanced solving method that focuses on pairs of cells containing the same candidate number, forming a strong link between them. Using different colours, you can mark these cells, alternating the colours as you follow the strong links.

A colouring wrap occurs when you can assign the same colour to a cell that already has the opposite colour, indicating that there is a contradiction in the colouring. When this happens, you can eliminate the candidate number from cells with the conflicting colour.

To apply the colouring wrap technique, follow these steps:

1. Identify strong links between cells containing the same candidate number.
2. Assign different colours to the cells, alternating the colours as you follow the strong links.
3. If you find a situation where you can assign the same colour to a cell that already has the opposite colour, you’ve found a colouring wrap.
4. Eliminate the candidate number from cells with the conflicting colour.

The logic behind the colouring wrap is that the contradiction in the colouring highlights a situation where a candidate number cannot be placed in the cells with the conflicting colour. By eliminating this candidate from those cells, you can simplify the puzzle and make progress in solving it.

The colouring wrap technique can be a powerful tool for solving more difficult Sudoku puzzles, but it requires careful observation and a good understanding of the puzzle’s structure.

What is a unique loop in Sudoku?

A unique loop in Sudoku is an advanced solving technique that exploits the puzzle’s requirement of having a unique solution. A unique loop arises when a closed loop of cells containing only two candidates each is formed, with alternating strong and weak links between them. The loop is considered “unique” because it creates a situation where multiple solutions can exist, which is not allowed in a well-formed Sudoku puzzle.

To apply the unique loop technique, follow these steps:

1. Identify a closed loop of cells with only two candidates each.
2. Ensure that the loop has alternating strong and weak links between the cells.
3. Check for cells where both candidates in the cell are part of the loop (these cells are called “bivalue cells”).
4. If one of the candidates in a bivalue cell is weakly linked to its neighbour in the loop, it can be removed from all other cells in the loop.

The logic behind the unique loop technique is that, to ensure the puzzle has a unique solution, you need to break the potential multiple solutions that the loop creates. By removing a candidate that is weakly linked within the loop, you eliminate the possibility of multiple solutions and maintain the uniqueness of the puzzle.

The unique loop technique can be a powerful tool for solving more difficult Sudoku puzzles, but it requires careful observation and a good understanding of the puzzle’s structure.

What is a UR in Sudoku?

A UR in Sudoku stands for “Unique Rectangle.” It is an advanced solving technique that focuses on the puzzle’s requirement of having a unique solution. A Unique Rectangle arises when a rectangular-shaped pattern is formed by four cells containing only two candidate numbers, and these cells are located at the corners of a rectangle that spans across two rows and two columns, as well as two 3×3 blocks (boxes).

The Unique Rectangle technique is based on the premise that a well-formed Sudoku puzzle must have a unique solution. If a Unique Rectangle is left unsolved, it creates a situation where multiple solutions can exist, which is not allowed in a Sudoku puzzle.

To apply the Unique Rectangle technique, follow these steps:

1. Identify a rectangular pattern formed by four cells containing only two candidate numbers (e.g., cells with candidates {1, 2}).
2. Ensure that the cells are located at the corners of a rectangle that spans across two rows, two columns, and two 3×3 blocks.
3. Look for additional candidates in one or more of the corner cells.
4. If you find a corner cell with an additional candidate, you can eliminate the original two candidates from that cell, as keeping them would lead to multiple solutions.

The logic behind the Unique Rectangle technique is that removing the candidates that would cause ambiguity in the puzzle ensures its uniqueness. By eliminating the candidates that would create multiple solutions, you can maintain the uniqueness of the puzzle and make progress in solving it.

The Unique Rectangle technique can be a powerful tool for solving more difficult Sudoku puzzles, but it requires careful observation and a good understanding of the puzzle’s structure.

What is a remote pair in Sudoku?

A remote pair in Sudoku is an advanced solving technique that involves identifying two cells in the puzzle that have the same pair of candidates, also known as a conjugate pair. A remote pair is a chain of these conjugate pairs, with alternating strong and weak links between them. The technique is used to eliminate other occurrences of the two candidate numbers in cells that can “see” (share a row, column, or block) both ends of the chain.

To apply the remote pair technique, follow these steps:

1. Identify a chain of conjugate pairs with the same two candidate numbers (e.g., cells with candidates {1, 2}).
2. Ensure that the chain has alternating strong and weak links between the pairs.
3. Identify cells in the grid that can see both ends of the chain.
4. Eliminate the two candidate numbers from those cells.

The logic behind the remote pair technique is that one of the two candidate numbers in the conjugate pairs must be true. Therefore, any cell that can see both ends of the chain cannot contain either of the two candidate numbers, as placing them there would break the alternating strong and weak links in the chain.

The remote pair technique can be a powerful tool for solving more difficult Sudoku puzzles, but it requires careful observation and a good understanding of the puzzle’s structure.

What is a XYZ-Wing in Sudoku?

An XYZ-Wing in Sudoku is an advanced solving technique that involves three cells forming a specific pattern to eliminate candidates in other cells. The pattern consists of:

1. A pivot cell containing three candidates (XYZ).
2. Two other cells (called wings) sharing a unit (row, column, or block) with the pivot cell. Each wing cell contains a pair of candidates, with one candidate common to both wing cells and the pivot cell (e.g., XY and XZ, where X is the common candidate).

To apply the XYZ-Wing technique, follow these steps:

1. Identify a pivot cell containing three candidates (XYZ).
2. Find two other cells that share a unit with the pivot cell and contain two candidates each, with one candidate common to both wing cells and the pivot cell (e.g., XY and XZ).
3. Identify cells in the grid that can “see” (share a row, column, or block) all three cells involved in the XYZ-Wing pattern.
4. Eliminate the common candidate (X) from those cells.

