LONG ago (several decades), Scientific American ran a short how-to
piece on a game called "sprouts." It is played with pencil and paper,
with players alternately drawing lines, placing dots on lines, and
connecting dots. I would love to know the rules for this game.

Hi basenjiguy,

The following is an excerpt of an excellent site which explains the
game of Sprouts you remember reading about. I suggest you read the
link in its entirety for a better understanding of the game.

Sprouts
Article by Jennifer Piggott and Jo Scholten

"This article invites you to get familiar with a strategic game called
"sprouts". It can be found on the nrich web site in the games archive.
The game is simple enough for younger children to understand, and has
also provided experienced mathematicians with significant food for
thought..."

The game: 
The game of Sprouts was invented in 1967 by two mathematicians John H.
Conway and Michael S. Paterson, when they were both at the University
of Cambridge in the UK. The game was popularised by one of Martin
Gardner's "Mathematical Games" columns in Scientific American. Here is
a quote from Conway:

"The day after sprouts sprouted, it seemed that everyone was playing
it, at coffee or tea times, there were little groups of people peering
over ridiculous to fantastic sprout positions."

Sprouts is a game for two players. All you really need is paper and a
pencil. The game starts by drawing any number of spots. In this
example we are going to look at 3 spots.

The first player has a turn by joining two of the spots and marking a
new spot in the middle of the line. Or the line may start and end on
the same spot.

Rules: 
You are not allowed to draw a line which crosses another line. This is
important to remember!

A spot cannot have more than three lines leading to or from it. 

The idea is to make it impossible for the other player to draw a line. 

So the last person to draw a line is the winner. 

Source: Nrich
http://nrich.maths.org/public/viewer.php?obj_id=2413&part=index&refpage=monthindex.php


Another good explanation of the game:
Nationmaster: Sprouts
http://www.nationmaster.com/encyclopedia/Sprouts-%28game%29


More explanations of the rules of Sprouts:

http://www.math.eku.edu/Greenwell/MAT303/sprouts/

http://www.geocities.com/chessdp/rules.htm


Search criteria:
game called sprouts

I hope this is helpful. If you have any questions regarding my answer
please don?t hesitate to ask before rating it.

Best regards,
Rainbow

Fast, clear, well-organized writing, and with helpful links. Thank you!

Hi basenjiguy,
I'm glad I could help. Thank you very much for the rating and tip.
Best wishes,
Rainbow

The Wikipedia article on John H. Conway has a link to even more online
explanations of games, including Sprouts, at
http://www.madras.fife.sch.uk/maths/games/index.html

It refers to his monumental but readable book on the subject of
Sprouts and other games:

"Winning Ways for your Mathematical Plays" (ISBN 1568811306) by Elwyn
R. Berlekamp, John H. Conway, and Richard K. Guy is a compendium of
information on mathematical games. It was first published in 1982 in
two volumes.
... The second volume ... including nim, sprouts, dots and boxes, ...
and Conway's game of life.
A republication of the work by A K Peters splits the content into four volumes.

Another related book of his is "On Numbers and Games", published by
Academic Press Inc in 1976, ISBN 0121863506, and re-released by AK
Peters in 2000 (ISBN 1568811276).

Wow -- there really IS a pot of gold at the end of the rainbow! (I'm
sure I'm not the first to say that, but I couldn't resist.)