---
key: mechanic/metroidbrainia--family-10
type: mechanic
id: metroidbrainia--family-10
lang: en
title: Deriving Formal Rules
summary: >-
  Players infer the condition for correctness from examples and use it to solve
  the next puzzle.
updatedAt: '2026-10-22'
status: active
url: 'https://gamemechanics.pro/en/knowledge/mechanic/metroidbrainia--family-10/'
jsonUrl: >-
  https://gamemechanics.pro/api/v1/knowledge/en/mechanic/metroidbrainia--family-10.json
markdownUrl: >-
  https://gamemechanics.pro/content/knowledge/en/mechanic/metroidbrainia--family-10.md
aliases: []
tags:
  - Metroidbrainia
  - Mechanics catalog
sourceIds:
  - source-c05c2407fe414b8f
  - source-ee038a4e63ad2ca4
sources:
  - id: source-c05c2407fe414b8f
    title: Description of Taiji
    url: 'https://store.steampowered.com/app/1141580/Taiji/'
    verifiedAt: null
  - id: source-ee038a4e63ad2ca4
    title: Hexcells
    url: 'https://store.steampowered.com/app/265890/'
    verifiedAt: null
relations: []
placements:
  - catalogId: metroidbrainia
    id: family-10
    title: Metroidbrainia
    url: 'https://gamemechanics.pro/en/mechanics/metroidbrainia/#family-10'
    categoryIds:
      - section-1
supersededBy: []
attributes:
  preview:
    updatedAt: '2026-10-22'
    title: Deriving Formal Rules
    description: >-
      Players infer the condition for correctness from examples and use it to
      solve the next puzzle.
    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:
      - >-
        Help players distinguish an inferred rule from an accidentally correct
        answer.
    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/metroidbrainia
---
# Deriving Formal Rules

id: metroidbrainia--family-10
type: mechanic
key: mechanic/metroidbrainia--family-10
lang: en
status: active
url: https://gamemechanics.pro/en/knowledge/mechanic/metroidbrainia--family-10/

Players infer the condition for correctness from examples and use it to solve the next puzzle.

## 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

- Help players distinguish an inferred rule from an accidentally correct answer.

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

## How it works

The player discovers a correctness condition and then solves new problems using it. Taiji shows how a single interface can support multiple unlockable rules: the player switches cells, but must understand what is required in each task system. Description Taiji.

## Variants

### Variants and applications

<a id="family-10-variants"></a>

- Classification rule. We need to determine which objects belong to the same category and which property is truly significant <a id="variant-metroidbrainia-10-01"></a>
- Quantity rule. Success depends on the number, sum, ratio or distribution of elements <a id="variant-metroidbrainia-10-02"></a>
- Rule of neighborhood and connectivity. What matters are contacts, continuous areas, insulation and connection of parts <a id="variant-metroidbrainia-10-03"></a>
- Rule of order. Elements must follow a detected sequence, hierarchy, or dependency <a id="variant-metroidbrainia-10-04"></a>
- Symmetry and invariant. Some properties must be preserved when rotated, flipped, or transformed <a id="variant-metroidbrainia-10-05"></a>
- Composition of rules. Several known constraints act simultaneously, creating a new class of problems <a id="variant-metroidbrainia-10-06"></a>
- Priority and scope. The player figures out which rule applies first and which elements apply <a id="variant-metroidbrainia-10-07"></a>
- Exception rule. A special sign or condition cancels, inverts, or modifies another restriction <a id="variant-metroidbrainia-10-08"></a>

## Context and limits

In metroidbrainia, progression depends heavily on the player's knowledge: an open rule changes the available actions, routes, or decisions. 91 mechanics in 12 groups, progression techniques, training techniques and edge cases are stored here. For a project, check what knowledge is acquired, how it is derived, what it reveals, and where it is reused. Specific game solutions are not disclosed.

## 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.

- [Description of Taiji](https://store.steampowered.com/app/1141580/Taiji/) (id: source-c05c2407fe414b8f)
- [Hexcells](https://store.steampowered.com/app/265890/) (id: source-ee038a4e63ad2ca4)

CC-BY-4.0 · gamemechanics.pro contributors