The logic behind the XYZ-Wing technique is that at least one of the three cells involved in the pattern must be true, but only one of the wing cells can contain the common candidate (X). Therefore, any cell that can see all three cells in the pattern cannot contain the common candidate (X).

The XYZ-Wing technique can be a powerful tool for solving more difficult Sudoku puzzles, but it requires careful observation and a good understanding of the puzzle’s structure.

What is a w-wing in Sudoku?

A W-Wing in Sudoku is an advanced solving technique that involves two cells (bivalue cells) containing the same pair of candidates (e.g., XY). These two cells are connected through a common “bridge” candidate, which appears in two other cells (called bridge cells) that share a unit (row, column, or block) with each of the original bivalue cells.

To apply the W-Wing technique, follow these steps:

1. Identify two bivalue cells with the same pair of candidates (e.g., XY).
2. Ensure that the bivalue cells do not share a row, column, or block.
3. Find a common bridge candidate (e.g., Y) that appears in two other cells (bridge cells), each sharing a unit with one of the bivalue cells.
4. Identify cells in the grid that can “see” (share a row, column, or block) both bivalue cells.
5. Eliminate the other candidate (X) from those cells.

The logic behind the W-Wing technique is that, since the bivalue cells contain the same pair of candidates, at least one of them must be true. The presence of the bridge candidate (Y) in the bridge cells guarantees that at least one of the bivalue cells will contain the candidate Y. Therefore, any cell that can see both bivalue cells cannot contain the other candidate (X).

The W-Wing technique can be a powerful tool for solving more difficult Sudoku puzzles, but it requires careful observation and a good understanding of the puzzle’s structure.

What is a BUG+1 in Sudoku?

A BUG+1 in Sudoku stands for “Bivalue Universal Grave plus one.” It is an advanced solving technique that exploits the requirement of a unique solution in a Sudoku puzzle. A BUG occurs when every unsolved cell in the grid contains exactly two candidates, and each candidate number appears exactly twice in each row, column, and 3×3 block. This situation is called “Bivalue Universal Grave” because it would lead to multiple solutions, which is not allowed in a well-formed Sudoku puzzle.

A BUG+1 refers to a BUG situation where there is one additional candidate in the grid, which is the “+1.” This extra candidate is the key to unlocking the puzzle’s unique solution and avoiding the multiple solutions that a BUG creates.

To apply the BUG+1 technique, follow these steps:

1. Verify that the grid is in a BUG situation (every unsolved cell contains exactly two candidates, and each candidate number appears twice in each row, column, and block).
2. Identify the cell with the extra candidate (the “+1”).
3. Place the extra candidate in the cell, as it is the only way to maintain the puzzle’s unique solution.

The logic behind the BUG+1 technique is that by placing the extra candidate in the cell, you break the Bivalue Universal Grave pattern and eliminate the possibility of multiple solutions. This ensures that the Sudoku puzzle maintains its unique solution, allowing you to progress in solving it.

The BUG+1 technique can be a powerful tool for solving more difficult Sudoku puzzles, but it requires careful observation and a good understanding of the puzzle’s structure.

What is a nice loop in Sudoku?

A nice loop in Sudoku is an advanced solving technique that involves a closed loop of cells with alternating strong and weak links between candidate numbers. The loop is considered “nice” because it can lead to candidate eliminations when certain conditions are met. There are several types of nice loops, such as the XY-Chain, Remote Pairs, and X-Cycles.

To apply the nice loop technique, follow these steps:

1. Identify a closed loop of cells with alternating strong and weak links between candidate numbers.
2. Ensure that the loop starts and ends with a weak link.
3. Check the cells in the loop for the following conditions:

1. If a candidate appears twice in the loop with two weak links, it can be eliminated from any cells that can “see” (share a row, column, or block) both of those occurrences.
2. If a candidate appears twice in the loop with two strong links, it can be eliminated from any cells within the loop that also contain that candidate but are not part of the strong links.

The logic behind the nice loop technique is that the closed loop of strong and weak links creates constraints on the placement of the candidate numbers. These constraints can then be used to eliminate candidates in other cells, simplifying the puzzle and making progress in solving it.

The nice loop technique can be a powerful tool for solving more difficult Sudoku puzzles, but it requires careful observation and a good understanding of the puzzle’s structure.

What is a Kraken in Sudoku?

A Kraken in Sudoku is a term that refers to a particularly challenging and complex solving technique or situation in a puzzle. It usually involves advanced logic, multiple nested chains, or interconnected patterns that make it difficult to identify and resolve. The term “Kraken” is borrowed from the legendary sea monster, symbolizing the difficulty and complexity of the technique.

Kraken techniques may involve various advanced methods such as:

1. Forcing chains
2. Colouring
3. Fish patterns (like Swordfish, Jellyfish, etc.)
4. Almost Locked Sets (ALS)
5. X-Cycles, XY-Chains, and other loop techniques

It’s important to note that “Kraken” is not a specific solving technique but rather a descriptor for complex situations or techniques that require a deep understanding of the puzzle’s structure and a high level of skill to solve. These techniques may be combined or used in conjunction to resolve particularly difficult Sudoku puzzles.

To tackle a Kraken in Sudoku, you should have a strong grasp of advanced techniques, be patient, and be prepared to carefully analyse the puzzle, looking for subtle patterns and connections that can help you make progress.