Kayles
E637318
Kayles is a classic impartial combinatorial game in which players alternately remove one or two adjacent pins from a row, with the goal of making the last move.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
impartial combinatorial game
ⓘ
mathematical game ⓘ take-and-break game ⓘ |
| analyzedIn | Sprague–Grundy theory NERFINISHED ⓘ |
| appearsIn |
On Numbers and Games
NERFINISHED
ⓘ
Winning Ways for your Mathematical Plays NERFINISHED ⓘ |
| boardType | finite row of pins ⓘ |
| decomposesInto | disjoint subgames formed by separated blocks of pins ⓘ |
| doesNotRequire |
chance
ⓘ
hidden information ⓘ |
| firstDescribedIn | early 20th century ⓘ |
| generalizationOf | Dawson’s Kayles is a variant with different adjacency rules NERFINISHED ⓘ |
| hasCategory | impartial normal-play subtraction game ⓘ |
| hasComplexityNote | exact Sprague–Grundy values known for many heap sizes ⓘ |
| hasEndCondition | game ends when no pins remain ⓘ |
| hasGoal | to make the last move ⓘ |
| hasGrundySequence | aperiodic for long initial segment ⓘ |
| hasMoveEffect | removing pins may split the row into two smaller rows ⓘ |
| hasMoveRule |
a player may remove one pin from the row
ⓘ
a player may remove two adjacent pins from the row ⓘ |
| hasNameOrigin | name derived from the game of skittles ⓘ |
| hasNoChanceMoves | true ⓘ |
| hasOctalCode | 0.77 ⓘ |
| hasOptimalPlayOutcome | first player wins for all positive row lengths ⓘ |
| hasOutcomeCondition | player who makes the last legal move wins ⓘ |
| hasPerfectInformation | true ⓘ |
| hasPlayConvention | no passing allowed ⓘ |
| hasPlayerCount | 2 ⓘ |
| hasSymmetryProperty | positions symmetric under reflection of the row ⓘ |
| hasTeachingUse | example game in combinatorial game theory courses ⓘ |
| inventedBy | Henry Dudeney NERFINISHED ⓘ |
| isDeterministic | true ⓘ |
| isFinite | true ⓘ |
| isImpartial | true ⓘ |
| isLoopFree | true ⓘ |
| isNormalPlay | true ⓘ |
| isPartOf | combinatorial game theory ⓘ |
| playStructure | normal play convention ⓘ |
| playStructure | players move alternately ⓘ |
| positionRepresentation | row of tokens or pins in a line ⓘ |
| publication | The Strand Magazine NERFINISHED ⓘ |
| relatedTo |
Dawson’s Kayles
NERFINISHED
ⓘ
Nim ⓘ octal game 0.77 NERFINISHED ⓘ |
| requires | logical reasoning ⓘ |
| strategyType | winning strategy depends on heap length modulo pattern ⓘ |
| typicalRepresentation | row of bowling pins ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.