Conway’s Game of Sprouts
E29420
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.
Observed surface forms (2)
| Surface form | Occurrences |
|---|---|
| Sprouts (game) | 1 |
| misère Sprouts | 1 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial game
ⓘ
mathematical game ⓘ pencil-and-paper game ⓘ topological game ⓘ |
| basicMove |
draw a curve connecting two distinct dots
ⓘ
draw a curve from a dot to itself ⓘ |
| complexity | exact general winning strategy is not known for arbitrary starting size ⓘ |
| educationalUse |
illustrating ideas in topology and graph theory
ⓘ
teaching basic combinatorial game theory concepts ⓘ |
| feature |
game length is finite for any finite starting number of dots
ⓘ
game tree grows rapidly with the number of starting dots ⓘ positions can be represented as planar graphs with degree at most three at each vertex ⓘ supports deep combinatorial analysis despite simple rules ⓘ |
| gameCategory | two-player impartial game ⓘ |
| inventor |
John H. Conway
ⓘ
surface form:
John Horton Conway
Michael S. Paterson ⓘ |
| lineType | curves drawn in the plane ⓘ |
| mathematicalArea |
combinatorial game theory
ⓘ
combinatorics ⓘ graph theory ⓘ topology ⓘ |
| maximumMovesFormula | 3n - 1 for a game starting with n dots ⓘ |
| minimumMovesLowerBound | 2n for a game starting with n dots ⓘ |
| misèreRule | in misère play the player who makes the last move loses ⓘ |
| playConvention | normal play ⓘ |
| playEnvironment |
classroom demonstrations
ⓘ
informal recreational mathematics settings ⓘ |
| positionRepresentation | planar embedding of a graph with degree constraints ⓘ |
| publicationContext | studied in the context of Conway’s work on combinatorial games ⓘ |
| relatedConcept |
Euler’s polyhedron formula
ⓘ
surface form:
Euler characteristic
combinatorial game value ⓘ planar graph ⓘ |
| relatedGame | Sprouts ⓘ |
| researchTopic |
analysis of nim-values for small starting positions
ⓘ
computer search of game trees ⓘ pattern conjectures for winning positions ⓘ |
| rule |
a player who cannot move loses under normal play
ⓘ
each dot has a maximum degree of three incident lines or line-ends ⓘ each move must create a new dot on the drawn line ⓘ lines must not cross existing lines ⓘ players alternate turns making legal moves ⓘ |
| startingDotsNotation | n-sprouts for a game starting with n dots ⓘ |
| startingPosition | finite set of dots on a sheet of paper ⓘ |
| terminationCondition | no legal moves remain ⓘ |
| typicalMedium | paper ⓘ |
| typicalTools | pencil ⓘ |
| variantOf |
Conway’s Game of Sprouts
self-linksurface differs
ⓘ
surface form:
misère Sprouts
|
| winningCondition | last player to move wins under normal play ⓘ |
| yearInvented | 1967 ⓘ |
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
John H. Conway
this entity surface form:
Sprouts (game)
this entity surface form:
misère Sprouts