Once upon a time, a long time ago, a time so long ago, when I wasn’t born and you were not born too, that long ago, there lived an emperor in India. He was very fond of board games. In fact, he had been fascinated with them since his childhood. But, off late he was feeling rather bored with all that he had. He wanted something more challenging and exciting. So, one day, in his sabha ( assembly), he challenged the wise men of his kingdom to think of and invent a game that would not just fascinate him but be innovative, exciting, and challenging as well. He promised to suitably reward the winner.
These men got to work. They thought and they thought and then a few days later, Ram Prasad who was believed to be very intelligent appeared before the king and presented to him a game called Chess. When he explained the game to the king, he was so impressed that he said to Ram Prasad, “Name your reward and you shall have it”.
Your Majesty, I ask you for just one thing. Take your chessboard and place on the first square one grain of wheat. On the second square 2 grains, 3rd square 4 and continue this way ensuring each square has double the rice than the previous square. Do it for all the 64 squares Then my reward will be complete.
The emperor was shocked. He asked Ram Prasad to rethink his reward. He offered him land, gold, rubies, this and that but Ram Prasad, politely repeated his request. He just wanted what he had asked for.
This sounds like a small price to pay for your invention of such a fascinating game, I will see that your request is granted immediately still amazed that the man had asked for such a small reward – or so he thought.
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 to 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 realize 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 around 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 meter-high layer of rice.
Was Ram Prasad a simple man of simple wishes? What do you think of the reward he asked for?
Notes
Please draw a chessboard before you narrate this story and as you progress fill in the numbers on the chessboard to show the power of exponents.
