The Legend of the Chess Board and the grain of Rice
There is a
legend that an Emperor of old rewarded the inventor of chess for introducing the game to his kingdom, with
compensation of his choosing.
This story cannot be historically confirmed and comes in many variations. One such version is
that the Emperor asked the man what he would like to receive for this fantastic new game of tactics, strategy
and planning. As the story goes the inventor chose for a grain of rice to be placed on the first square of
the board and that amount doubled for the second and in turn that quantity multiplied by two on the third
square until all sixty-four squares were paid out in full.
This tale, be it factual or not, is often used by mathematicians to explain the concept
of exponential growth. It is difficult to fathom that by using this simple formula the accumulative amount is
18,446,744,073,709,551,615 grains of rice, and that in only 64 steps.
How much is that?
Let’s put the same concept into another practical example. Imagine one person had to write down the
name of only two people he or she knows and every one of those people had to do the same, but no name or
person may be used twice or be duplicated.
By comparing this exercise with the above analogy of the rice grain on the chess board, it quickly
becomes evident that there are simply not even nearly enough people in the entire world to complete the
The baffling concept of exponential growth in the speed in which the number of units increase from
level to level is also commonly used in Multi Level marketing and Pyramid Scheme models. In these instances the concept of the chess board
and grain of rice analogy is often used to demonstrate the money making potential of the system and the pure
unlikelihood of running out of new recruits or participants into the system.
It is, however, the same chess board and grain of rice analogy described above that proves that any
pyramid scheme is destined to collapse as there are not nearly enough people in any single area to sustain
the exponential duplication over a significant period.
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