{"schemaVersion":1,"record":{"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}],"sections":[{"id":"principle","title":"How it works","body":"Recover the unknown from system constraints, observations, and responses."},{"id":"variants","title":"Variants","body":"### Variants and applications\n\n<a id=\"family-deduction-variants\"></a>\n\n- 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. <a id=\"variant-logic-grid\"></a>\n- 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. <a id=\"variant-truth-liars\"></a>\n- 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”. <a id=\"variant-conditional-deduction\"></a>\n- 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. <a id=\"variant-code-feedback\"></a>\n- Hidden object localization. Definition: Determine position based on directions, distances and intersecting observations. Conditional example: Find a transmitter using several bearings. <a id=\"variant-hidden-location\"></a>\n- 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. <a id=\"variant-probe-black-box\"></a>\n- Troubleshooting. Definition: Identify a broken component based on symptoms and test results. Conditional example: Find one damaged circuit node. <a id=\"variant-fault-diagnosis\"></a>\n- 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. <a id=\"variant-information-query\"></a>\n- 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. <a id=\"variant-common-knowledge\"></a>\n- 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. <a id=\"variant-proof-impossibility\"></a>"},{"id":"context","title":"Context and limits","body":"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."}],"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"}}