Once upon a time a long time ago, a girl named Rachana lived in a small village in Tdaravati Kingdom. Rachana loved elephants. She also loved numbers. So of course she loved all numbers to do with elephants. One day, it was Rent Collection Day, Rachana passed through the marketplace, she saw the Raja’s elephants parade carrying rice bags. No wonder that the people looked sad. The Raja had taken so much rice for himself that the whole village would be hungry. For thousands of years, the villagers had farmed on the Raja’s land.
The next day, all the Raja’s elephants were sick. Doctors spent all day & most night in the elephant yard chanting & burning incense or other things to cure the elephants, but they got even sicker.
One morning, the Raja returned from a walk in the gardens found Rachana at the gate. Rachana asked Raja if she could help, and Raja allowed her and promised if Rachana could save them, she may choose her own reward. Rachana studied their feet, the pads, mouths, tusks, tongues, and the throat. When Rachana got the the first ear, she discovered a painful-looking infection inside the ear canal. She cleaned their ears and sang them a soothing song and went home.
At dawn the next day, when Rachana returned, the elephants were walking unsteadily around their yard. Raja was overjoyed. He declared a festival day and invited everyone in the land to the palace. Raja asked Rachana to name her reward. Rachana looked at the beautiful jewels on the table, diamonds.. She thought about hundreds of sack of rice they carried away from the village each year. And then she noticed the chessboard.
Rachana asked the Raja to place 2 grains of rice on the first square of the chessboard, then 4 grains on the second square, 8 on the next, and so on, doubling each pile of rice till the last square. The villagers shook their heads sadly at Rachana’s choice. Raja was secretly delighted. A few piles of rice would certainly be far cheaper then this precious jewelry. Then he honored her request.
Two servants brought out a small bowl of rice and carefully placed 2 grains on the first square of the board, 4 on the second, 8 on the third, 16 on the fourth, 32 on the fifth, 64 on the sixth, 128 on the seventh, and finally 256 on the eighth square at the end of the row. Although 256 grains filled the eighth squared completely, they amounted to only a single teaspoon of rice.
The first square of the second row, the servants stood awkwardly, not knowing how to count out the rice which is 512 that is too high to count quickly. Rachana started to explain if the servant had 1 teaspoon of rice at the end of the first row, why not just put 2 teaspoons! So Raja ordered.
2 teaspoons on the first square of the board, 4 on the second, 8 on the third, 16 on the fourth, 32 on the fifth, 64 on the sixth, 128 on the seventh, and finally 256 on the eighth square at the end of the row which is filled another bowl.
On the third row, the servant started to count by teaspoons again, but Raja cut in. Showing off his knowledge of math, Raja explain if the sixteenth square took two bowls of rice, the servants don’t need to count by teaspoon.
So the servant counted by bowls. 2 bowls on the first square of the board, 4 on the second, 8 on the third, 16 on the fourth, 32 on the fifth, 64 on the sixth, 128 on the seventh, and finally 256 on the eighth square at the end of the row which can completely filled a large wheelbarrow. The servants worked through the fourth row, wheelbarrow by wheelbarrow. The servants took elephants to get more rice from the first storehouse.
By late afternoon, the Raja had collapsed onto his couch. The servants started on the fifth row of the chessboard, and soon they where emptying entire storehouse into the courtyard. Within several square, rice poured from the windows of the palace and into the gardens beyond. By the middle of the fifth row, all of the Raja’s storehouses were empty. As Raja could not fill the chessboard but he could not break a promise as well. He asked Rachana what he could give her to be released from his vow.
Rachana answered softly with a little smile that the Raja could give the people of the village the land they farm, and take only as much rice as the Raja need. Raja gazed at the mountains of rice that filled his palace and gardens, then out beyond the gardens to the fields the villagers farmed, stretching as far as he could see. He agreed her request.
“ I am a rich man, and it took all of the rice I owned to fill little more then one-half of the chessboard. How much rice would it have taken to fill the whole board?” Raja asked.
“ If you had kept doubling the rice to the last square of the chessboard, all of the Kingdom would be knee deep in rice” said Rachana, and smiled.
Apologize for my poor English writing!!