Sudoku glossary
71 words solvers use, in plain language, each linked to the lessons where it matters.
- 2-string kite
A digit with only two spots in a row and only two in a column, where one end of each shares a box. Those two ends can't both hold the digit, so one of the far ends does. Remove the digit from cells that see both far ends.
- 45 rule
The digits 1 to 9 add up to 45, so every row, column and box sums to 45. Compare that with the cage totals inside a house to find the sum of the cells left over.
- AIC
Alternating inference chain: strong and weak links alternating across different digits and cells. The most general chain the hint engine uses. One end of the chain must be true, which rules out anything that clashes with both ends.
- Anti-king
Two cells a chess king's move apart, including diagonally, can't hold the same digit. In a sudoku, the only new pairs this adds are diagonal neighbors in different boxes.
- Anti-knight
Two cells a chess knight's move apart (2 steps one way and 1 step the other) can't hold the same digit.
- Arrow circle
The circle at the start of an arrow. The digits along the arrow add up to the digit in the circle.
- Arrow pill
A long oval covering 2 or 3 cells at the start of an arrow. Its digits are read as one number, such as 1 and 4 making 14, and the arrow's digits add up to that number.
- Between line
A line with a circle at each end. Every digit on the line is strictly greater than one circle and strictly less than the other.
- Bifurcation
Trying one option in a cell and following it to see if it breaks. Many solvers treat it as a last resort, and well-made puzzles can be solved without it.
- Bivalue cell
A cell with exactly two candidates. These cells are the start of most pair and chain deductions.
- Black dot
A black Kropki dot joins two digits where one is double the other, such as 3 and 6. The pair 1 and 2 fits both a white dot and a black dot.
- Box/line reduction
When a digit's only spots in a row or column all sit inside one box, the digit must be in that part of the box. You can remove it from the rest of the box. It is the mirror image of a pointing pair.
- Break-in
The first deduction in a puzzle, often the hardest to find. Setters usually hide it where two rules meet.
- Cage
A group of cells outlined with a dashed line. In most puzzles the digits in a cage can't repeat, and a clue in its corner gives their sum.
- Cage combination
A set of distinct digits that fits a cage's size and total. Some totals allow only one set: 2 cells summing to 3 must be 1 and 2, and 2 cells summing to 17 must be 8 and 9.
- Candidate
A digit that could still go in a cell. Solving is mostly the work of removing candidates until one is left.
- Center mark
Small digits in the middle of a cell. They list every digit the cell could still be.
- Coloring
Shading cells to track how they relate. One common use is to give two colors to two options and follow each until one leads to a clash.
- Corner mark
A small digit in the corner of a cell. It means this digit goes in one of the cells marked this way in the house.
- Deadly pattern
Four cells in two rows, two columns and two boxes that could all swap between the same two digits. That would give two solutions, so in a unique puzzle at least one of those cells must hold something else. The Unique Rectangle step is built on this. Solvers name four common types: one corner with extra digits (type 1), two corners sharing one extra digit (type 2), extra digits that make a naked subset (type 3), and a digit locked into the two extra corners (type 4).
- Diagonal sudoku
A puzzle where one or both main diagonals also hold 1 to 9 with no repeats. It is also called sudoku X.
- Disjoint subsets
Cages in the same house can't share a digit. So their combinations must fit together without overlap, which often rules out options that look fine on their own.
- Dutch whispers
A line where neighboring digits differ by at least 4. A 5 can go on it only if both its neighbors on the line are 1 or 9.
- Empty rectangle
A box where a digit's spots all lie on one row and one column of the box. Paired with a strong link outside the box, it removes the digit from one cell where the two lines meet.
- Entropic line
A line where any 3 cells in a row along it hold one low digit (1 to 3), one middle digit (4 to 6) and one high digit (7 to 9). The pattern repeats every 3 cells.
- Extra region
A shaded group of 9 cells that works like an extra box. The digits 1 to 9 appear in it once each.
- Fog of war
Most of the grid starts hidden. Placing correct digits clears the fog around them and shows clues that were covered.
- Full house
The last empty cell in a row, column or box. Only one digit is missing, so that digit goes there.
- German whispers
A line, usually green, where neighboring digits differ by at least 5. A 5 can never go on it, and digits alternate between high (6 to 9) and low (1 to 4).
- Givens
The digits printed in the grid at the start. You can't change them. Many variant puzzles have very few givens, and some have none, because the extra rules carry the information instead.
- Global constraint
A rule that applies everywhere in the grid with no markings, such as anti-knight or non-consecutive. You have to check it for every cell you fill.
- House
A row, column or 3x3 box. Each house holds 1 to 9 exactly once. Extra regions and marked diagonals work as extra houses.
- Innie
A cell inside a house (or group of houses) that isn't covered by cages lying fully inside it. The 45 rule gives you its value or the sum of all such cells.
- Jellyfish
The four-row version of the X-wing and swordfish. Rare in practice.
- Killer cage
A cage with a sum clue. Its digits add up to the clue and don't repeat.
- Kropki dot
A dot on the border between two cells. The color tells you how the two digits relate. White and black are the usual colors, but check the puzzle's rules.
