# Logic puzzle

Logic puzzles are puzzles that revolve around linear thinking and logical deduction. Logic puzzle are fairly common in puzzle hunts, but are also a very common puzzle type in general due to their prevalence in casual puzzle-solving mediums such as newspapers and printed puzzle publications. However, they are not to be underestimated simply due to their commonality, as puzzle hunts often create variations on classics, or introduce constraints not normally seen in the wild.

## Core Characteristics

Logic puzzles in general require an aspect of mathematical or logical thinking to solve, and often involve a specific path of deductions to be made and followed in order to reach the singular solution at the end.

One key component of a logic puzzle is a lack of ambiguity. A logic puzzle (at least at base level within the genre, without additional puzzle hunt-y twists) should have a single solution. While there may be multiple ways to reach that solution, there should not be any way to reach an alternate solution.

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## History of Use

Logic puzzles in their more deductive and wordy forms originate primarily from figures such as author Lewis Carroll (who wrote the book The Game of Logic that included various syllogism-based puzzles) and mathematician/philosopher Raymond Smullyan (who wrote several books combining mathematical and logical puzzles with narrative settings).

While some popular grid-based logic puzzles have early origins in newspapers as small novelty activities, many originate from the Japanese puzzle company Nikoli, which was established in 1980 and is most famous for popularizing (although not inventing) Sudoku puzzles.

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## Subtypes

### Grid Constraint

Grid constraint logic puzzles, as the name suggests, involve filling in or manipulating parts of a grid based on a series of rules and constraints that vary depending on the specific puzzle type. The vast majority of grid constraint logic puzzles involve drawing lines, shading spaces, or placing numbers, and can therefore be divided into the following categories:

#### Path Drawing

Path-drawing logic puzzles involve connecting points, drawing walls, and making loops within the constraints set by the puzzle. The goals in path-drawing puzzles are often loop-based, requiring solvers to draw a continuous path through the grid. Other goals include creating interconnected systems and dividing a grid into specific regions.

• Corral - A loop (representing walls) is drawn around a series of numbers so that the amount of squares visible in cardinal directions from those numbers is equal to the numbers themselves (including the space the number is on).
• Hashi wo Kakero (Bridges) - Lines (representing bridges) are drawn between numbered circles indicating the number of lines connected to them. The goal is to have all circles be connected, with a maximum of two lines existing between any given pair of circles.
• Knight's Tour - A path must be found around a grid, hitting every available square while only moving in an L-shape like a knight in chess.
• Masyu - A closed loop is drawn around a grid, passing through black and white circles that dictate when the path has to turn.
• Numberlink - A puzzle where matching pairs of numbers need to be connected in a grid without the paths overlapping or crossing.
• Slitherlink - A loop must be drawn around a grid so that numbered cells only have a particular number of sides being used in the path.
• Yajilin - A closed loop must be drawn through a grid. Numbered cells with arrows indicate the number of unused cells (not counting other numbered cells) between that cell and the edge of the grid in the direction the arrow is pointing. Also a grid-shading puzzle.

Grid-shading puzzles involve coloring in cells within the grid based on a series of rules, and can vary between greyscale and full-color depending on the type and difficulty.

• Heyawake - A puzzle in which certain cells need to be shaded so that particular 'rooms' (marked with a number) contain the correct number of shaded cells, and that all unshaded cells are connected.
• Hitori - A puzzle in which a grid of numbers must have certain cells shaded so that no more than one of the same number appears in a given row or column (and all of the unshaded cells are connected orthogonally)
• LITS - A puzzle where a grid divided into polyomino regions must have a single tetromino shaded within each region, so that all shaded squares are connected orthogonally and no two of the same tetromino are adjacent.
• Nonogram - A puzzle where numbered clues next to each row and column of a grid indicate the number of consecutive shaded squares are present in that row/column, and the pattern in which they appear. This puzzle often results in an image.
• Nurikabe (Islands in the Stream) - A puzzle where cells are shaded in order to make numbered cells part of an 'island' containing the number of white cells equal to their number. In addition, all shaded cells must be connected.
• Tapa - A puzzle where cells must be shaded so that clues give lengths of runs of shaded cells around the clue cell.
• Yajilin - Numbered cells with arrows indicate the number of shaded cells (not counting other numbered cells) between that cell and the edge of the grid in the direction the arrow is pointing. A loop is then drawn through the grid, going through every available space. Also a path-drawing puzzle.

#### Number Crunching

Number-crunching logic puzzles can involve math-based logic, but can also simply involve placing numbers within the grid in a certain way.

• Crossnumber - Similar to a crossword, but involving math equations, mathematical properties, and mathematical relationships between entries.
• Fillomino - A puzzle in which a grid with some numbered cells must be filled with other numbers so that all connected regions of the same number contain that many cells (so a region of 3s must contain 3 cells), and no regions with the same number are adjacent.
• Kakuro - A puzzle in which the digits 1-9 are placed in a grid so that clues indicating the sum of the digits in a given row or column are true, and so that no number is used more than once in the same row or column.
• Sudoku - One of the most famous logic puzzles. It involves placing the numbers 1-9 in a grid so that every 3x3 square, row, and column has each digit occur exactly once.

#### Object Placement

Object placement logic puzzles involve placing objects on a grid. This type can sometimes be interchangeable with grid shading genres since in many genres it's sufficient to know whether a square is occupied or not.

• Akari - A puzzle about placing lights in a grid of white and black squares based on clues given by certain numbered black squares (that indicate the number of adjacent lights), so that every white square is in view of a light and no two lights are in view of each other.
• Battleship - A puzzle where clues at the ends of the rows and columns of a grid indicate the number of cells in them that contain part of a battleship, allowing a set of different sized ships to be placed in the grid.
• Star Battle - A puzzle where stars are placed in a grid with marked regions. Every row, column, and marked region must contain a fixed number of stars, and stars may not touch each other, even diagonally.

### Deduction

• Black Box - A game, program, or device takes an input and gives an output, with the goal being to determine how the transformation works, or how to achieve a specific result
• Optimization - Puzzles about making the perfect move, taking the shortest route, and getting the best possible outcome in a given situation.
• Truths and Lies - Puzzles involving true and false statements, determining which is which, and drawing conclusions based on them.
• Zebra Puzzles - Puzzles in which a series of true, relative statements are given about a set of people, things, and characteristics, allowing solvers to uniquely match them to each other.