What is a puzzle?

Puzzles don’t have a single precise definition.

A puzzle is the game type itself. A challenge is each specific instance of a puzzle.^[1] In mathematics, a puzzle is a problem. A puzzle challenge is a problem instance.
Hence I say “A puzzle is a problem often with entertainment value.”

Whether questions in exams are puzzle challenges depends on test takers. If an examinee enjoys solving the questions, the questions are puzzle challenges.

Schuh’s characterization identifies three properties: (1) a puzzle can be solved by pure reasoning alone, (2) it must have a complete analysis, and (3) you are your own opponent. Browne disputes point 3, proposing instead that a puzzle is a two-player game between a setter and a solver. The setter encodes a challenge; the solver decodes it. The puzzle is the game type itself; a challenge is each specific instance presented to the solver.

From the procedural puzzle generation literature: a puzzle is a problem with defined steps for achieving one or more defined solutions, such that the challenge contains all information needed to achieve its own solution. This self-contained property distinguishes puzzles from open-ended problems. A related observation from the same tradition: “Puzzles are solved. Games are won.” This marks the absence of an adversarial element as a defining feature.

For logic puzzles specifically, Milicevic defines: a logic puzzle consists of a set of natural-language rules representing constraints on the set of solutions to the puzzle, and a query to which the correct answer represents a proof that the user has solved the puzzle correctly. This definition is structural and formal, but it does not account for logic grid puzzles or pattern-based puzzles.

2. The Puzzle Challenge vs. the Puzzle Type

A challenge of a puzzle is an instance of a problem. The person or tool that attempts a puzzle challenge is called the puzzler or solver. The author of a puzzle challenge is called the author or setter.

Browne also distinguishes:
– Form: the degrees of freedom the setter can manipulate (symmetry, motifs, dependency chains)
– Function: the conceptual framework and necessary conditions for the puzzle to work at all

This setter-solver framing explains puzzle addictiveness via the Zeigarnik Effect (the brain latches onto unsolved subproblems) and authorial control (the setter can drip-feed information to guide the solver’s experience).

3. What Makes Something a Puzzle (and What Does Not)

The criterion from Higashida is useful: a puzzle requires deduction based on its rules. By this criterion:

“When was Einstein born?” is not a puzzle. It has a right answer, but no rules or constraints are given. The solver must recall a memorized fact, not deduce anything. There is no setter-solver dynamic, no dependency chain, and no authorial control. It is a trivia question.

“Let x = 1, y = 2. What is x + y?” is not a puzzle in any meaningful sense. It structurally resembles a logic puzzle (explicit constraints, single correct answer), but it fails every qualitative criterion: it is not fun, it does not challenge the solver, it has no dependency chain of deductions, no traps or deceptions, and no authorial engagement. It is a simple arithmetic substitution.

Both fail to be puzzles: the first because it requires recall rather than deduction from rules; the second because it offers no challenge, dependency, or authorial engagement, even though it superficially provides constraints.

4. Structure of a Puzzle Text

A logic puzzle challenge typically consists of three parts:
– Preamble: background context and scenario setup
– Clues (constraints): the logical rules that constrain the solution space
– Query: the question the solver must answer

Good puzzles satisfy two properties: (i) each piece of information is necessary, and (ii) no unnecessary information is provided. These properties make puzzles strong candidates for machine comprehension tasks, because every sentence is load-bearing.

Lev argued that logic puzzles should have exactly one correct answer (solution). The unique-answer restriction also helps resolve ambiguities: if one reading of the puzzle text yields no or multiple answers, the reader can use this constraint to eliminate incorrect interpretations.

5. Difficulty and Dependency

The concept of dependency measures the degree to which the steps required to solve a challenge depend on prior steps. A high dependency means the challenge has fewer “weak points” at which a solver can attack. Dependency has been used to measure puzzle difficulty.

A long minimal solution length does not necessarily mean a puzzle is difficult, because the path may have no branches. An element of surprise — establishing a pattern in the solution process and then disrupting it — can keep a challenge engaging.

6. Classification of Puzzles

6.1 By Modality and Surface Form

The broadest informal taxonomy divides puzzles by the medium or surface form of their challenge:
– Word puzzles: rely on language (crosswords, anagrams)
– Jigsaw puzzles: physical or visual assembly
– Logic puzzles: pure deductive reasoning
– Dexterity puzzles: require manual skill
– Physical puzzles: involve physical manipulation
– Physics-based puzzles: governed by physical simulation

A broader informal list includes guessing games (riddles), logic puzzles (knights and knaves, zebra puzzles), mechanical puzzles (Rubik’s cube, Sokoban), word games (crossword and Sudoku), and mazes.

