# of Sand Grains in a Beach
c
1 x 1015
(100m
x 10km x 1m) :
# of Chess Games Played
< 1 x 1016
in the past:
# of Stars in the Universe:
1 x 1022
# of p's & n's in a Drop
of Water: 5 x 1022
Avogadro's
Number (= a mole) : 6 x 1023
# of Sand Grains in the worldd
:
1 x 1026 ~200
moles
# of Air Molecules
in this room e:
1 x 1028
(30ft x 40ft x 12ft)
# of p's & n's in a human
body : 1 x 1028
# of Chess Games Possible
f,g
:
1 x 1040 (Western)
(under estimations)
1 x 1060 (Korean/Chinese)
# of Water Molecules
5 x 1046
in Ocean Water :
# of p's & n's in Ocean
Water : 1 x
1048
# of p's & n's in the
Earth :
1 x 1051
# of p's & n's in the
Sun :
1 x 1057
# of p's & n's in the
Milky Way : 1 x 1068
# of p's & n's in the
Universe :
1 x 1080
Googol
:
1 x 10100
# of Go Games Possible h:
1 x 10375 (=200!)
Googolplex: 1 x 10googol
a. Based on an average mass of a salt grain which is about 0.15
mg.
b. US Population ~ 4.5% of World Population
c. Assuming an average volume of a sand is 0.001cm3,
100m x 10,000m x 1m (106cm3/m3)
/ 0.001cm3.
d. Assumed that 0.01% of the volume of the Earth is sand.
Volume of the Earth = (4/3)(3.14)(6,400 km)3
= 1.1 x 1027 cm3.
e. (30ft x 40ft x 12ft)(0.3048m/ft)3(1,000L/m3)
= 410,000 L
Divide thi volume with 24.5 L (molar volume of air
at 25oC),
then, multiply it withe Avogadro's Number, 6.022x1023.
f. Based on the average number of movement to finish a chess
game:
g. Probability of repeating a same chess game
~ 1016/1040
= 1/ 1024 (a trillionth of a trilllionth).
h. This is a rough estimation again based on an average
number of movement to finish a Go(Badook) game.
(09/95, 09/01, revised, MHK)