Hundreds
and hundreds of years ago there was a King in India who loved to play
games. But he had gotten bored of the games that were present at the
time and wanted a new game that was much more challenging. He
commissioned a poor mathematician who lived in his kingdom to come up
with a new game. After months of struggling with all kinds of ideas
the mathematician came up with the game of Chaturanga. The game had
two armies each lead by a King who commanded the army to defeat the
other by capturing the enemy King. It was played on a simple 8x8
square board. The King loved this game so much that he offered to
give the poor mathematician anything he wished for. "I would
like one grain of rice for the first square of the board, two grains
for the second, four grains for the third and so on doubled for each
of the 64 squares of the game board" said the mathematician. "Is
that all?" asked the King, "Why don't you ask for gold or
silver coins instead of rice grains". "The rice should be
sufficient for me." replied the mathematician. The King ordered
his staff to lay down the grains of rice and soon learned that all
the wealth in his kingdom would not be enough to buy the amount of
rice needed on the 64th square. In fact the whole kingdoms supply of
rice was exhausted before the 30th square was reached. "You have
provided me with such a great game and yet I cannot fulfill your
simple wish. You are indeed a genius." said the King and offered
to make the mathematician his top most advisor instead.
After
hearing that story I was obsessed with wanting to know exactly how
many grains of rice would be needed on the 64th square and how much
total rice would be needed for all 64 squares. Personal computers
were not available then (this is around 1978) and so I set out to
find the answer using my dads' TI calculator. I think the calculator
had about ten digits on it; and that was considered top of the line
then. Within a minute or two of starting the calculator hit its
limit. But I really wanted to know the answer, so I kept going and
did the calculations by hand. After spending most of my Sunday
morning doing arithmetic I finally had the answers:
9,223,372,036,854,775,808
on the 64th square and
18,446,744,073,709,551,615
total for the whole board
That's
about 18 billion billion. So if a bag of rice contained a billion
grains, you would need 18 billion such bags. But actually a real bag
of rice weighing 100 pounds has less than 3 million grains.
This
story about the King is most likely not true. But it is true that
there was an ancient Indian game called Chaturanga and it is believed
that modern Chess evolved from it. However some scholars argue that
China is the true birthplace of Chess. So we may never know the real
answer.
