SP.268 Syllabus
Melissa Gymrek (mgymrek), Jing Li (lijing)
Supervisor: Erik Demaine (edemaine)
Spring 2011
Course Description
We will explore the mathematical strategies behind popular games, toys, and
puzzles. Each week will consist of a lecture and disc
The Mathematics of the Rubiks Cube
Introduction to Group Theory and Permutation Puzzles
March 17, 2009
Introduction
Almost everyone has tried to solve a Rubiks cube. The rst attempt often
ends in vain with only a jumbled mess of colored cubies (as I will
Markov and Mr. Monopoly Make Millions
Sp.268 Spring 2010
Probability
Probability is key to many elds, a mere few of which are econometrics,
quantum mechanics, signal processing, statistical physics, and theoretical
computer science. This section will be a
Intro to A.I. Topics
Connect Four
March 12, 2009
Introduction
Connect Four is a tic-tac-toe like game in which two players drop discs into
a 7x6 board. The rst player to get four in a row (either vertically, horizontally, or diagonally) wins.
The game was
Theory of Impartial Games
February 3, 2009
Introduction
Kinds of Games Well Discuss
Much of the game theory we will talk about will be on combinatorial
games which have the following properties:
There are two players.
There is a nite set of positions av
Introduction to AI Techniques
Game Search, Minimax, and Alpha Beta Pruning
June 8, 2009
Introduction
One of the biggest areas of research in modern Articial Intelligence is in
making computer players for popular games. It turns out that games that
most hu
In 1974, Erno Rubik created the Rubiks Cube. It is the most popular puzzle
worldwide. But now that it has been solved in 7.08 seconds, it seems that the world is in
need of a new challenge. Melinda Green, Don Hatch, and Jay Birkenbilt took it upon
themsel
The Strategy of Risk
Garrett Robinson
Risk
Risk is a complex board game produced by Hasbro that involves both luck and skill. The
goal is simple: take over the world. Despite this simple goal, the game is very complicate d and
dynamic. Players attempt to
Amoeboid: A Partisan Combinatorial
Game of Chance
Sebastien Dabdoub
Santiago Cuellar
Rules
Set up
This game can be played on any graph (or n-dimensional board). For simplicity we will consider a n n Board. The game starts with two amoebae, of
size 1, in d
HEX
SP.268
SPRING 2011
1. Introduction
The game of Hex was rst invented in 1942 by Piet Hein, a Danish
scientist, mathematician, writer, and poet. In 1948, John Nash at
Princeton re-discovered the game, which became popular among the
math graduate student
http:/erikdemaine.org/papers/AlgGameTheory_GONC3/
k = cfw_
for n in range(0, 1000):
k[n] = mex ([k[i] ^ k[n-i-1] for i in range(n)] +
[k[i] ^ k[n-i-2] for i in range(n-1)])
print n, "-", k[n]
def mex(nimbers):
nimbers = set(nimbers)
n=0
while n in nimbers