{"schemaVersion":1,"record":{"key":"mechanic/puzzle--family-arithmetic","type":"mechanic","id":"puzzle--family-arithmetic","lang":"en","title":"Numbers, operations and combinatorics","summary":"The player constructs expressions or allocations that satisfy a numerical requirement.","updatedAt":"2026-10-22","status":"active","url":"https://gamemechanics.pro/en/knowledge/mechanic/puzzle--family-arithmetic/","jsonUrl":"https://gamemechanics.pro/api/v1/knowledge/en/mechanic/puzzle--family-arithmetic.json","markdownUrl":"https://gamemechanics.pro/content/knowledge/en/mechanic/puzzle--family-arithmetic.md","aliases":["Numbers and operations"],"tags":["Puzzles","Mechanics catalog"],"sourceIds":["source-2fb392d4831688b7"],"sources":[{"id":"source-2fb392d4831688b7","title":"Human Resource Machine","url":"https://store.steampowered.com/app/375820/","verifiedAt":null}],"sections":[{"id":"principle","title":"How it works","body":"Construct expressions and distributions that satisfy numerical conditions."},{"id":"variants","title":"Variants","body":"### Variants and applications\n\n<a id=\"family-arithmetic-variants\"></a>\n\n- An expression with a target result. Definition: Make a calculation from given numbers and operations. Conditional example: Get 24 from four numbers. <a id=\"variant-target-expression\"></a>\n- Restoring operations. Definition: Insert missing characters, parentheses or values ​​for a true equality. Conditional example: Arrange operations between four digits. <a id=\"variant-missing-operator\"></a>\n- Letter arithmetic. Definition: Replace letters with numbers while maintaining equality and matching rules. Conditional example: Decipher the addition column. Terms: cryptarithm; alphametic. <a id=\"variant-alphametic\"></a>\n- Matching amounts. Definition: Arrange numbers so that given lines or groups have the required amount. Conditional example: Construct a magic square. <a id=\"variant-magic-sums\"></a>\n- Dividing the number set. Definition: Divide numbers into groups with given amounts or properties. Conditional example: Divide weights into two equal groups. <a id=\"variant-number-partition\"></a>\n- Cyclic arithmetic. Definition: Manage values ​​that cross the modulo boundary. Conditional example: Set the clock by connected turns of the hands. <a id=\"variant-modular-state\"></a>\n- Numerical pattern. Definition: Derive a rule for a number sequence under sufficient restrictions. Conditional example: Recover a gap in a series with a given type of rule. <a id=\"variant-number-sequence\"></a>\n- Rearranging and changing numbers. Definition: To achieve equality by moving, flipping or adding elements of a record. Conventional example: To move one matchstick in a digital equality. Terms: matchstick arithmetic. <a id=\"variant-digit-manipulation\"></a>\n- Counting valid options. Definition: Count configurations with restrictions, avoiding repeated counting. Conditional example: Find the number of different routes along a small grid. <a id=\"variant-counting-configurations\"></a>\n- Choice with a probabilistic condition. Definition: Derive a probability or strategy in an explicitly specified random model. Conditional example: Select the sequence of tests with the highest chance of success. <a id=\"variant-probability-choice\"></a>\n- Derivation of a winning state. Definition: Find a move that guarantees a goal for all admissible responses of the opponent. Conditional example: Leave the opponent a losing configuration of heaps. Terms: Nim; him. <a id=\"variant-forced-win\"></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-arithmetic","title":"Puzzles","url":"https://gamemechanics.pro/en/mechanics/puzzle/#family-arithmetic","categoryIds":["section-1"]}],"supersededBy":[],"attributes":{"preview":{"updatedAt":"2026-10-22","title":"Numbers and operations","description":"The player constructs expressions or allocations that satisfy a numerical requirement.","image":{"src":"images/mechanics/adventure-human-resource-machine-00.webp","width":1440,"height":810,"game":"Human Resource Machine","sourceUrl":"https://store.steampowered.com/app/375820/","originalUrl":"https://shared.akamai.steamstatic.com/store_item_assets/steam/apps/375820/ss_5de238ca62f67dc97c940bd6af61c03a4320c981.1920x1080.jpg?t=1692721273","credit":"Tomorrow Corporation","rights":"Game imagery © its respective rights holders. Publisher-distributed Steam screenshot; all rights reserved. Excluded from MIT and CC BY 4.0.","caption":"A program triples a number from the input queue","alt":"A program triples a number from the input queue","markers":[{"x":14,"y":58,"label":"Input value to transform"},{"x":82,"y":70,"label":"Operations on the numerical value"}]},"tips":["Let players test the calculation with a small understandable example."],"examples":[{"title":"Human Resource Machine","url":"https://store.steampowered.com/app/375820/"}]}},"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"}}