---
key: mechanic/puzzle--family-arithmetic
type: mechanic
id: puzzle--family-arithmetic
lang: en
title: 'Numbers, operations and combinatorics'
summary: >-
The player constructs expressions or allocations that satisfy a numerical
requirement.
updatedAt: '2026-10-22'
status: active
url: 'https://gamemechanics.pro/en/knowledge/mechanic/puzzle--family-arithmetic/'
jsonUrl: >-
https://gamemechanics.pro/api/v1/knowledge/en/mechanic/puzzle--family-arithmetic.json
markdownUrl: >-
https://gamemechanics.pro/content/knowledge/en/mechanic/puzzle--family-arithmetic.md
aliases:
- Numbers and operations
tags:
- Puzzles
- Mechanics catalog
sourceIds:
- source-2fb392d4831688b7
sources:
- id: source-2fb392d4831688b7
title: Human Resource Machine
url: 'https://store.steampowered.com/app/375820/'
verifiedAt: null
relations: []
placements:
- catalogId: puzzle
id: family-arithmetic
title: Puzzles
url: 'https://gamemechanics.pro/en/mechanics/puzzle/#family-arithmetic'
categoryIds:
- section-1
supersededBy: []
attributes:
preview:
updatedAt: '2026-10-22'
title: Numbers and operations
description: >-
The player constructs expressions or allocations that satisfy a numerical
requirement.
image:
src: images/mechanics/adventure-human-resource-machine-00.webp
width: 1440
height: 810
game: Human Resource Machine
sourceUrl: 'https://store.steampowered.com/app/375820/'
originalUrl: >-
https://shared.akamai.steamstatic.com/store_item_assets/steam/apps/375820/ss_5de238ca62f67dc97c940bd6af61c03a4320c981.1920x1080.jpg?t=1692721273
credit: Tomorrow Corporation
rights: >-
Game imagery © its respective rights holders. Publisher-distributed
Steam screenshot; all rights reserved. Excluded from MIT and CC BY 4.0.
caption: A program triples a number from the input queue
alt: A program triples a number from the input queue
markers:
- x: 14
'y': 58
label: Input value to transform
- x: 82
'y': 70
label: Operations on the numerical value
tips:
- Let players test the calculation with a small understandable example.
examples:
- title: Human Resource Machine
url: 'https://store.steampowered.com/app/375820/'
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
---
# Numbers, operations and combinatorics
id: puzzle--family-arithmetic
type: mechanic
key: mechanic/puzzle--family-arithmetic
lang: en
status: active
url: https://gamemechanics.pro/en/knowledge/mechanic/puzzle--family-arithmetic/
The player constructs expressions or allocations that satisfy a numerical requirement.
## At a glance
[Human Resource Machine](https://store.steampowered.com/app/375820/) · Game imagery © its respective rights holders. Publisher-distributed Steam screenshot; all rights reserved. Excluded from MIT and CC BY 4.0.
1. Input value to transform
2. Operations on the numerical value
- Let players test the calculation with a small understandable example.
- [Human Resource Machine](https://store.steampowered.com/app/375820/)
## How it works
Construct expressions and distributions that satisfy numerical conditions.
## Variants
### Variants and applications
- An expression with a target result. Definition: Make a calculation from given numbers and operations. Conditional example: Get 24 from four numbers.
- Restoring operations. Definition: Insert missing characters, parentheses or values for a true equality. Conditional example: Arrange operations between four digits.
- Letter arithmetic. Definition: Replace letters with numbers while maintaining equality and matching rules. Conditional example: Decipher the addition column. Terms: cryptarithm; alphametic.
- Matching amounts. Definition: Arrange numbers so that given lines or groups have the required amount. Conditional example: Construct a magic square.
- Dividing the number set. Definition: Divide numbers into groups with given amounts or properties. Conditional example: Divide weights into two equal groups.
- Cyclic arithmetic. Definition: Manage values that cross the modulo boundary. Conditional example: Set the clock by connected turns of the hands.
- Numerical pattern. Definition: Derive a rule for a number sequence under sufficient restrictions. Conditional example: Recover a gap in a series with a given type of rule.
- Rearranging and changing numbers. Definition: To achieve equality by moving, flipping or adding elements of a record. Conventional example: To move one matchstick in a digital equality. Terms: matchstick arithmetic.
- Counting valid options. Definition: Count configurations with restrictions, avoiding repeated counting. Conditional example: Find the number of different routes along a small grid.
- Choice with a probabilistic condition. Definition: Derive a probability or strategy in an explicitly specified random model. Conditional example: Select the sequence of tests with the highest chance of success.
- Derivation of a winning state. Definition: Find a move that guarantees a goal for all admissible responses of the opponent. Conditional example: Leave the opponent a losing configuration of heaps. Terms: Nim; him.
## 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.
- [Human Resource Machine](https://store.steampowered.com/app/375820/) (id: source-2fb392d4831688b7)
CC-BY-4.0 · gamemechanics.pro contributors