Glossary of Terms

Welcome to the Puzzuzu Glossary! Whether you’re a casual solver or a puzzle fanatic, understanding the language of puzzles and algorithms can unlock new strategies and make solving even more fun. This glossary breaks down the key terms you’ll encounter in our articles and games, with clear explanations and links for deeper dives. Curious minds are encouraged to explore further—just follow the links for more details and examples!

Terms

A* search

A powerful pathfinding and puzzle-solving algorithm that always chooses the most promising option first. It uses a formula, f(n) = g(n) + h(n), where g(n) is the cost so far and h(n) is an estimate of the remaining cost. If the estimate (heuristic) is good, A* finds the shortest solution efficiently.

Admissible heuristic

An estimate used in search algorithms that is always equal to or less than the actual cost to reach the goal. This property is essential for guaranteeing that algorithms like A* find the best (optimal) solution.

Backtracking

A method for solving puzzles by trying out possible options and undoing (backtracking) when you hit a dead end. Imagine filling in a Sudoku: if you realize a number doesn’t fit, you erase and try a different path. It’s a classic approach for logic and constraint puzzles.

See also: Backtracking on Wikipedia.

Branch and bound

A strategy for finding the best solution by exploring all possibilities, but skipping (pruning) any path that can’t possibly beat the best answer found so far. It’s especially useful for puzzles where you want the fewest moves or the most efficient solution.

See also: Branch and bound on Wikipedia.

Branching factor

The average number of choices you have at each step in a puzzle or game. A high branching factor means more options to consider, which can make solving much harder and slower.

See also: Branching Factor on Wikipedia.

Breadth-first search (BFS)

An algorithm that explores all possible moves at one depth before moving deeper. It’s guaranteed to find the shortest solution in puzzles without move costs, but can use a lot of memory. Great for small puzzles or finding the shortest path.

Constraint satisfaction problem (CSP)

A type of puzzle where you must assign values to variables while following specific rules (constraints). Sudoku, crosswords, and games like Tetravex are classic examples. Solving often involves backtracking, clever guessing, and rule propagation.

Source: Constraint satisfaction problem on Wikipedia.

Heuristic

A rule of thumb or educated guess that helps guide a search algorithm toward the goal faster. In sliding puzzles, heuristics like counting misplaced tiles or using Manhattan distance help the computer (or you!) focus on promising moves.

Manhattan distance

The total number of steps needed to move from one spot to another if you can only move up, down, left, or right—like a taxi driving city blocks. It’s a popular way to estimate moves in sliding puzzles.

NP-hard

A class of problems so tough that no one knows a fast way to solve them (and maybe never will). Many puzzles—especially when you want the absolute best solution—are NP-hard, meaning they’re at least as hard as the hardest problems computers can check quickly.

See also: NP-hardness on Wikipedia.

Orthogonal

In puzzles and mathematics, orthogonal means at right angles—think up/down and left/right on a grid. Orthogonal-shaped pieces are pieces whose sides meet at right angles, forming shapes like rectangles or L-shapes that align with the grid. These type of pieces can also be referred to as "Tetrominoes" and is likely where the game Tetris got its name.

See also: Tetromino and Orthogonality on Wikipedia.

Parity (and inversions)

In puzzles, parity often refers to whether something is even or odd—like the number of swaps needed to solve a puzzle. In sliding-tile games, counting "inversions" can reveal if a puzzle is unsolvable from a given scramble.

See also: Parity (mathematics) and the solvability section of the 15 puzzle on Wikipedia.

Queue puzzle

A type of puzzle where pieces are a placed in several lines or queues. Typically pieces are moved in a way where the first piece placed in a queue is the first piece moved out (FIFO). Play Sequence Queue for an example of this mechanic.

Sliding puzzle

A type of puzzle where you slide pieces around a board to reach a target arrangement, without ever picking them up. Famous examples include the 15-puzzle and Klotski. These puzzles challenge your planning and spatial skills! There are several types of these puzzles on Puzzuzu such as Classic Sliding Tile and Orthogonal Slide.

See also: Sliding puzzle on Wikipedia.

Stack puzzle

A type of puzzle where pieces are stacked on top of each other. Typically pieces in a way where the last piece placed in a stack is the first piece moved out (LIFO). Tower of Hanoi and Ball Stacks are examples of puzzles with the mechanic on Puzzuzu.

State space

The complete set of all possible positions or arrangements a puzzle can have, along with the moves that connect them. Visualizing the state space helps you understand the puzzle’s complexity and plan your solving strategy.