- Little killer
A clue outside the grid with a small arrow pointing along a diagonal. The digits on that diagonal add up to the clue, and they may repeat unless another rule stops it.
- Naked pair
Two cells in one house that can each only be the same two digits. Those two digits must go in those two cells, so you can remove them from every other cell in the house.
- Naked single
A cell with only one candidate left. Its row, column and box already rule out the other 8 digits.
- Naked triple
Three cells in one house whose candidates, taken together, are only three digits. Those three digits are used up by those cells and can be removed from the rest of the house.
- Negative constraint
A rule saying all possible clues of a type are shown. Where a dot, X or V is missing, the two cells do not have that relationship.
- Non-consecutive
Cells that share an edge can't hold digits that are one apart. A 5 can't sit beside a 4 or a 6.
- Odd and even cells
Shaded shapes that fix a cell's parity. A gray circle usually means odd and a gray square usually means even, but check the puzzle's rules.
- Outie
A cell outside a house that belongs to a cage sticking into it. Subtracting 45 from the total of the cages that cover the house gives the outies' sum.
- Palindrome line
A line that reads the same from either end. Cells in matching spots hold the same digit, so they can never share a house.
- Parity
Whether a digit is odd or even. The digits 1 to 9 include 5 odd digits and 4 even ones, which helps when counting what a house still needs.
- Parity line
A line where digits alternate between odd and even along its length.
- Pointing pair
When a digit's only spots in a box all sit in one row or column, the digit must be in that box's part of the line. You can remove it from the rest of that row or column.
- Quadruple
A circle on the corner where 4 cells meet, holding up to 4 digits. Each digit shown must appear in at least one of those 4 cells.
- Region sum line
A line that crosses box borders. Each piece of the line inside one box adds up to the same total.
- Renban
A line, usually purple, holding a set of consecutive digits in any order with no repeats. A 4-cell renban could be 3, 6, 4, 5 but not 2, 3, 5, 6.
- Sandwich sum
A clue outside the grid giving the sum of the digits between the 1 and the 9 in that row or column. A 0 means the 1 and 9 are next to each other, and 35 means they sit at the two ends.
- Sees
One cell sees another when they can't hold the same digit, because they share a house or because a variant rule links them. Anti-knight and anti-king rules make cells see each other across the grid.
- Set theory
Comparing two groups of cells that must hold the same digits, such as a row and a matching set of cages. Cells that are in one group and not the other must hold the same digits as each other.
- Skyscraper
Two rows where a digit has only two spots each, with one end of each in the same column. At most one of those lined-up ends holds the digit, so one of the other two ends does. Remove the digit from cells that see both of them.
- Snyder notation
A corner-marking habit: you mark a digit in a box only when it can go in just two cells there, sometimes three. It keeps notes short and makes pairs easy to spot.
- Strong link
Two candidates where one must be true: a digit with only two spots in a house, or a cell with only two candidates. Chains alternate strong links with weak links (two candidates that can't both be true).
- Swordfish
An X-wing across three rows and three columns. A digit's spots in three rows all fall in the same three columns, so it can be removed from the rest of those columns. Rows and columns can swap.
- Thermo bulb
The round end of a thermometer. Digits rise from the bulb toward the other end, so the bulb holds the smallest digit on the thermo.
- Uniqueness
A well-made puzzle has exactly one solution. Some solvers use this as a logic step, ruling out any pattern that would allow two solutions.
- W-wing
Two cells with the same two candidates, X and Y, that don't see each other, joined by a strong link on X. If neither cell were Y, both would be X and the link would have no X left. So one is Y, and Y can go from cells that see both.
- White dot
A white Kropki dot joins two digits that are one apart, such as 4 and 5.
- X-chain
A chain on one digit that alternates strong and weak links. If it starts and ends on strong links, one end holds the digit, so any cell that sees both ends can't. Skyscrapers and kites are short X-chains.
- X-sum
A clue outside the grid. Read the first digit from that side (call it X), then add up the first X cells, including that first one. The total equals the clue.
- X-wing
A digit is limited to the same two columns in two different rows. The four cells form a rectangle, and the digit takes two opposite corners, so it can be removed from the rest of those two columns. The same works with rows and columns swapped.
- XV
An X between two cells means they add to 10. A V means they add to 5. If the puzzle says all X and V clues are given, every other pair of neighbors adds to something else.
- XY-chain
A chain of bivalue cells, each linked to the next by a shared digit. If the first and last cells both hold the digit Z, one of them is Z, so remove Z from cells that see both ends. An XY-wing is a three-cell XY-chain.
- XY-wing
Three bivalue cells: a pivot holding XY and two pincers holding XZ and YZ, each seeing the pivot. Whatever the pivot is, one pincer is Z, so Z can go from any cell that sees both pincers.
- XYZ-wing
An XY-wing whose pivot also holds Z (XYZ). One of the three cells must be Z, so Z can go from any cell that sees all three.
No terms match.
About this glossary
These are the terms you will meet in variant sudoku rules, solving videos and puzzle comments. Some name a type of marking on the grid, some name a solving technique and some name a way of taking notes. Each definition links to the lessons where the term matters most. Setters don't always use words the same way, so when a puzzle's rules text defines a term, go with the puzzle.