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Sudoku glossary

The words Sudoku players use, in plain English. Each one comes with an example you can picture on a board.

Almost locked set (ALS)

A group of N cells in one house containing N+1 distinct candidate digits: one extra choice beyond the number of cells.

For exampleTwo cells with {2,5} and {5,7} form an ALS: 2 cells, 3 distinct digits. If 2 becomes impossible throughout the group, the two cells must use 5 and 7.

Alternating inference chain (AIC)

A chain that alternates strong and weak logical steps, sometimes changing digits inside bivalue cells.

For exampleStrong: "not this implies that". Weak: "that implies not the next". The full endpoint argument, not the line drawing, creates the deduction.

Assumption

A temporary "suppose this is true" used to test consequences. It is not written into the working puzzle as a proven answer.

For exampleIf both possible values of a pivot lead to a wing being 8, you have a proof that one of the wings is 8.

Base house

The rows or columns you START from in a fish pattern. You must account for all copies of the chosen candidate in these houses.

For exampleFor a row-based X-Wing, the two rows are the bases. Each row needs one 7.

Bivalue cell

An empty cell with exactly two remaining possibilities.

For exampleA cell with {2,8} is bivalue. If it is not 2, it must be 8. A pair of 7 locations in a row is a different kind of "pair".

Box / block

One of the nine large squares outlined with a thicker border. Each box contains nine cells.

For exampleBox 1 is at the upper left. Box 5 is in the middle. Box 9 is at the lower right.

Bridge

The link that connects two parts of a pattern.

For exampleA W-Wing connects two identical bivalue cells through a strong link on one of their digits.

BUG / BUG+1

Bivalue Universal Grave: a specific repeating two-choice structure. BUG+1 adds one exceptional candidate that can resolve it.

For exampleOne three-candidate cell plus many two-candidate cells is NOT enough on its own. The candidate occurrence counts in all houses also matter.

Candidate / pencil mark

A small number that has not been ruled out of an empty cell. It is a possibility, not an answer.

For exampleA cell showing 2, 5, 7 might be any one of those numbers. Removing 7 still leaves a choice between 2 and 5.

Cell

One of the 81 small squares where a single final number belongs.

For exampler4c6 is the cell in row 4, column 6. Rows count down from the top; columns count across from the left.

Chain

A sequence of small if-then deductions. Each step must follow a real Sudoku constraint.

For example"If this is not 7, that must be 7; then the next cannot be 7; so the last must be 7." Chains connect candidate statements, not just nearby squares.

Coloring

Using two colors to label alternating possibilities in a network of strong links. The colors represent logical alternatives, not guesses.

For exampleWithin one connected component, a target seeing a 7 of each color loses 7 because one color group must be true.

Connected component

One connected group of links. Every member can be reached from every other by following those links.

For exampleTwo separate coloring groups cannot automatically share the same "teal is true" assumption.

Contradiction

An impossible result, such as two 7s in one row or an empty cell with no possible digit.

For exampleIf a clearly tracked assumption inevitably creates a contradiction, that assumption must be false.

Cover house

The columns or rows that contain the candidate locations from a fish pattern's bases.

For exampleFor a row-based X-Wing, two columns cover the four corners. Eliminate other 7s in those columns, outside the base rows.

Deadly pattern

An arrangement whose digits could be swapped to create another solution without changing the original clues.

For exampleCertain unique-rectangle deductions avoid a two-digit rectangle spanning exactly two boxes, because a verified unique puzzle cannot finish that way.

Digit

One of the symbols 1 through 9. Sudoku uses them as labels, not as quantities to add or multiply.

For example"All 7 locations" means every cell that still contains the candidate number 7. It does NOT mean there must be seven cells.

Elimination

A logical reason to erase one small possibility. An elimination does not necessarily fill the cell.

For exampleErase 7 from {2,5,7} and {2,5} remain. Only when one possibility remains can you place that number.

Endpoint

A candidate at one end of the chain being discussed. Many patterns prove that at least one of their two endpoints must be true.

For exampleIf one of two endpoints must be 7, a different cell sharing a row, column or box with BOTH endpoints cannot be 7.

Fin

An extra candidate that prevents an otherwise ordinary fish from being a perfect fish.

For exampleA finned fish needs additional restrictions: a target must also see every relevant fin. Do not make all the ordinary fish eliminations.

Fish

A family of single-digit patterns matching a fixed number of rows to the same number of columns (or the reverse).

For exampleAn X-Wing uses 2 base rows and 2 cover columns. Swordfish uses 3 of each; Jellyfish uses 4 of each.

Hidden

Look at where particular digits can go within a house. Their only locations can be hidden among other notes.

For exampleIf only two cells in a row contain 2 or 8, those cells must take 2 and 8. Their other notes can be erased.

Hinge

An informal name for the middle connection in a pattern such as a kite.

