Sudoku Solving Algorithms & Help
Master Sudoku with our comprehensive guide to solving techniques, from beginner basics to expert logic.
Easy Techniques
Medium Techniques
Hidden Pair
Two numbers appear as candidates in only two cells within a unit.
Intersection (Box/Line)
When a candidate in a row or column is restricted to a single box, it eliminates that candidate from the rest of the box.
Intersection (Pointing)
When candidates in a box are restricted to a single row or column, they point outwards.
Naked Pair
Two cells in a unit contain only the same two candidates, meaning those numbers must go there.
Naked Triple
Three cells in a unit contain combinations of only three candidates, meaning those numbers must go there.
Hard Techniques
Hidden Triple
Three numbers are "hidden" as candidates in only three cells, forming a secret alliance that eliminates everything else.
Naked Quad
Four cells in a unit contain combinations of only four candidates.
X-Wing (Col)
A rectangular pattern formed by a candidate appearing twice in two columns.
X-Wing (Row)
A rectangular pattern formed by a candidate appearing twice in two rows.
Y-Wing
A pattern involving three cells with bi-value candidates (Pivot and two Wings).
Expert Techniques
2-String Kite
Two strong links (one row, one column) connected in a box, eliminating candidates from the intersection.
Finned X-Wing (Col)
A Column X-Wing with an extra "Fin" that allows for localized eliminations.
Finned X-Wing (Row)
A Row X-Wing with an extra "Fin" that allows for localized eliminations.
Remote Pairs
A chain of cells containing the same pair of numbers. If the chain is long enough, the ends eliminate candidates.
Sashimi X-Wing (Col)
Column-based Sashimi X-Wing.
Sashimi X-Wing (Row)
A degenerate Finned X-Wing where a corner is missing.
Skyscraper (Col)
Two vertical columns linked by a base row, forming two "towers" of different heights.
Skyscraper (Row)
Two horizontal rows linked by a base column, forming two "towers" lying on their sides.
Swordfish (Column)
A 3x3 pattern where a candidate appears in only three columns, restricted to the same three rows.
Swordfish (Row)
A 3x3 pattern where a candidate appears in only three rows, restricted to the same three columns.
Unique Loop Type 1
Eliminate candidates from a single rescue cell to prevent a deadly pattern in a loop of 4 or more cells.
Unique Rectangle (Type 1)
Use the "Deadly Pattern" rule to eliminate candidates that would cause the puzzle to have two valid solutions.
Unique Rectangle (Type 2)
A variation of the Unique Rectangle where two corners have the same extra candidate.
Unique Rectangle (Type 3 Hidden)
A variation of UR Type 3 using hidden subsets.
Unique Rectangle (Type 3)
When extra candidates in the "roof" cells form a Naked Subset with neighboring cells.
Unique Rectangle (Type 4)
When one UR candidate is "locked" in a row or column, the other candidate can be eliminated.
W-Wing
A fan-favorite "secret shortcut" using two identical pairs connected by a Strong Link.
XY-Chain
An advanced chain strategy using multiple bivalue cells to connect a number from start to finish.
XYZ-Wing
A more advanced version of the Y-Wing that involves three cells and an extra candidate in the pivot.
Expert+ Techniques
BUG Type 1 (BUG+1)
When only one cell has 3 candidates and all others have 2, the extra candidate must be the solution.
BUG Type 2
When multiple BUG cells share the same extra candidate, eliminate it from cells that see all of them.
BUG Type 3
When BUG cells' extras form a Naked Subset with other cells in a shared region, eliminate subset values from the region.
BUG Type 4
When a common value is locked to BUG cells in a shared region, eliminate other candidates from them.
Unique Loop Type 2
When multiple loop cells share the same extra candidate, eliminate it from cells that see all of them.
Unique Loop Type 3
Eliminate candidates when loop extras form a Naked Subset with other cells in a shared region.
Unique Loop Type 4
When one loop value is locked to rescue cells in a shared region, eliminate the other loop value from them.
Extreme Techniques
3D Medusa
An advanced coloring strategy that links multiple candidates across the grid to find contradictions.
Aligned Pair Exclusion
A strategy that eliminates candidates by analyzing all possible combinations of values for two cells and excluding impossible ones.
Complex Logic (Trial and Contradiction)
Last resort strategy that tests candidates and eliminates those that lead to contradictions.
Jellyfish (Column)
A 4x4 pattern where a candidate appears in only four columns, restricted to the same four rows.
Jellyfish (Row)
A 4x4 pattern where a candidate appears in only four rows, restricted to the same four columns.
Simple Coloring
Use two colors to trace a single candidate across the grid. If a cell sees both colors, it can be eliminated.
X-Cycle (Continuous)
A continuous loop of strong and weak links for a single digit that validates the chain and eliminates peers.
X-Cycle (Discontinuous)
A single-digit chain that forms a loop with a contradiction, forcing an elimination.
XY-Cycle (Continuous)
A perfect loop of bivalue cells that turns weak links into strong links, causing eliminations outside the loop.
XY-Cycle (Discontinuous)
A chain through bivalue cells that loops back to contradict itself, forcing an elimination.
Y-Cycle (Continuous)
A continuous loop of bivalue cells that forms a stable logic ring, eliminating candidates from peers.
Y-Cycle (Discontinuous)
A chain of bivalue cells that forms a loop with a "break," proving the starting candidate is impossible.
Hidden Quad
Four numbers find a secret hiding spot in four cells, locking out all other candidates.