Standard Constraint Phrasing

Anti-king: Cells that are a chess king’s move apart cannot contain the same digit.

Anti-knight: Cells that are a chess knight’s move apart cannot contain the same digit.

Disjoint Groups: Each position in the 3x3 boxes contains a full set of the digits 1 to 9. That is, no digit can show up in the same position in two different 3x3 boxes.

Dynamic Fog: Part of the grid is covered with fog. Correctly placed digits clear fog from their own cell and possibly other cells.

Fog: Part of the grid is covered with fog. As correct digits are placed, the fog will clear from cells surrounding the correct digit, potentially revealing additional clues.

Global Entropy: Each 2x2 area must contain a low digit (123), a middle digit (456), and a high digit (789).

Global Modularity: Each 2x2 area must contain digits with three different remainders when divided by 3; that is, a remainder-0 digit (369), a remainder-1 digit (147), and a remainder-2 digit (258).

Non-consecutive: Digits in orthogonally adjacent cells cannot be consecutive.

159 Indexing: Digits in red-shaded cells in column 1 indicate the position of 1 in the corresponding row. The same is true in columns 5 and 9 for 5's and 9's respectively.

Anti-Diagonal: Each of the main diagonals may only contain 3 distinct digits.

Anti-Quadruples: Digits in an Anti-Quadruple circle may not appear in any of the four cells touching that circle.

Arrows: Digits along an arrow sum to the number in the circle or pill from which the arrow emerges. Multi-digit sums in pills are read top-to-bottom or left-to-right.

Arrows: Digits along an arrow sum to the number in the circle or pill from which the arrow emerges. Multi-digit sums in pills are read top-to-bottom or left-to-right.

Arrows: Digits along an arrow sum to the number in the circle from which the arrow emerges.

Arrows: Digits along an arrow sum to the number in the circle from which the arrow emerges. If multiple arrows emerge from the same circle, each arrow is summed separately.

Between Lines: Digits placed on the line must be strictly between the digits placed in the circles at the ends of the line.

Cages: Digits in cages cannot repeat and must sum to the value shown in the upper left corner of the cage, if given.

Cages: Digits in cages cannot repeat and must sum to the value shown in the upper left corner of the cage.

Clone regions: Each clone region contains the same digits in the same relative positions as its clone.

Column Indexing: Digits placed in red cells indicate the position of the corresponding column number in that row.

Diagonal: Digits along a marked diagonal cannot repeat.

Diagonal Sums: Clues outside the grid give the sum of the digits along the indicated diagonal. Digits may repeat if allowed by other rules.

Difference dots: Digits separated by a white dot differ by the amount shown in the dot. If no value is given in the dot, the digits differ by 1.

Double Arrows: Digits along a line sum to same total as the digits in the circles connected to the line.

Entropic Line: Any set of three adjacent cells along an entropic line must contain a low digit (12), a middle digit (34), and a high digit (56).

Entropic Line: Any set of three adjacent cells along an entropic line must contain a low digit (123), a middle digit (456), and a high digit (789).

Even/Odd: Cells marked with a grey square contain even digits. Cells marked with a grey circle contain odd digits.

Even: Cells marked with a grey square contain even digits.

Fortress cells: Shaded cells must be larger than any orthogonally adjacent unshaded cell.

Consecutive Pairs: Digits separated by a white dot are consecutive. ALL POSSIBLE DOTS ARE GIVEN.

Consecutive Pairs: Digits separated by a white dot are consecutive.

Kropki Pairs: Digits separated by a black dot are in 2:1 ratio. Digits separated by a white dot are consecutive. ALL POSSIBLE DOTS ARE GIVEN.

Kropki Pairs: Digits separated by a black dot are in a 2:1 ratio. Digits separated by a white dot are consecutive.

Ratio Pairs: Digits separated by a black dot are in 2:1 ratio. ALL POSSIBLE DOTS ARE GIVEN.

Ratio Pairs: Digits separated by a black dot are in a 2:1 ratio.

Variable Difference Pairs: Digits separated by a white dot differ by n, where n is the value shown in the dot. If no value is shown, the digits differ by 1.

Variable Kropki Pairs: Digits separated by a black dot are in an n:1 ratio where n is the value shown inside the dot. If no value is shown, the digits are in a 2:1 ratio. Digits separated by a white dots differ by n where n is the value shown inside the dot. If no value is shown, the digits differ by 1.

Variable Ratio Pairs: Digits separated by a black dot are in an n:1 ratio where n is the value shown inside the dot. If no value is shown, the digits are in a 2:1 ratio.

Lockout lines: Digits in the diamonds at the ends of a lockout line must differ by at least 4. Digits on a line must fall outside the range defined by their attached diamonds and may repeat if allowed by other rules. A diamond terminates a line segment.

Look-and-say Cages: The number in the top left of the cage is split up into pairs XY, each read as 'there are X Ys in the cage'. For example, if you had a cage that was labeled '1432', there would be one of the digit 4 and three of the digit 2 in the cage.

Look-and-say Diagonals: Clues outside the grid are split up into pairs XY, each read as 'there are X Ys on the indicated diagonal'. For example, if a diagonal clue is 1221, this means there are one 2 and two 1's on the diagonal.

Maximum cells: Digits placed in cells with arrows pointing out must be greater than all orthogonally adjacent cells.

