the hex game - university of california, berkeleyee100/fa08/handouts/hex.pdf · bad news there is...

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Page 1: THE HEX GAME - University of California, Berkeleyee100/fa08/handouts/Hex.pdf · Bad News There is no known general winning strategy for Hex boards of size larger than 9 x 9. Shannon’s

Page 2: THE HEX GAME - University of California, Berkeleyee100/fa08/handouts/Hex.pdf · Bad News There is no known general winning strategy for Hex boards of size larger than 9 x 9. Shannon’s

THE

HEX

GA

ME

Page 3: THE HEX GAME - University of California, Berkeleyee100/fa08/handouts/Hex.pdf · Bad News There is no known general winning strategy for Hex boards of size larger than 9 x 9. Shannon’s

Page 4: THE HEX GAME - University of California, Berkeleyee100/fa08/handouts/Hex.pdf · Bad News There is no known general winning strategy for Hex boards of size larger than 9 x 9. Shannon’s

Goo

d N

ews

Ther

e ex

ists

a w

inni

ng st

rate

gy

such

that

if y

ou b

egin

, you

will

alw

ays

win

.Pr

oved

by

: Joh

n N

ash

Nob

el L

aure

ate

in E

cono

mic

s

Exis

tenc

e Th

eore

m

Page 5: THE HEX GAME - University of California, Berkeleyee100/fa08/handouts/Hex.pdf · Bad News There is no known general winning strategy for Hex boards of size larger than 9 x 9. Shannon’s

Bad

New

s

Ther

e is

no

know

n ge

nera

l win

ning

stra

tegy

for H

ex b

oard

s of s

ize

larg

er

than

9 x

9.

Page 6: THE HEX GAME - University of California, Berkeleyee100/fa08/handouts/Hex.pdf · Bad News There is no known general winning strategy for Hex boards of size larger than 9 x 9. Shannon’s

Page 7: THE HEX GAME - University of California, Berkeleyee100/fa08/handouts/Hex.pdf · Bad News There is no known general winning strategy for Hex boards of size larger than 9 x 9. Shannon’s

Page 8: THE HEX GAME - University of California, Berkeleyee100/fa08/handouts/Hex.pdf · Bad News There is no known general winning strategy for Hex boards of size larger than 9 x 9. Shannon’s

Shan

non’

s Hex

Circ

uit G

ame

Win

ning

Stra

gegy

Play

er 1

: Cut

the

resi

stor

with

the

larg

est c

urre

nt m

agni

tude

.

Play

er 2

: Short

the

resi

stor

with

the

larg

est c

urre

nt m

agni

tude

.

Page 9: THE HEX GAME - University of California, Berkeleyee100/fa08/handouts/Hex.pdf · Bad News There is no known general winning strategy for Hex boards of size larger than 9 x 9. Shannon’s

Page 10: THE HEX GAME - University of California, Berkeleyee100/fa08/handouts/Hex.pdf · Bad News There is no known general winning strategy for Hex boards of size larger than 9 x 9. Shannon’s

Shan

non’

s Hex

Circ

uit G

ame

Win

ning

The

orem

If b

oth

play

ers f

ollo

w

Shan

non’

s win

ning

stra

tegy

,

then

the

play

er w

ho b

egin

s win

s.

Page 11: THE HEX GAME - University of California, Berkeleyee100/fa08/handouts/Hex.pdf · Bad News There is no known general winning strategy for Hex boards of size larger than 9 x 9. Shannon’s

A+

Proj

ect

Writ

e a

com

pute

r pro

gram

to e

xhau

st

all p

ossi

ble

outc

omes

of t

he S

hann

on

Hex

circ

uit-g

ame

win

ning

stra

tegy

and

prov

e or

dis

prov

e Sh

anno

n’s c

onje

ctur

e.

If fa

lse,

pro

pose

you

r win

ning

stra

tegy

.

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