Hackenbush
E163079
Hackenbush is a combinatorial game played on colored line-graphs, famous in recreational mathematics for illustrating concepts in game theory and surreal numbers.
All labels observed (6)
| Label | Occurrences |
|---|---|
| Hackenbush canonical | 4 |
| Blue-Red Hackenbush | 1 |
| Blue-Red-Green Hackenbush | 1 |
| Green Hackenbush | 1 |
| finite Hackenbush | 1 |
| infinite Hackenbush | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1422433 — 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: Hackenbush Context triple: [Winning Ways for your Mathematical Plays, coversConcept, Hackenbush]
-
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.
Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays is a multi-volume book on combinatorial game theory that popularizes and systematically explores mathematical games and their underlying structures.
-
C.
Mathematical Games
"Mathematical Games" is a long-running Scientific American column by Martin Gardner that popularized recreational mathematics and puzzles for a broad audience.
-
D.
On Numbers and Games
On Numbers and Games is a mathematical book by John H. Conway that introduces surreal numbers and explores combinatorial game theory in a rigorous yet playful style.
-
E.
Surreal numbers
Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
- 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: Hackenbush Target entity description: Hackenbush is a combinatorial game played on colored line-graphs, famous in recreational mathematics for illustrating concepts in game theory and surreal numbers.
-
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.
Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays is a multi-volume book on combinatorial game theory that popularizes and systematically explores mathematical games and their underlying structures.
-
C.
Mathematical Games
"Mathematical Games" is a long-running Scientific American column by Martin Gardner that popularized recreational mathematics and puzzles for a broad audience.
-
D.
On Numbers and Games
On Numbers and Games is a mathematical book by John H. Conway that introduces surreal numbers and explores combinatorial game theory in a rigorous yet playful style.
-
E.
Surreal numbers
Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
- F. None of above. chosen
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial game
ⓘ
impartial game ⓘ mathematical game ⓘ partizan game ⓘ |
| analyzedIn |
On Numbers and Games
ⓘ
Winning Ways for your Mathematical Plays ⓘ |
| application |
recreational puzzle design
ⓘ
teaching combinatorial game theory ⓘ visualizing surreal numbers ⓘ |
| category | two-player perfect-information game ⓘ |
| chanceElement | no randomness ⓘ |
| field |
combinatorial game theory
ⓘ
recreational mathematics ⓘ surreal number theory ⓘ |
| hasColor |
blue
ⓘ
green ⓘ red ⓘ |
| hasComponent |
branches
ⓘ
ground line ⓘ vertical edges ⓘ |
| hasRule |
players alternately remove edges of their own color
ⓘ
the player unable to move loses under normal play ⓘ when an edge is removed all disconnected components not touching the ground are removed ⓘ |
| hasVariant |
Blue-Red Hackenbush
ⓘ
linked to:
Hackenbush
Blue-Red-Green Hackenbush ⓘ
linked to:
Hackenbush
Green Hackenbush ⓘ
linked to:
Hackenbush
finite Hackenbush ⓘ
linked to:
Hackenbush
infinite Hackenbush ⓘ
linked to:
Hackenbush
|
| illustrates |
cold games
ⓘ
fuzzy games ⓘ game values ⓘ hot games ⓘ infinitesimal game values ⓘ numbers in combinatorial game theory ⓘ surreal numbers ⓘ switches in combinatorial game theory ⓘ |
| informationType | no hidden information ⓘ |
| introducedBy |
John Horton Conway
ⓘ
linked to:
John H. Conway
|
| moveType | edge deletion ⓘ |
| notableProperty |
finite blue-red strings represent dyadic rational numbers
ⓘ
game values can form infinitesimal and infinite numbers ⓘ positions correspond to surreal numbers in certain cases ⓘ |
| playerRole |
Left
ⓘ
Right ⓘ |
| solvedClass | finite blue-red strings ⓘ |
| typicalConvention |
Left plays blue edges
ⓘ
Right plays red edges ⓘ |
| uses |
colored graphs
ⓘ
edge-colored graphs ⓘ planar graphs ⓘ |
| winCondition | last move wins under normal play ⓘ |
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: Hackenbush Description of subject: Hackenbush is a combinatorial game played on colored line-graphs, famous in recreational mathematics for illustrating concepts in game theory and surreal numbers.
Referenced by (9)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Hackenbush
linked to: Hackenbush
linked to: Hackenbush
linked to: Hackenbush
linked to: Hackenbush