6.2 By Reasoning Mechanism

Browne’s key distinction separates:
– Pure deduction puzzles (also called Japanese logic puzzles): simple rules, a single deducible solution, no language-dependent content. Examples: Slitherlink, Sudoku, Masyu, Nonograms, Hitori.
– Other puzzles: require background knowledge, chance, or social interaction.

Logic puzzles are solved through deductive reasoning, whereas riddles may rely on wordplay or commonsense knowledge that is difficult to formalize.

6.3 Logic Puzzle Subtypes

Within logic puzzles, common subtypes include:
– Comparison (ordering) puzzles: order or rank entities by attributes (e.g., “A is taller than B; B is taller than C — is A taller than C?”)
– Knights and knaves: truth-teller/liar deduction
– Zebra / Einstein puzzles: map entities to attributes via clues; multiple domains/sorts; total order over positions
– Multiple-choice logic puzzles: LSAT/GRE analytic style

The Agatha (Dreadbury Mansion) puzzle differs from Zebra-style puzzles in being single-sorted (one type of entity: people), while Zebra puzzles have multiple typed attribute sets. Agatha-style puzzles use universally-scoped relational constraints, requiring full first-order logic theorem proving rather than constraint satisfaction over a finite grid.

6.4 By Reasoning Challenge (AI/NLP Perspective)

Used especially in AI and NLP benchmarking:
– Grid-based puzzles: constraint satisfaction over a grid
– Logic-grid / ZebraLogic puzzles: formal deductive inference, CSP
– Detective / mystery puzzles: abductive reasoning
– Knights-and-knaves puzzles: propositional or FOL inference

7. Logic Puzzle Properties: A Precise Characterization

The most precise label for a logic puzzle such as the Dreadbury Mansion (Agatha) puzzle, drawing on multiple sources, is:

A rule-based, pure deduction, language-dependent logic puzzle, expressed in informal natural language, translatable to first-order logic, with a finite domain, a single unambiguous solution, and no required background knowledge.

Such a puzzle is:
– Rule-based: all constraints are explicitly stated as rules, unlike riddles or commonsense puzzles that rely on unstated knowledge
– Pure deduction: solvable by reasoning alone, with a complete analysis
– Language-dependent: constraints are given as natural-language sentences, not as a grid, diagram, or symbolic notation
– FOL-translatable: representable in first-order logic, admitting formal proof or model finding
– Axiomatically complete: every fact needed is stated; no external knowledge assumed
– Single-solution: only one assignment satisfies all constraints

It is not a Japanese logic puzzle (which are language-independent), not an Einstein-like grid puzzle (which requires only attribute assignment, not full FOL quantification), and not a detective/abductive puzzle (where the solution requires inference to the best explanation rather than strict deduction).

8. Historical Note

The logic puzzle was first produced by Charles Lutwidge Dodgson, better known as Lewis Carroll, the author of Alice’s Adventures in Wonderland. In his book The Game of Logic he introduced a game to solve syllogisms such as confirming “Some greyhounds are not fat” from “No fat creatures run well” and “Some greyhounds run well.” Dodgson went on to construct much more complex puzzles with up to 8 premises.

9. Challenges for Computers

For humans, the language-understanding part of logic puzzles is trivial but the reasoning is difficult. For computers, the situation is reversed: a machine can solve constraint satisfaction problems fairly efficiently, but does not have the same background knowledge that a human does.

An obvious approach to solving logic puzzles automatically is to use off-the-shelf FOL reasoners such as theorem provers and model builders. Although logic puzzles can also be cast as constraint satisfaction problems (CSPs), FOL representations are more general and more broadly applicable, and they are closer to natural language semantics.

A prerequisite for successful inference is precise understanding of semantic phenomena such as modals and quantifiers. Even a carefully designed logic puzzle contains many potential ambiguities: multiple possibilities for syntactic structures, pronominal reference, and quantifier scope. The unique-answer restriction helps resolve such ambiguities.

References

1. Cameron Browne; . The Nature of Puzzles. Game and Puzzle Design. 2015, (): [].[↩]