Sprouts (game)

SproutsSprout'' (game)
Sprouts is a paper-and-pencil game that can be enjoyed simply by both adults and children.wikipedia
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Paper-and-pencil game

paper and pencilpen and paperpencil and paper game
Sprouts is a paper-and-pencil game that can be enjoyed simply by both adults and children.
Examples of paper-and-pencil games are Tic-tac-toe, Sprouts, and Dots and Boxes.

John Horton Conway

John H. ConwayJohn ConwayConway
It was invented by mathematicians John Horton Conway and Michael S. Paterson at Cambridge University in the early 1960s.
For instance, he discussed Conway's game of Sprouts (Jul 1967), Hackenbush (Jan 1972), and his angel and devil problem (Feb 1974).

Mike Paterson

PatersonMichael Stewart PatersonMichael S. Paterson
It was invented by mathematicians John Horton Conway and Michael S. Paterson at Cambridge University in the early 1960s.

Winning Ways for your Mathematical Plays

Winning Ways
Winning Ways for your Mathematical Plays reports that the 6-spot normal game was proved to be a win for the second player by Denis Mollison, with a hand-made analysis of 47 pages.
The second volume applies the theorems of the first volume to many games, including nim, sprouts, dots and boxes, Sylver coinage, philosopher's football, fox and geese.

Misère

BettelMisère gamemisere
In misère play, the player who makes the last move loses.

David Applegate

David L. ApplegateApplegate
It stood as the record for a long time, until the first computer analysis, which was done at Carnegie Mellon University, in 1990, by David Applegate, Guy Jacobson, and Daniel Sleator.
With Guy Jacobsen and Daniel Sleator, Applegate was the first to computerize the analysis of the pencil-and-paper game Sprouts.

Mathematics

mathematicalmathmathematician
Yet it also can be analyzed for its significant mathematical properties.

Mathematician

mathematiciansapplied mathematicianMathematics
It was invented by mathematicians John Horton Conway and Michael S. Paterson at Cambridge University in the early 1960s.

University of Cambridge

Cambridge UniversityCambridgeUniversity
It was invented by mathematicians John Horton Conway and Michael S. Paterson at Cambridge University in the early 1960s.

Dots and Boxes

Dotsdots-and-boxesStar Link
Setup is even simpler than the popular Dots and Boxes game, but game-play develops much more artistically and organically.

Hebrew language

HebrewHebrew grammarHeb.
All other dead spots (not neighbors of a survivor) are called pharisees (from the Hebrew for "separated ones").

Pharisees

PhariseePharisaicPharisaism
All other dead spots (not neighbors of a survivor) are called pharisees (from the Hebrew for "separated ones").

Game tree

game-tree searchsearch treetree
The outcome is determined by developing the game tree of the starting position.

Carnegie Mellon University

Carnegie Institute of TechnologyCarnegie MellonCarnegie-Mellon University
It stood as the record for a long time, until the first computer analysis, which was done at Carnegie Mellon University, in 1990, by David Applegate, Guy Jacobson, and Daniel Sleator.

Daniel Sleator

SleatorDanny SleatorDaniel
It stood as the record for a long time, until the first computer analysis, which was done at Carnegie Mellon University, in 1990, by David Applegate, Guy Jacobson, and Daniel Sleator.

Nimber

nim-sumnim additionnim-addition
In 2007, Julien Lemoine and Simon Viennot introduced an algorithm based on the concept of nimbers to accelerate the computation, reaching up to 32 spots.

Modulo operation

modulomodmodulus
The results for misère play are now conjectured to follow a pattern of length six (with some exceptional values): the first player wins in misère Sprouts when the remainder (mod 6) is zero, four, or five, except that the first player wins the one-spot game and loses the four-spot game.

Brussels sprout

Brussels sproutssproutssprout
A variant of the game, named Brussels Sprouts after the cruciferous vegetable, starts with a number of crosses, i.e. spots with four free ends.

Euler characteristic

Euler's formulaEuler–Poincaré characteristicElements
The Euler characteristic for planar graphs is 2, so

Impartial game

impartialimpartial games
Impartial games include Nim, Sprouts, Kayles, Quarto, Cram, Chomp, Subtract a square, Notakto, and poset games.

Macroscope (novel)

MacroscopeMacroscope'' (novel)
The plot involves, among other things, an extension of the Peckham Experiment, mathematicians John Conway and Michael Paterson's game of sprouts, astrology, the poetry of Sidney Lanier, the history of Phoenicia, and commentary on the value of a dedicated teacher of a subject contrasted with a practicing engineer of that subject attempting to teach it, all in a kaleidoscopic combination.