# 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**

### 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

### Elwyn Berlekamp

**Elwyn R. BerlekampBerlekampE. R. Berlekamp**

### University of Utah

**UtahUniversity of DeseretThe University of Utah**

### List of abstract strategy games

**chess like gameStacking games**

### 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.