Nim
E653412
Nim is a classic impartial combinatorial game of removing objects from heaps, fundamental in game theory and central to the development of the Sprague–Grundy theorem.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Nim canonical | 2 |
| Moore’s Nim | 1 |
| misère Nim | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7278061 — 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: Nim Context triple: [Sprague–Grundy theorem, relatedTo, Nim]
-
A.
Kayles
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.
-
B.
Hackenbush
Hackenbush is a combinatorial game played on colored line-graphs, famous in recreational mathematics for illustrating concepts in game theory and surreal numbers.
-
C.
Domineering
Domineering is a two-player abstract strategy board game in which players alternately place dominoes in restricted orientations on a grid, aiming to block the opponent from making a legal move.
-
D.
Twixt
Twixt is a 2011 gothic horror film written and directed by Francis Ford Coppola, blending supernatural mystery with a meta-narrative about a struggling writer.
-
E.
Tentyris
Tentyris is the ancient Greek name for the Egyptian city of Dendera, renowned for its well-preserved temple complex dedicated primarily to the goddess Hathor.
- 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: Nim Target entity description: Nim is a classic impartial combinatorial game of removing objects from heaps, fundamental in game theory and central to the development of the Sprague–Grundy theorem.
-
A.
Kayles
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.
-
B.
Hackenbush
Hackenbush is a combinatorial game played on colored line-graphs, famous in recreational mathematics for illustrating concepts in game theory and surreal numbers.
-
C.
Domineering
Domineering is a two-player abstract strategy board game in which players alternately place dominoes in restricted orientations on a grid, aiming to block the opponent from making a legal move.
-
D.
Twixt
Twixt is a 2011 gothic horror film written and directed by Francis Ford Coppola, blending supernatural mystery with a meta-narrative about a struggling writer.
-
E.
Tentyris
Tentyris is the ancient Greek name for the Egyptian city of Dendera, renowned for its well-preserved temple complex dedicated primarily to the goddess Hathor.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
finite game
ⓘ
mathematical game ⓘ normal-play game ⓘ two-player game ⓘ |
| hasCategory | abstract strategy game ⓘ |
| hasHistoricalAnalysisBy | Charles L. Bouton ⓘ |
| hasInformationStructure |
no chance moves
ⓘ
no hidden information ⓘ |
| hasKeyConcept |
Grundy numbers
ⓘ
linked to:
Sprague–Grundy theorem
N-positions ⓘ Nim-sum ⓘ P-positions ⓘ Sprague–Grundy theorem ⓘ binary representation of heap sizes ⓘ |
| hasMathematicalProperty |
disjunctive sum of impartial games reduces to a Nim heap via Grundy numbers
ⓘ
every position has a unique Grundy number ⓘ |
| hasMoveType | removal of objects from heaps ⓘ |
| hasObjective | force opponent into a position with no legal moves under normal play ⓘ |
| hasOutcomeClass | first player win under optimal play except when initial Nim-sum is zero ⓘ |
| hasPlayerCount | 2 ⓘ |
| hasRepresentation |
heaps of tokens
ⓘ
piles of matches ⓘ rows of stones ⓘ |
| hasRule |
on each move a player chooses exactly one heap
ⓘ
on each move a player removes one or more objects from the chosen heap ⓘ two players move alternately ⓘ under normal play the player who takes the last object wins ⓘ |
| hasRuleVariant | misère play where the player who takes the last object loses ⓘ |
| hasSolutionDescribedIn | Bouton’s theorem ⓘ |
| hasStrategy | optimal play is to move to a position with Nim-sum zero ⓘ |
| hasTurnStructure | sequential turns ⓘ |
| hasVariant |
Moore’s Nim
ⓘ
linked to:
Nim
Turning Toads and Frogs (as a related impartial game) ⓘ Wythoff Nim ⓘ misère Nim ⓘ
linked to:
Nim
|
| hasWinningCondition |
Nim-sum of heap sizes equals zero for losing positions
ⓘ
Nim-sum of heap sizes nonzero for winning positions ⓘ |
| influenced |
algorithmic game solving methods
ⓘ
the general theory of impartial games ⓘ
linked to:
Sprague–Grundy theorem
|
| isCentralTo | development of the Sprague–Grundy theorem ⓘ |
| isExampleOf |
game solvable by complete mathematical analysis
ⓘ
normal-play impartial game ⓘ |
| isFundamentalTo | combinatorial game theory ⓘ |
| isUsedAs |
canonical example in teaching combinatorial game theory
ⓘ
test case for impartial game algorithms ⓘ |
| wasSolvedIn | 1901 ⓘ |
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: Nim Description of subject: Nim is a classic impartial combinatorial game of removing objects from heaps, fundamental in game theory and central to the development of the Sprague–Grundy theorem.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Nim
linked to: Nim