This is an awesome short story about the power of exponential growth. Many have probably heard this one, but if you haven't it's a wonderful way to understand the power of mathematics and exponential growth.
Rice on a Chessboard - An Exponential Story
This is a story about a chessboard, a game of chess and the incredible power of exponential numbers.
Once upon a time, the king who ruled over the region of Ambalappuzha was visited by a traveling sage, who challenged the king to a game of chess. The king was well known for his love of chess and so he readily accepted the challenge. Before the game started, the king asked the sage what he would like as a prize if he won. The sage, being a traveling man with little need for fine gifts, asked for some rice, which was to be counted out in the following way:
Give me one grain of rice on the first square of this chessboard, then two grains on the second square, four grains on the third square, eight grains on the fourth square and so on, so that each square contains double the amount of rice of the previous square.
Now the king was taken aback by this. He had expected the sage to request gold or treasures or any of the other fine things at his disposal, not just a few handfuls of rice. He asked the sage to add other things to his potential prize, but the sage declined. All he wanted was the rice.
So the king agreed and the chess game was played. The king lost and so, being true to his word, the king told his courtiers to collect some rice so that the sage's prize could be counted out.
The rice arrived and the king started counting it out onto the chessboard; one grain on the first square, two grains on the second square, four grains on the third square and so on. He completed the top row, putting 128 grains of rice on the eighth square. He then moved onto the second row; 256 grains on the ninth square, 512 on the tenth square, then 1024, then 2048, doubling each time until he needed to put 32 768 grains of rice on the last square of the second row.
The king now started to realise that something was amiss. This was going to cost more rice than he had originally thought, and there was no way he would be able to fit it all onto the chessboard, but he continued counting. By the end of the third row, the king would have needed to put 8.4 million grains of rice down. By the end of the fourth row, 2.1 billion grains were needed. The king brought his best mathematicians in, who calculated that the final square of the chessboard would require more than 9 x 10^18 grains of rice (9 followed by 18 zeroes) and that in total the king would be required to give 18 446 744 073 709 551 615 grains to the sage.
It was at this point that the sage revealed himself to be the God Krishna in disguise. He told the king that he did not have to pay him his prize all in one go, but instead could pay it over time. The king agreed to this and that is why to this day, pilgrims to the Ambalapuzzha temple are served the rice dish paal payasam as the king continues to pay his debt.
How much rice was this?
The total number of grains of rice needed to fill the chessboard would have been 18 446 744 073 709 551 615. This is more than 18 quintillion grains of rice, which would weigh approximately 210 billion tonnes and would be enough rice to cover the entire country of India with a metre-high layer of rice. To put this into perspective, India currently grows approximately 100 million tonnes of rice per year. At this rate, it would take over 2 000 years to grow enough rice to pay the king's debt.
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