---
key: mechanic/education--family-12
type: mechanic
id: education--family-12
lang: en
title: 'Constraints, grids and placement'
summary: >-
  The learner fills a grid or places objects while satisfying all constraints at
  once.
updatedAt: '2026-10-22'
status: active
url: 'https://gamemechanics.pro/en/knowledge/mechanic/education--family-12/'
jsonUrl: >-
  https://gamemechanics.pro/api/v1/knowledge/en/mechanic/education--family-12.json
markdownUrl: >-
  https://gamemechanics.pro/content/knowledge/en/mechanic/education--family-12.md
aliases:
  - Constraints and grids
tags:
  - Educational games
  - 'Structures, logic and space'
sourceIds:
  - source-ee038a4e63ad2ca4
sources:
  - id: source-ee038a4e63ad2ca4
    title: Hexcells
    url: 'https://store.steampowered.com/app/265890/'
    verifiedAt: null
relations: []
placements:
  - catalogId: education
    id: family-12
    title: Educational games
    url: 'https://gamemechanics.pro/en/mechanics/education/#family-12'
    categoryIds:
      - logic
supersededBy: []
attributes:
  preview:
    updatedAt: '2026-10-22'
    title: Constraints and grids
    description: >-
      The learner fills a grid or places objects while satisfying all
      constraints at once.
    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:
      - >-
        Identify the violated constraint while preserving the rest of the
        solution.
    examples:
      - title: Hexcells
        url: 'https://store.steampowered.com/app/265890/'
endsAt: null
provenance: >-
  Educational reference expanded from all 64 families and 749 variants of the
  original children-education taxonomy, with original editorial additions dated
  2026-10-20. Sources support specific methods and examples, not the entire
  classification or its effectiveness.
license: CC-BY-4.0
codeLicense: MIT
attribution: gamemechanics.pro contributors
catalogKey: catalog/education
---
# Constraints, grids and placement

id: education--family-12
type: mechanic
key: mechanic/education--family-12
lang: en
status: active
url: https://gamemechanics.pro/en/knowledge/mechanic/education--family-12/

The learner fills a grid or places objects while satisfying all constraints at once.

## 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

- Identify the violated constraint while preserving the rest of the solution.

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

## How it works

Fill a grid without repetition

## Variants

### Variants

<a id="family-12-branch-1"></a>

- Fill a grid without repetition <a id="family-12-variant-1"></a>
- Place objects next to each other <a id="family-12-variant-2"></a>
- Respect adjacency prohibitions <a id="family-12-variant-3"></a>
- Satisfy row sums <a id="family-12-variant-4"></a>
- Connect pairs without crossings <a id="family-12-variant-5"></a>
- Cover a board with specified shapes <a id="family-12-variant-6"></a>
- Place under several conditions <a id="family-12-variant-7"></a>
- Find a unique solution <a id="family-12-variant-8"></a>
- Find all valid solutions <a id="family-12-variant-9"></a>
- Determine that no solution exists <a id="family-12-variant-10"></a>

## Design example

Seat animals so predators are not beside their prey.

## Context and limits

A mechanic map for games with explicit learning goals, from first encounters with a topic to professional practice. It covers children, teenagers and adults; choose subject, difficulty, context and controls for the learner. Player actions, subject content, instructional support and assessment are distinct layers. Scores and game completion alone do not establish mastery or skill transfer.

## Connected materials


## Sources and provenance

Educational reference expanded from all 64 families and 749 variants of the original children-education taxonomy, with original editorial additions dated 2026-10-20. Sources support specific methods and examples, not the entire classification or its effectiveness.

- [Hexcells](https://store.steampowered.com/app/265890/) (id: source-ee038a4e63ad2ca4)

CC-BY-4.0 · gamemechanics.pro contributors