Can Every Sudoku Be Solved Without Guessing?
Learn the difference between blind guessing, Trial & Error, and a temporary assumption used to produce a reproducible contradiction proof.
Read the guideLogic First · No Guessing
Sudoku Solving Guides
Sudoku Paradise explains not only what a technique eliminates, but why the elimination must be true. This growing library follows the same human-solvable doctrine used to evaluate and certify our puzzles.
Hardest Sudoku Compared
AI Escargot, Everest, and the Golden Nugget face the same Sudoku Paradise logic deck. See why three Monsters produce three different kinds of difficulty.
Read the benchmarkHow Sudoku Difficulty Is Measured
Why the techniques required to solve a grid matter more than its givens count.
How Difficulty Is MeasuredLocked Candidates
Pointing and claiming interactions between boxes, rows, and columns.
Locked Candidates LessonPairs, Triples, Quads, and an Introduction to Uniqueness
Learn how Naked and Hidden Pairs, Triples, and Quads restrict candidates, reveal one another, and lead toward more advanced Sudoku strategies.
Pairs, Triples, Quads, and RectanglesX-Wing
Learn how exactly two positions for one candidate in each of two rows or columns create aligned Strong Links—and why the resulting rectangle permits eliminations. This is your first Fish.
How to find the X-Wing Pattern.Swordfish
Bigger Fish to Fry.
Learn how the X-Wing is a Fish Pattern along with the Swordfish to the Leviathan.Skyscrapers, 2-String Kites, and Strong Links
Learn more about candidate positions and Strong Links, how two links align parallel to form Skyscrapers or align perpendicular to form Kites, and further explore rectangular geometry.
Skyscraper and 2-String KiteThe Empty Rectangle
Follow one candidate as it bends through a box, connects to an outside Strong Link, and eliminates the candidate where the two logical paths meet.
The Empty RectangleXY-Wing (Y-Wing)
Unlike the X-Wing, an XY-Wing is not a Fish. Connect three bivalue cells through one pivot and two pincers, then remove their shared candidate from every cell that sees both pincers.
XY-WingXYZ-Wing
Connect two Bivalue Cell pincers through a three-candidate pivot, then remove their shared candidate from every cell that sees the pivot and both pincers.
XYZ-WingUnique Rectangles
Under the one-solution assumption, learn how four cells can threaten a two-solution Deadly Pattern—and how the extra candidates that prevent that ambiguity can also prove eliminations.
Unique RectanglesW-Wing
Connect two matching Bivalue Cells through an outside Strong Link, then remove their other candidate from every cell that sees both wings.
Remote Pairs
Spot the same Bivalue Pair repeated across the grid, link an even number of cells, and use the opposite endpoints to eliminate both digits from a common target.
Learn Remote PairsXY-Chain
Connect Bivalue Cells into an alternating relay, then remove the shared endpoint candidate from every cell that sees both ends.
Grouped X-Chain
Follow one candidate through alternating Strong and Weak Links, allowing several confined candidates to act as one logical node.
Alternating Inference Chains (AICs)
Follow candidate states through alternating Strong and Weak Links. When the endpoint logic guarantees that at least one endpoint is true, any candidate conflicting with both can be eliminated.
Almost Locked Sets and ALS-XZ
Begin with the bivalue cell as the simplest Almost Locked Set, then connect two ALSs through a Restricted Common Candidate X to eliminate shared candidate Z from a cell that sees every possible Z source.
Sue de Coq: From Two ALSs to Two Sectors
Balance candidates across a box-line intersection, a line companion set, and a box companion set—then eliminate the digits locked into each sector.
Simple Coloring and Multi-Coloring
Use two colors to remember opposite truth states as one candidate travels through conjugate pairs. Find Color Wraps and Color Traps, then extend the same reasoning to disconnected networks with Multi-Coloring.
3D Medusa
Use two colors to track opposite truth states across multiple candidate digits. Follow Strong Links through conjugate pairs and Bivalue Cells, then use color contradictions or candidates caught by both states to force eliminations.
Explain My Next Sudoku Move
Import any Sudoku position and receive one logical next move: the strategy, relevant candidates, exact action, and reason it works—without revealing the rest of the solution.
Nishio and Logical Contradiction
Why a documented contradiction proof is not the same as guessing and backtracking.
Put the logic into practice
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