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Logicholic · Logic and strategy

Game techniques

Clear explanations and examples of useful techniques for logic games.

2048 1 guide

2048 · 2 min read

Keep the Largest Tile in a Corner in 2048

Anchor the largest tile in one corner and arrange nearby tiles in descending order.

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Sudoku 27 guides

Sudoku · 2 min read

Naked Single in Sudoku

A cell with only one valid candidate must contain that digit.

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Sudoku · 2 min read

Hidden Single in Sudoku

If a digit has only one possible cell in a row, column, or box, place it there, even if the cell has other candidates.

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Sudoku · 2 min read

Naked Pairs in Sudoku

Two cells in one unit containing the same two candidates reserve those digits for themselves.

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Sudoku · 2 min read

Hidden Pairs in Sudoku

If two digits can occur only in the same two cells of a unit, those cells form a hidden pair.

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Sudoku · 2 min read

Naked Triples in Sudoku

Three cells in one unit that collectively contain only three digits reserve those digits.

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Sudoku · 2 min read

Hidden Triples in Sudoku

If three digits are restricted to the same three cells in a unit, remove other candidates from those cells.

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Sudoku · 2 min read

Naked Quads in Sudoku

Four cells whose combined candidates are exactly four digits reserve those digits in their unit.

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Sudoku · 2 min read

Hidden Quads in Sudoku

Four digits limited to the same four cells form a hidden quad.

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Sudoku · 2 min read

Pointing Pairs and Triples in Sudoku

If every candidate for a digit in a box lies on one row or column, that digit cannot appear elsewhere on that line.

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Sudoku · 2 min read

Box-Line Reduction in Sudoku

If all candidates for a digit on a row or column lie in one box, remove that digit from the other cells of the box.

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Sudoku · 2 min read

X-Wing in Sudoku

When a digit occurs in exactly the same two columns in two rows, those corners form an X-Wing.

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Sudoku · 2 min read

Swordfish in Sudoku

A Swordfish extends the X-Wing pattern to three rows and three columns.

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Sudoku · 2 min read

Jellyfish in Sudoku

A Jellyfish uses four rows and four columns to restrict one digit.

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Sudoku · 2 min read

Skyscraper in Sudoku

Two strong links for one digit share an aligned end; at least one of their unaligned ends must be true.

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Sudoku · 2 min read

Two-String Kite in Sudoku

A row strong link and a column strong link connect through one box, forcing one of their outer endpoints.

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Sudoku · 2 min read

Empty Rectangle in Sudoku

A box can form an empty-rectangle pattern for a digit when its candidates lie on a crossing row and column.

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Sudoku · 2 min read

Y-Wing (XY-Wing) in Sudoku

A two-candidate pivot sees two two-candidate wings. The wings share a third digit that one of them must contain.

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Sudoku · 2 min read

XYZ-Wing in Sudoku

A three-candidate pivot sees two wings whose candidates each include one pivot digit and a shared digit.

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Sudoku · 2 min read

W-Wing in Sudoku

Two cells with the same two candidates can be linked by a strong link for one candidate.

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Sudoku · 2 min read

Unique Rectangles in Sudoku

In puzzles with a unique solution, avoid a four-cell rectangle that would allow two digits to swap without changing the grid.

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Sudoku · 2 min read

Simple Coloring in Sudoku

Color candidates of one digit along strong links using two alternating colors.

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Sudoku · 2 min read

XY-Chains in Sudoku

Connect two-candidate cells so each neighboring pair shares one candidate.

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Sudoku · 2 min read

X-Cycles in Sudoku

Trace alternating strong and weak links for a single digit.

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Sudoku · 2 min read

3D Medusa in Sudoku

Color strong links between individual candidates, including links within a cell and within a unit.

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Sudoku · 2 min read

Alternating Inference Chains in Sudoku

Follow a chain of alternating strong and weak links to connect candidate statements.

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Sudoku · 2 min read

ALS-XZ in Sudoku

An almost-locked set has one more candidate digit than cells. Two such sets can interact through a restricted common digit.

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Sudoku · 2 min read

Forcing Chains in Sudoku

Test each possible value of a candidate and follow its logical consequences.

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Klotski 1 guide

Klotski · 2 min read

Shortest Paths in Klotski with BFS

Breadth-first search explores board positions one move at a time, guaranteeing the shortest solution when every move has equal cost.

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Bridges (Hashi) 2 guides

Bridges (Hashi) · 2 min read

Bridge Totals in Hashi

An island number equals the total bridges touching it; each neighboring pair can have at most two bridges.

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Bridges (Hashi) · 2 min read

Islands Marked 8 and 7 in Hashi

An island with four neighbors can support at most eight bridges: two in each direction.

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Light Up 1 guide

Light Up · 2 min read

Light Visibility in Akari

A bulb lights cells along its row and column until a wall blocks the light; bulbs may not illuminate each other.

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Kakuro 2 guides

Kakuro · 2 min read

Sum Combinations in Kakuro

For each run, list distinct digits that add up to its clue, then use crossing runs to remove impossible combinations.

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Kakuro · 2 min read

Required Digits in Kakuro Runs

When every valid combination for a run contains a digit, that digit must appear somewhere in the run.

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Nonogram 2 guides

Nonogram · 2 min read

Line Solving in Nonograms

Place each run in every position allowed by the clue and mark cells shared by all possibilities.

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Nonogram · 2 min read

Crossing Clues in Nonograms

Row and column clues constrain the same cells; use each confirmed or empty cell to update both lines.

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Futoshiki 1 guide

Futoshiki · 2 min read

Inequality Chains in Futoshiki

A chain of inequalities limits which numbers can fit at each position.

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Maze 1 guide

Maze · 2 min read

Shortest Maze Paths with BFS

Breadth-first search checks reachable cells by distance from the start.

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Minesweeper 1 guide

Minesweeper · 2 min read

Number Clues in Minesweeper

Each number counts mines in its neighboring squares. Compare that count with confirmed flags and unknown squares.

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Nim 1 guide

Nim · 2 min read

Nim-Sum and XOR Strategy

XOR the heap sizes to find the Nim-sum. In normal-play Nim, a nonzero result means the player to move can leave a zero Nim-sum.

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Water Jug 1 guide

Water Jug · 2 min read

Water Jug Puzzles: GCD and BFS

With two jug capacities A and B, a target no greater than the larger jug is measurable exactly when it is divisible by gcd(A, B).

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