{"schemaVersion":1,"record":{"key":"mechanic/puzzle--family-permutation","type":"mechanic","id":"puzzle--family-permutation","lang":"en","title":"Sliding and rearranging","summary":"The player changes a configuration through permitted slides, rotations or swaps.","updatedAt":"2026-10-22","status":"active","url":"https://gamemechanics.pro/en/knowledge/mechanic/puzzle--family-permutation/","jsonUrl":"https://gamemechanics.pro/api/v1/knowledge/en/mechanic/puzzle--family-permutation.json","markdownUrl":"https://gamemechanics.pro/content/knowledge/en/mechanic/puzzle--family-permutation.md","aliases":["Sliding and rearrangement"],"tags":["Puzzles","Mechanics catalog"],"sourceIds":["source-10d1df6f36fd4358"],"sources":[{"id":"source-10d1df6f36fd4358","title":"Patrick's Parabox","url":"https://store.steampowered.com/app/1260520/","verifiedAt":null}],"sections":[{"id":"principle","title":"How it works","body":"Change the system configuration with limited transformations."},{"id":"variants","title":"Variants","body":"### Variants and applications\n\n<a id=\"family-permutation-variants\"></a>\n\n- Moving through the void. Definition: Move tiles only to the adjacent free space. Conditional example: Restore the order of tags. Terms: 15-puzzle; tag. <a id=\"variant-sliding-gap\"></a>\n- Clearing the passage with blocks. Definition: Move parts in limited directions to produce a target block. Conventional example: Bring a long block out of a tight field. Terms: Klotski; Rush Hour. <a id=\"variant-sliding-blocks\"></a>\n- Shift of a whole series. Definition: Rearrange elements by general row or column shift only. Conventional example: Align characters by cyclic shifts. <a id=\"variant-row-shift\"></a>\n- Rotate a local fragment. Definition: In one move, rotate several adjacent elements as a group. Conditional example: Arrange numbers by rotating 2x2 squares. <a id=\"variant-local-rotation\"></a>\n- Rotate layers of a volumetric object. Definition: Restore a state by rotating connected layers or sections. Conditional example: Collect the colored faces of a cube. Terms: twisty puzzle; Rubik's cube. <a id=\"variant-twisty\"></a>\n- Chained cyclic permutations. Definition: Change the order on rings that have common elements. Conditional example: Separate colors along two intersecting circles. <a id=\"variant-linked-rings\"></a>\n- Exchanges according to the permitted schedule. Definition: Swap only pairs connected by given connections. Conditional example: Arrange exchange tokens along the edges of the star. <a id=\"variant-restricted-swap\"></a>\n- Reversal of a segment. Definition: Change the sequence only by reversing the selected section. Conditional example: Order a stack by turning its upper part. Terms: pancake sorting. <a id=\"variant-segment-reversal\"></a>\n- Removal by jumping. Definition: Jump over tiles and remove them for the target end position. Conventional example: Leave one tile in the center. Terms: peg solitaire; tapeworm. <a id=\"variant-peg-solitaire\"></a>\n- Exchange of counter groups. Definition: Swap two groups through steps and jumps with limited direction. Conditional example: Swap two groups of frogs. <a id=\"variant-crossing-counters\"></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-permutation","title":"Puzzles","url":"https://gamemechanics.pro/en/mechanics/puzzle/#family-permutation","categoryIds":["section-1"]}],"supersededBy":[],"attributes":{"preview":{"updatedAt":"2026-10-22","title":"Sliding and rearrangement","description":"The player changes a configuration through permitted slides, rotations or swaps.","image":{"src":"images/mechanics/adventure-patrick-parabox-00.webp","width":1440,"height":810,"game":"Patrick's Parabox","sourceUrl":"https://store.steampowered.com/app/1260520/","originalUrl":"https://shared.akamai.steamstatic.com/store_item_assets/steam/apps/1260520/ss_fc9994b3d063276aaaeacbc86c6d740dabeebdc0.1920x1080.jpg?t=1745611653","credit":"Patrick Traynor","rights":"Game imagery © its respective rights holders. Publisher-distributed Steam screenshot; all rights reserved. Excluded from MIT and CC BY 4.0.","caption":"Block positions change the available configuration","alt":"Block positions change the available configuration","markers":[{"x":43,"y":56,"label":"Movable block within a constrained passage"}]},"tips":["Show movement constraints and allow reversible steps to be undone."],"examples":[{"title":"Patrick's Parabox","url":"https://store.steampowered.com/app/1260520/"}]}},"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"}}