For exampleIn a kite, two middle 7 candidates share a box. They cannot both be 7. That connection lets the two separate strong links work together.

House / unit

A complete row, a complete column, or a complete 3-by-3 box. Each needs the numbers 1 through 9 exactly once.

For exampleThere are 27 houses: 9 rows, 9 columns and 9 boxes. Every cell belongs to three houses.

Implication / inference

An if-then consequence that is guaranteed by the stated rules.

For exampleIf r2c2 is 7, every other cell in its row is not 7. The direction matters: not being 7 somewhere else does not necessarily force r2c2.

Link

A logical connection between two possibilities. A line drawn on the board shows that connection, not a route that a number travels.

For exampleA solid line in this lab uses a strong rule: "not here means there". A dashed line uses a weak rule: "here means not there".

Loop

A chain whose logical connections return to its starting point.

For exampleReturning to the start can force or exclude candidates, but the strong/weak connection types must satisfy the loop rule.

Naked

Look at what is inside the selected cells: their remaining digits are restricted.

For exampleTwo cells in one house that each contain only {2,8} reserve 2 and 8 for those two cells. Remove 2 and 8 from other cells in that house.

Node

One statement in a chain or graph, usually "this particular digit goes in this particular cell".

For exampleThe candidate 7 in r2c2 and the candidate 5 in r2c2 are different nodes even though they share a cell.

Pattern

A set of candidate restrictions that supports a repeatable deduction. It is not just a visual shape.

For exampleFour 7s forming a rectangle are not automatically an X-Wing: the base rows must have no other possible 7 locations.

Pivot

The central cell used to connect the two wings in a wing pattern. It is not necessarily the middle of the board.

For exampleIn an XY-Wing, a {2,5} pivot sees a {2,8} wing and a {5,8} wing. Whichever pivot value wins, one wing must be 8.

Placement

Writing a final, large number into a cell because the logic proves it belongs there.

For exampleA placement answers "what goes here?" An elimination only answers "what cannot go here?"

Restricted common candidate (RCC)

A digit appearing in two almost locked sets, with every possible location in one set seeing every possible location in the other. Both sets cannot use that digit.

For exampleIf all the 2 candidates in both sets share a row, placing 2 in either set prevents the other set from using 2. Merely sharing a digit is not enough.

Roof

A nickname for certain outside or extra-candidate cells in a pattern. Its exact role depends on the technique.

For exampleIn a skyscraper, the roofs are the two unaligned endpoints. In a unique rectangle, the roof cells contain extra candidates.

Sashimi

A finned-fish variant in which the remaining fish core has a missing corner or a thin base.

For exampleIt still needs the full finned-fish proof. The visual shape alone does not justify an elimination.

Sees / peers

Two DIFFERENT cells see each other when they share a row, a column, or a 3-by-3 box. The same final number cannot go in both.

For exampler2c2 sees r2c8 (same row), r8c2 (same column), and r3c3 (same box). It does not see r8c8. Seeing is not a ray or a path: other cells do not block it.

Set

A group of cells or candidate digits being considered together. Read the lesson to see which kind of group it means.

For exampleSet A might mean two cells whose combined possible digits are {2,5,7}. Repeated copies of 7 still count as one distinct digit.

Strong link

At least one of two candidate statements must be true. If the first is false, the second has to be true.

For exampleIf row 2 has only two possible places for 7, at r2c2 and r2c8, ruling out r2c2 forces r2c8 to be 7. In this ordinary same-digit pair they also cannot both be true. A strong link does not mean either one is more likely.

Subset / locked set

A group of cells in one house that has exactly enough distinct digits to fill the group.

For exampleThree cells collectively containing only 2,5,8 reserve those three digits for themselves. Count distinct digits, not repeated pencil marks.

Target

The cell or pencil mark we are testing for removal. It is a role in this deduction, not a special type of Sudoku square.

For exampleIn "the target loses 7", we erase only its little 7. We do not erase the cell, fill it with 7, or assume all its other notes are correct.

Trivalue cell

An empty cell with exactly three remaining possibilities.

For example{2,5,8} is trivalue. Removing 2 leaves two possibilities, so it does not yet force an answer.

Uniqueness

The extra condition that the original clues allow exactly one complete solution.

For exampleUnique rectangles and BUG+1 rely on this condition. It is not implied merely by the usual row, column and box rules.

Weak link

The two candidate statements cannot both be true. If the first is true, the second must be false. Both may be false.

For exampleTwo 7 candidates in the same row are weakly linked even when that row has a third possible 7. Erasing one does NOT force the other: the third location might be right. A strong pair can also supply a weak link when the chain needs it.

Wing

One of the outside cells connected to a pivot or bridge in a wing pattern.

For exampleAn XY-Wing uses two different bivalue wing cells. A target must see both wings to lose the candidate they force between them.