Transcript
![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](https://reader034.vdocuments.us/reader034/viewer/2022050505/5f96eb9caec4222ffe2de46f/html5/thumbnails/1.jpg)
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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](https://reader034.vdocuments.us/reader034/viewer/2022050505/5f96eb9caec4222ffe2de46f/html5/thumbnails/3.jpg)
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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
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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](https://reader034.vdocuments.us/reader034/viewer/2022050505/5f96eb9caec4222ffe2de46f/html5/thumbnails/6.jpg)
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![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](https://reader034.vdocuments.us/reader034/viewer/2022050505/5f96eb9caec4222ffe2de46f/html5/thumbnails/8.jpg)
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](https://reader034.vdocuments.us/reader034/viewer/2022050505/5f96eb9caec4222ffe2de46f/html5/thumbnails/9.jpg)
![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](https://reader034.vdocuments.us/reader034/viewer/2022050505/5f96eb9caec4222ffe2de46f/html5/thumbnails/10.jpg)
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.
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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
.