--- key: mechanic/puzzle--family-deduction type: mechanic id: puzzle--family-deduction lang: en title: Deduction and the hidden state summary: >- The player infers hidden state from constraints, observations and system responses. updatedAt: '2026-10-22' status: active url: 'https://gamemechanics.pro/en/knowledge/mechanic/puzzle--family-deduction/' jsonUrl: >- https://gamemechanics.pro/api/v1/knowledge/en/mechanic/puzzle--family-deduction.json markdownUrl: >- https://gamemechanics.pro/content/knowledge/en/mechanic/puzzle--family-deduction.md aliases: - Deduction and hidden state tags: - Puzzles - Mechanics catalog sourceIds: - source-ee038a4e63ad2ca4 sources: - id: source-ee038a4e63ad2ca4 title: Hexcells url: 'https://store.steampowered.com/app/265890/' verifiedAt: null relations: [] placements: - catalogId: puzzle id: family-deduction title: Puzzles url: 'https://gamemechanics.pro/en/mechanics/puzzle/#family-deduction' categoryIds: - section-1 supersededBy: [] attributes: preview: updatedAt: '2026-10-22' title: Deduction and hidden state description: >- The player infers hidden state from constraints, observations and system responses. image: src: images/mechanics/adventure-hexcells-02.webp width: 1440 height: 810 game: Hexcells sourceUrl: 'https://store.steampowered.com/app/265890/' originalUrl: >- https://shared.akamai.steamstatic.com/store_item_assets/steam/apps/265890/ss_b011707202d23cf553d6f1aa6c68cc1c93115151.1920x1080.jpg?t=1667308643 credit: Matthew Brown rights: >- Game imagery © its respective rights holders. Publisher-distributed Steam screenshot; all rights reserved. Excluded from MIT and CC BY 4.0. caption: Revealed numbers determine hidden cell states alt: Revealed numbers determine hidden cell states markers: - x: 50 'y': 41 label: A clue constrains unknown states tips: - Distinguish proven deductions from assumptions and random choices. examples: - title: Hexcells url: 'https://store.steampowered.com/app/265890/' endsAt: null provenance: >- Original editorial design catalog consolidated from project discussions on 2026-10-20. Complete discussion item lists and contextual limitations are preserved; linked primary sources support specific techniques, not the entire classification. English translation was prepared with machine assistance and editorial review. license: CC-BY-4.0 codeLicense: MIT attribution: gamemechanics.pro contributors catalogKey: catalog/puzzle --- # Deduction and the hidden state id: puzzle--family-deduction type: mechanic key: mechanic/puzzle--family-deduction lang: en status: active url: https://gamemechanics.pro/en/knowledge/mechanic/puzzle--family-deduction/ The player infers hidden state from constraints, observations and system responses. ## At a glance ![Revealed numbers determine hidden cell states](https://gamemechanics.pro/images/mechanics/adventure-hexcells-02.webp) [Hexcells](https://store.steampowered.com/app/265890/) · Game imagery © its respective rights holders. Publisher-distributed Steam screenshot; all rights reserved. Excluded from MIT and CC BY 4.0. 1. A clue constrains unknown states - Distinguish proven deductions from assumptions and random choices. - [Hexcells](https://store.steampowered.com/app/265890/) ## How it works Recover the unknown from system constraints, observations, and responses. ## Variants ### Variants and applications - Correspondence table. Definition: Establish one-to-one relationships between several sets of features. Conditional example: Determine who lives in which house. Terms: zebra puzzle; logical table. - True and false statements. Definition: Determine the state of the world and the truthfulness of speakers based on compatible statements. Conditional example: Find out which of the guards is lying. Terms: knights and knaves. - Chains of conditions. Definition: Derive the only valid combination from implications and exceptions. Conditional example: Determine the culprit using the conditions “if” and “only if”. - Feedback code. Definition: Select a hidden sequence based on information about matching features and positions. Conditional example: Restore the code based on the number of exact and inaccurate matches. Terms: Mastermind; bulls and cows; bulls and cows. - Hidden object localization. Definition: Determine position based on directions, distances and intersecting observations. Conditional example: Find a transmitter using several bearings. - Black box research. Definition: Deduce an internal device based on its response to input influences. Conditional example: Restore the location of obstacles based on the beam outputs. Terms: Black Box. - Troubleshooting. Definition: Identify a broken component based on symptoms and test results. Conditional example: Find one damaged circuit node. - Selecting an informative check. Definition: Select a question or experiment that distinguishes the remaining hypotheses. Conditional example: Find a hidden number in a limited number of questions. - Inference from the awareness of others. Definition: Use participants' knowledge and public statements about what they know or don't know. Example: Determine the color of your hat after everyone else answers. Terms: hat puzzles; general knowledge. - Proof of impossibility. Definition: Detect an invariant or contradiction that excludes the required configuration. Conditional example: Explain why the layout cannot be assembled with valid moves. ## Context and limits A wide catalog of mechanics for digital puzzles, paper logic problems and physical puzzles. Each position contains an action or rule and a conditional example of application. ## Connected materials ## Sources and provenance Original editorial design catalog consolidated from project discussions on 2026-10-20. Complete discussion item lists and contextual limitations are preserved; linked primary sources support specific techniques, not the entire classification. English translation was prepared with machine assistance and editorial review. - [Hexcells](https://store.steampowered.com/app/265890/) (id: source-ee038a4e63ad2ca4) CC-BY-4.0 · gamemechanics.pro contributors