The Concept of Chess
- Erik Spiller
and Keon
Massey
Sissa Ben Dahir
• According to legend, Sissa Ben
Dahir invented the game of chess
which impressed King Shirham so
much he offered him the reward
of his choosing. Sissa Ben Dahir
requested one grain on the first
square, two grains on the second
square, four on the third, eight on
the fourth, and kept the pattern
for all sixty-four squares. The king
accepted and granted Sissa Ben
Dahir his wish.
Wheat on chess Board
Square
number, n
Number of
grains wheat
on square n
Total
number of
grains of
wheat on
squares 1
through n
1
2
3
4
5
6
7
1
2
4
8
16
32
64
1
1+2
3
3+4
7
7+8
15
15 + 16
31
31 + 32
63
63 + 64
127
1+2+22 + 23 + 24 +25 +26
• N=0 20 =1
• N=1 21 1+2=3
• N=2 22 1+2+22 (4)=7
• N=3 23 1+2+4+23 (8)=15
• N=4 24 1+2+4+8+24 (16)=31
• N=5 25 1+2+4+8+16+25 (32)=63
• N=6 26 1+2+4+8+16+32+26 (64)=127
How many grains
of wheat are on the
chessboard?
If all 64 squares of the
chessboard are piled
high with wheat as
requested, how many
grains of wheat are on
the board?
N= 63
1+2+22 +
23 +24 … +263
1-263 = 1-263
1-2
-1
263 − 1 =
9.22337204*1018
A grain of wheat weighs approximately 0.00008
•
•
•
•
•
1 grain wheat = 8* 10−6 kg
9.22337204*1018
(9.22337024*1018 ∗8* 10−6 )
9.22337024*8 ∗ 1012 kg
73.7869763*1012 kg