---
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
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
---
# Number and symbol grids

id: puzzle--family-grids
type: mechanic
key: mechanic/puzzle--family-grids
lang: en
status: active
url: https://gamemechanics.pro/en/knowledge/mechanic/puzzle--family-grids/

The player fills or marks cells while satisfying local and overlapping constraints.

## At a glance

![Numbers constrain valid cell markings](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 number constrains neighboring cells

- Show which constraints apply to the selected position.

- [Hexcells](https://store.steampowered.com/app/265890/)

## How it works

Fill positions with values, matching intersecting constraints.

## Variants

### Variants and applications

<a id="family-grids-variants"></a>

- 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>
- 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>
- 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>
- 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>
- 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>
- 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>
- 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>
- 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>
- 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>
- 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>
- 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>
- 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>
- 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>
- 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>
- 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>

## 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.

- [Nikoli: Sudoku](https://www.nikoli.co.jp/en/puzzles/sudoku/) (id: source-931860813914584c)
- [Hexcells](https://store.steampowered.com/app/265890/) (id: source-ee038a4e63ad2ca4)

CC-BY-4.0 · gamemechanics.pro contributors