Calculate the Chessboard Problem
Calculator for the chessboard problem, which determines the number of grains at a doubling or other multiplication rate per square. The chessboard problem originates from an arab legend, after which the inventor of the chess game was granted a wish. He wished for one grain of wheat on the first square of the chessboard, two on the second, four on the third and so on, twice the amount on each further square. Which at first doesn't seem much, would be more than 18 quintillion grains of wheat or more than 700 gigatons, much more than there is on Earth.
Here, for any amount of squares (at a chessboard 64), for any multiplication factor (at the original chessboard problem 2) and any start value (usually 1), the number of grains per square and in total can be calculated.
The default setting is that of the famous task. The values can, of course, be adjusted as desired. Doubling in each step, i.e., a power of two or squaring, seems like a rather small factor. Nevertheless, absurdly high values are reached with a large number of steps. As the factor increases, these values are simply reached more quickly. Often, all that is needed is the number of digits of the result; for this see Count Decimal Places.
Although the legend was passed down by the Arabs, it takes place in ancient India around 2500 years ago. Instead of wheat, it is often told using grains of rice. This legend tells that game of chess was invented by the underling Sissa ibn Dahir to point out to the king that a king, while important, is powerless without his people, and thus to encourage him to rule less tyrannically. This seems to have worked out. The king initially considered the demanded reward very modest, but then realized it was impossible to raise such an amount. He helped himself out of this misery by commanding Sissa to count the grains himself, one by one.
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