Hackenbush

E163079

combinatorial game impartial game mathematical game partizan game

Hackenbush is a combinatorial game played on colored line-graphs, famous in recreational mathematics for illustrating concepts in game theory and surreal numbers.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (6)

Label	Occurrences
Hackenbush canonical	3
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	Hackenbush self-linksurface differs ⓘ surface form: Blue-Red Hackenbush Hackenbush self-linksurface differs ⓘ surface form: Blue-Red-Green Hackenbush Hackenbush self-linksurface differs ⓘ surface form: Green Hackenbush Hackenbush self-linksurface differs ⓘ surface form: finite Hackenbush Hackenbush self-linksurface differs ⓘ surface form: infinite 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 H. Conway ⓘ surface form: John Horton 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

Referenced by (8)

Full triples — surface form annotated when it differs from this entity's canonical label.

Winning Ways for your Mathematical Plays → coversConcept → Hackenbush ⓘ

On Numbers and Games → topic → Hackenbush ⓘ

Part Two: Games → hasWorkExample → Hackenbush ⓘ