Conway’s soldiers
E163258
Conway’s soldiers is a mathematical puzzle and thought experiment in combinatorial game theory that explores how far checkers-like pieces can advance on an infinite grid under specific movement rules.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Conway's soldiers | 1 |
| Conway’s soldiers canonical | 1 |
| Conway’s soldiers on different lattices | 1 |
| Conway’s soldiers with diagonal moves | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1428688 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Conway’s soldiers Context triple: [John Horton Conway, notableWork, Conway’s soldiers]
-
A.
Conway’s Game of Sprouts
Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
-
B.
Game of Life
Game of Life is a famous cellular automaton devised by mathematician John H. Conway that simulates complex patterns and behaviors using simple grid-based rules.
-
C.
the Fifteen
The Fifteen was a major early 18th-century Jacobite rebellion in Britain that sought to restore the exiled Stuart dynasty to the throne.
-
D.
Room for Squares
Room for Squares is John Mayer's breakthrough debut studio album, blending pop-rock and acoustic songwriting and featuring hits like "No Such Thing" and "Your Body Is a Wonderland."
-
E.
The Bishop’s Move
"The Bishop’s Move" is a humorous short story by P. G. Wodehouse featuring one of Mr Mulliner’s comic tales of romantic and clerical mishaps.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Conway’s soldiers Target entity description: Conway’s soldiers is a mathematical puzzle and thought experiment in combinatorial game theory that explores how far checkers-like pieces can advance on an infinite grid under specific movement rules.
-
A.
Conway’s Game of Sprouts
Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
-
B.
Game of Life
Game of Life is a famous cellular automaton devised by mathematician John H. Conway that simulates complex patterns and behaviors using simple grid-based rules.
-
C.
the Fifteen
The Fifteen was a major early 18th-century Jacobite rebellion in Britain that sought to restore the exiled Stuart dynasty to the throne.
-
D.
Room for Squares
Room for Squares is John Mayer's breakthrough debut studio album, blending pop-rock and acoustic songwriting and featuring hits like "No Such Thing" and "Your Body Is a Wonderland."
-
E.
The Bishop’s Move
"The Bishop’s Move" is a humorous short story by P. G. Wodehouse featuring one of Mr Mulliner’s comic tales of romantic and clerical mishaps.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial game theory problem
ⓘ
mathematical puzzle ⓘ peg solitaire variant ⓘ thought experiment ⓘ |
| appearsIn | Winning Ways for your Mathematical Plays ⓘ |
| application |
example problem in combinatorial game theory textbooks
ⓘ
pedagogical example in discrete mathematics courses ⓘ |
| boardOrientation | horizontal rows numbered relative to starting line ⓘ |
| boardSymmetry | translation-invariant in horizontal directions ⓘ |
| boardType | infinite rectangular grid ⓘ |
| category | Conway’s games ⓘ |
| constraint | only finitely many moves may be played in any actual play sequence ⓘ |
| creatorAffiliation | University of Cambridge (at time of Conway’s work in combinatorial games) ⓘ |
| demonstrates | that local improvements can be globally bounded ⓘ |
| field |
combinatorial game theory
ⓘ
recreational mathematics ⓘ |
| goal | advance a piece as far as possible above the starting line ⓘ |
| hasNameOrigin | named after John Horton Conway ⓘ |
| initialConfiguration |
all squares above the starting horizontal line are empty
ⓘ
all squares on or below a given horizontal line are occupied ⓘ |
| inventor |
John H. Conway
ⓘ
surface form:
John Horton Conway
|
| keyResult |
no sequence of legal moves can move a piece more than four rows above the starting line
ⓘ
the fifth row above the starting line is unreachable with only orthogonal jumps ⓘ |
| logicalStatus | mathematically solved in the standard formulation ⓘ |
| movementRule |
a move consists of jumping over an adjacent piece into an empty square and removing the jumped piece
ⓘ
diagonal jumps are not allowed in the standard version ⓘ pieces move by orthogonal jumps over adjacent pieces ⓘ |
| notableFeature |
illustrates sharp boundary between reachable and unreachable positions
ⓘ
simple rules with nontrivial global constraint ⓘ |
| objectiveType | reachability maximization ⓘ |
| pieceType | identical checkers-like pieces ⓘ |
| proofMethod |
invariant based on weights assigned to board positions
ⓘ
potential function argument ⓘ |
| puzzleType | deterministic perfect-information puzzle ⓘ |
| relatedConcept |
checkers
ⓘ
invariants in combinatorial games ⓘ monovariants ⓘ peg solitaire ⓘ |
| resultForVariant | allowing diagonal moves increases the maximum reachable row ⓘ |
| solutionStatus | exact maximum height known for standard orthogonal version ⓘ |
| teaches |
limitations of local move rules on global reachability
ⓘ
use of invariants to prove impossibility results ⓘ |
| uses | infinite checkerboard grid ⓘ |
| usesTool | geometric series in potential function construction ⓘ |
| variant |
Conway’s soldiers
self-linksurface differs
ⓘ
surface form:
Conway’s soldiers on different lattices
Conway’s soldiers self-linksurface differs ⓘ
surface form:
Conway’s soldiers with diagonal moves
|
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Conway’s soldiers Description of subject: Conway’s soldiers is a mathematical puzzle and thought experiment in combinatorial game theory that explores how far checkers-like pieces can advance on an infinite grid under specific movement rules.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
John Horton Conway
subject surface form:
John H. Conway
this entity surface form:
Conway's soldiers
this entity surface form:
Conway’s soldiers with diagonal moves
this entity surface form:
Conway’s soldiers on different lattices