{"schemaVersion":1,"record":{"key":"mechanic/puzzle--family-grids","type":"mechanic","id":"puzzle--family-grids","lang":"en","title":"Number and symbol grids","summary":"The player fills or marks cells while satisfying local and overlapping constraints.","updatedAt":"2026-10-22","status":"active","url":"https://gamemechanics.pro/en/knowledge/mechanic/puzzle--family-grids/","jsonUrl":"https://gamemechanics.pro/api/v1/knowledge/en/mechanic/puzzle--family-grids.json","markdownUrl":"https://gamemechanics.pro/content/knowledge/en/mechanic/puzzle--family-grids.md","aliases":[],"tags":["Puzzles","Mechanics catalog"],"sourceIds":["source-931860813914584c","source-ee038a4e63ad2ca4"],"sources":[{"id":"source-931860813914584c","title":"Nikoli: Sudoku","url":"https://www.nikoli.co.jp/en/puzzles/sudoku/","verifiedAt":null},{"id":"source-ee038a4e63ad2ca4","title":"Hexcells","url":"https://store.steampowered.com/app/265890/","verifiedAt":null}],"sections":[{"id":"principle","title":"How it works","body":"Fill positions with values, matching intersecting constraints."},{"id":"variants","title":"Variants","body":"### Variants and applications\n\n<a id=\"family-grids-variants\"></a>\n\n- Uniqueness in rows and columns. Definition: Arrange characters without repetition in each row and each column. Conditional example: Fill in a Latin square. Terms: Latin square. <a id=\"variant-latin-grid\"></a>\n- Uniqueness in additional areas. Definition: Match the constraints of rows, columns and given blocks. Conditional example: Distribute numbers across a Sudoku field. Terms: Sudoku; Sudoku. <a id=\"variant-sudoku-regions\"></a>\n- Arithmetic areas. Definition: Select numbers that satisfy the result of the operation within each cell group. Conditional example: Obtain the product of 24 in three cells. Terms: KenKen; killer sudoku. <a id=\"variant-cage-arithmetic\"></a>\n- Inequalities between neighbors. Definition: Fill out a table with greater than and less than conditions between positions. Conditional example: Arrange numbers by inequality signs. Terms: Futoshiki. <a id=\"variant-inequality-grid\"></a>\n- Heights and visibility. Definition: Restore values ​​based on how many objects are visible from the edge. Conditional example: Arrange towers based on the number of visible roofs. Terms: Skyscrapers. <a id=\"variant-visibility-grid\"></a>\n- Balanced binary grid. Definition: Fill the field with two characters with restrictions on series, number and repetition of lines. Conditional example: Distribute two types of chips equally. Terms: Takuzu; Binairo. <a id=\"variant-binary-balance\"></a>\n- Number of neighbors. Definition: Determine the filled cells by the number of marked adjacent positions. Conditional example: Restore a safe minefield. Terms: Minesweeper; sapper. <a id=\"variant-neighbor-count\"></a>\n- Lengths of consecutive groups. Definition: Restore the shaded cells based on the lengths of the series in rows and columns. Conditional example: Draw an image using numerical clues. Terms: nonogram; Japanese crossword; Picross. <a id=\"variant-nonogram-runs\"></a>\n- Overlapping amounts. Definition: Fill in intersecting number series with a given sum and prohibit repetitions. Conditional example: Reconcile horizontal and vertical sums. Terms: Kakuro; kakuro. <a id=\"variant-cross-sums\"></a>\n- Distance between repetitions. Definition: Place values ​​with a distance limit to the same value. Conditional example: Place identical numbers at acceptable distances. Terms: Ripple Effect. <a id=\"variant-distance-repetition\"></a>\n- Arrangement without mutual attack. Definition: Place the pieces so that none falls into the forbidden zone of the other. Conditional example: Place eight queens without mutual attacks. Terms: eight queens; eight queens. <a id=\"variant-nonattacking-placement\"></a>\n- Restoration of the fleet. Definition: Place objects given by length according to the sums of rows, columns and touch restrictions. Conditional example: Find the position of ships by edge numbers. Terms: Battleships; sea ​​battle. <a id=\"variant-fleet-placement\"></a>\n- Pair formation with no touch allowed. Definition: Compare objects of two types in the neighborhood and agree on their number along the lines. Conditional example: Place a tent near each tree. Terms: Tents; tents. <a id=\"variant-tents-placement\"></a>\n- Pairs of poles on a field. Definition: Fill paired positions with poles according to marginal quantities and neighborhood prohibitions. Conditional example: Arrange magnets, avoiding contact of identical poles. Terms: Magnets. <a id=\"variant-magnet-domino\"></a>\n- Diagonals by degrees of nodes. Definition: Draw diagonals in cells, observing the numbers of adjacencies and prohibition of cycles. Conditional example: Connect the corners of cells using numerical marks. Terms: Slant; Gokigen Naname. <a id=\"variant-diagonal-network\"></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-grids","title":"Puzzles","url":"https://gamemechanics.pro/en/mechanics/puzzle/#family-grids","categoryIds":["section-1"]}],"supersededBy":[],"attributes":{"preview":{"updatedAt":"2026-10-22","title":"Number and symbol grids","description":"The player fills or marks cells while satisfying local and overlapping constraints.","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":"Numbers constrain valid cell markings","alt":"Numbers constrain valid cell markings","markers":[{"x":50,"y":41,"label":"A number constrains neighboring cells"}]},"tips":["Show which constraints apply to the selected position."],"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"}}