Learn variant sudoku
Every rule you’ll meet in modern hand-set sudoku, from killer cages to fog of war. Short videos, the facts solvers memorize, and practice right on the page.
Start with Classic sudoku
Every variant starts from the classic rules. Learn them cold and every variant is just an extra rule on top.
The basics
2 lessonsSums and pairs
3 lessonsLines
10 lessonsThermometersDigits rise from the bulb to the tip. Longer thermos squeeze the digits hard.ArrowsThe digits along an arrow add up to the digit in its circle.German whispersNeighbors on a green line differ by at least 5. This one has a famous trick.Renban linesA purple line holds a run of consecutive digits in any order, with no repeats.PalindromesA gray line reads the same from either end.Dutch whispersLike German whispers, but neighbors only need to differ by at least 4.Entropic linesAny three cells in a row on the line hold one low (1–3), one middle (4–6) and one high (7–9) digit.Parity linesAlong the line, digits alternate between odd and even.Region sum linesWhere a line crosses box borders, each piece of it adds up to the same total.Between linesDigits on the line sit strictly between the two circled digits at its ends.Whole-grid rules
4 lessonsOutside clues and specials
7 lessonsSandwich sumsA clue outside the grid is the sum of the digits between the 1 and the 9 in that row or column.Little killerA clue outside the grid gives the sum of the diagonal it points along.Odd and even cellsA gray circle holds an odd digit. A gray square holds an even digit.QuadruplesDigits in a circle on a corner must appear in the four cells around it.Extra regionsA shaded region works like an extra box: no digit repeats inside it.X-sumsA clue gives the sum of the first X cells, where X is the first digit from that side.Fog of warMost of the grid starts hidden. Correct digits clear the fog around them.Solving techniques
12 lessonsTechniques are how you solve without guessing. Learn them in order.
SinglesA cell with one candidate left, or a digit with one place left in a house. The classic lesson covers both.Pointing and box/lineA digit stuck on one line inside a box clears that line outside the box. It works the other way round too.Naked and hidden pairsTwo cells that share the same two digits lock those digits in. Three cells with three digits work the same way.X-WingTwo rows with the same two spots for a digit fill those two columns. Nothing else in the columns can have it.SkyscraperTwo rows with two spots each share one column. Whatever sees both of the other ends loses the digit.2-String KiteA row and a column each have two spots for a digit, meeting in one box. The cell that sees both far ends loses the digit.XY-WingThree cells with two candidates each, bent around a middle cell, force a digit into one of two wings.XYZ-WingLike an XY-Wing, but the middle cell holds all three digits. The cell to clear must see all three.W-WingTwo matching two-candidate cells, linked through a digit with only two spots, force the other digit into one of them.SwordfishThe X-Wing with three rows: three rows whose spots use only three columns fill those columns.Simple ColoringFollow one digit through houses where it has two spots, painting the spots in two colors. One color is true.ChainsA string of “if not this, then that” links. If both ends are the same digit, one of them must be it.Variant techniques
5 lessonsThe logic behind each rule. These are the moves setters expect you to find.
Killer cagesCage totals with only one answer, the 45 rule, and cages that lock digits out of a box.ThermometersEvery cell on a thermometer has a range. Count along the line, then let the givens squeeze it.ArrowsAn arrow’s cells set a floor for its circle, and the circle sets a ceiling for the arrow.German whispersNo 5 on the line, cells that swap between high and low, and why 4 and 6 are so hard to place.Kropki dotsChains of dots, the digits that never touch a black dot, and dots that work together.
How the lessons work
What makes it variant
Variant sudoku keeps the classic rules and adds one or more extra rules. Each extra rule usually comes with a marking on the grid, such as a line, a cage, a dot or a clue outside the edge. The marking tells you something about the digits it touches. Because the rules carry so much information, a variant puzzle can start with very few digits, and some start with an empty grid. You solve it the same way as a classic puzzle, one logical step at a time, using the extra rules as another source of deductions.
How the path builds
The lessons run in five groups, and each one builds on the ones before it. The basics cover classic rules and pencil marks. Sums and pairs cover killer cages, XV and Kropki dots. Lines cover thermometers, arrows, whispers, renban and other line types. Whole-grid rules like anti-knight and non-consecutive apply everywhere without any markings. The last group covers outside clues and special rules, including sandwich sums, little killers, X-sums and fog of war. Later lessons reuse ideas from earlier ones, like the 45 rule from killer cages.
How each lesson works
Each lesson has a short video, the rule in the words setters use, a few facts worth memorizing and some quick drills. Watch the video once, then try the drills without it. After that, play a practice puzzle that uses the rule. If you get stuck, go back to the facts list and check each one against the grid before you guess. You can repeat a lesson's drills as often as you like, and it helps to come back to them after a few puzzles with the rule.
Reading a rules text
Every puzzle comes with a short rules text, and it is worth reading slowly. The first line usually says that normal sudoku rules apply. Each sentence after that adds a rule for one kind of marking. Match every marking on the grid to a sentence before you place a digit. Setters don't all use the same colors and symbols, so the text is the final word on what a marking means.
How to read a variant puzzle's rules
Start with the first sentence. "Normal sudoku rules apply" means every row, column and 3x3 box holds 1 to 9 once each. Every sentence after that adds a rule, and most of them name a marking: a cage, a line, a dot or an outside clue. Find each marking on the grid and match it to its sentence. If a marking has no sentence, read any notes under the rules before you assume what it means.
Next, look for the small words that change a rule. "All possible dots are given" means a missing dot is also a clue. "Digits may repeat" tells you a cage or diagonal can hold the same digit twice. Check whether a line must strictly increase and whether an outside clue counts cells or adds digits. Line and dot colors vary between setters, so trust the words over the color.
Last, notice what the rules leave out. A line only limits digits in the way its sentence says. Unless the text says digits on a line can't repeat, they can, as long as the normal sudoku rules allow it. Before you start, say the rules back to yourself in one line each, then look for the place where two rules touch the same cells. That is often where the first deduction sits.
Questions about variant sudoku
What is variant sudoku?
Variant sudoku is sudoku with one or more extra rules added. Most extra rules come with markings on the grid, such as cages, lines, dots or clues outside the edge. You still fill every row, column and box with 1 to 9, and the extra rules give you more ways to rule digits out.
What does "normal sudoku rules apply" mean?
It means the classic rules still hold. Every row, every column and every 3x3 box contains the digits 1 to 9 exactly once. The rest of the rules text adds to this and doesn't replace it.
Where should a beginner start?
Start with classic sudoku and pencil marks, then try killer cages and thermometers. These rules are easy to read on the grid and teach the habits later lessons need, like adding up cells and ruling digits out along a line. Take the lessons in order the first time through.
Are variant puzzles harder than classic sudoku?
Not always. The extra rules give you more information, so a variant puzzle can be easy even with few starting digits. Difficulty depends on the puzzle, so start with ones marked easy for each new rule.
Do I need to guess to solve a variant sudoku?
A well-made puzzle can be solved by logic alone, with no guessing. When you feel stuck, look for a spot where two rules touch the same cells, or recheck your pencil marks. Guessing and checking works too, but it teaches you less about the rule.
What does "all possible dots are given" mean?
It means the setter has drawn every dot that could appear. If two neighboring cells have no dot between them, their digits are not one apart and neither is double the other. This kind of rule is called a negative constraint, and it often gives the most useful clues in the puzzle.