Minimum/maximum cells: Digits placed in blue cells with arrows pointing in must be smaller than all orthogonally adjacent cells. Digits placed in yellow cells with arrows pointing out must be larger than all orthogonally adjacent cells.

Minimum cells: Digits placed in cells with arrows pointing in must be smaller than all orthogonally adjacent cells.

Modular Line: Any set of three adjacent cells along a modular line must have three different remainders when divided by 3.

Nabner Line: No two digits along a nabner line can be consecutive, regardless of their position on the line. Digits may not repeat on nabner lines.

Numbered Rooms: A clue outside the grid indicates the digit which has to be placed in the Nth cell in the corresponding direction, where N is the digit placed in the first cell in that direction.

Odd: Cells marked with a grey circle contain odd digits.

Palindromes: Digits along a palindrome line read the same forwards as backwards along the line.

Parity Lines: Digits along a parity line alternate odd/even.

Quadruples: Digits in a quadruple circle must be placed at least once in the four cells touching that circle.

Quadruples: Digits in a quadruple circle must be placed at least once in the four cells touching that circle. If a digit appears twice in a quadruple circle, it must be placed twice in the four cells touching that circle.

Renban Line: Digits along a renban line must form a set of non-repeating consecutive digits in some order.

Row and Column Indexing: Digits placed in red cells indicate the position of the corresponding column number in that row. Digits placed in green cells indicate the position of the corresponding row number in that column.

Row Indexing: Digits placed in green cells indicate the position of the corresponding row number in that column.

Region Sum Lines: Box borders split blue lines into sections, and the digits on those sections must sum to the same value. If a line has multiple sections within a box, all sections count towards the same total.

Region Sum Lines: Region borders split blue lines into sections, and the digits on those sections must sum to the same value. If a line has multiple sections within a region, all sections count towards the same total.

Region Sum Lines: Box borders split blue lines into sections, and the digits on those sections must sum to the same value.

Region Sum Lines: Region borders split blue lines into sections, and the digits on those sections must sum to the same value.

Region Sum Lines: Box borders split blue lines into sections, and the digits on those sections must sum to the same value. If a line has multiple sections within a box, each section is summed separately.

Region Sum Lines: Region borders split blue lines into sections, and the digits on those sections must sum to the same value. If a line has multiple sections within a region, each section is summed separately.

Sandwich Sums: Clues outside the grid indicate the sum of the digits between 1 and 9 in that row or column.

Shout-2 Lines: Adjacent digits along a Shout-2 Line differ by at most 2.

Shout-3 Lines: Adjacent digits along a Shout-3 Line differ by at most 3.

Shout-4 Lines: Adjacent digits along a Shout-4 Line differ by at most 4.

Shout-5 Lines: Adjacent digits along a Shout-5 Line differ by at most 5.

Shout-6 Lines: Adjacent digits along a Shout-6 Line differ by at most 6.

Shout-7 Lines: Adjacent digits along a Shout-7 Line differ by at most 7.

Shout-n Lines: Adjacent digits along a Shout-n Line differ by at most n, where n is the value indicated next to the line at one end.

Skyscrapers: Each cell represents a ‘skyscraper’ whose height is the digit in that cell. Taller skyscrapers obscure the view of smaller ones. Clues outside the grid tell how many skyscrapers are visible looking across the row or column from the direction of the clue.

Thermometers: Digits on thermometers are strictly increasing from bulb to tip.

Slow Thermometers: Digits along thermometers can repeat but cannot decrease as you move from bulb to tip.

V Pairs (Negative Constraint): Digits separated by a V sum to 5. All possible V clues are given.

V Pairs: Digits separated by a V sum to 5.

Whisper-2 Lines: Adjacent digits along a Whisper-2 Line must differ by at least 2.

Whisper-3 Lines: Adjacent digits along a Whisper-3 Line must differ by at least 3.

Whisper-4 Lines: Adjacent digits along a Whisper-4 Line must differ by at least 4.

Whisper-5 Lines: Adjacent digits along a Whisper-5 Line must differ by at least 5.

Whisper-6 Lines: Adjacent digits along a Whisper-6 Line must differ by at least 6.

Whisper-7 Lines: Adjacent digits along a Whisper-7 Line must differ by at least 7.

Whisper-n Lines: Adjacent digits along a Whisper-n Line must differ by at least n, where n is the value indicated next to the line at one end.

X-Sums: Clues outside the grid give the sum of the first X numbers placed in the corresponding row or column, where X is digit in the cell next to the X-sum clue.

XV Pairs: Digits separated by an X sum to 10. Digits separated by a V sum to 5.

XV Pairs (Negative Constraint): Digits separated by an X sum to 10. Digits separated by a V sum to 5. All possible X and V clues are given.

X Pairs (Negative Constraint): Digits separated by an X sum to 10. All possible X clues are given.

X Pairs: Digits separated by an X sum to 10.

Zipper Lines: Along Zipper lines, pairs of digits equidistant from the center of the line have the same sum. For Zipper lines of odd length, that sum is the central digit on the line.

Zipper Lines: Along Zipper lines, pairs of digits equidistant from the center of the line have the same sum.

Zipper Lines: Along Zipper lines, pairs of digits equidistant from the center of the line have the same sum as the central digit on the line.