Class 7 News

Maths - Indices | The Grains of Rice Problem 

Class 7 Maths have been exploring Indices, when a number is multiplied by itself a certain number of times, or ‘to the power of …’ After working through many examples together the students were given this problem to solve:

The Story:     There was a king in India who loved mental games and puzzles.  A wise, but poor man in his kingdom invented the game of chess for him.  The king enjoyed the game so much that he invited the wise man to his castle and told him that as a reward he could have anything in the kingdom that he desired.  The wise man thought for a moment and then said that since his village sometimes did not have enough food, that he would like a good amount of rice.   

When the king asked him how much rice he would like, the wise man stated his answer as a puzzle.  He said that a single grain of rice should be placed on the first square of the chessboard (which has a total of 64 squares).  Then two grains of rice should be placed on the second square, and then double that amount (4 grains) on the third square, and double that amount (8 grains) on the fourth square, and so on up to the last square.  That is how much rice he would like − if the king didn't feel that the request was too great. 

He warned the king that all the rice wouldn't fit nicely on the chessboard, but that didn't really matter − he just wanted that amount of rice.  The king thought to himself that the wise man was actually quite a fool since he could have had anything in the kingdom, and he was only requesting a few bags of rice.     

How much rice was the wise man requesting?   

I am loathe to give you the answer so easily as I would love you to play with it for a while. You can email me or drop in for the answer. I will share with you a hint…

The king ordered his servants to go into the royal kitchen and carry out the wishes of the wise man.  However, once they reached the 23rd square, they came to the king and told him that they had run out of rice in the kitchen.  The king was surprised, but told them to take as much rice as needed from the royal granary.  The servants worked for two whole days bringing rice from the granary. But when they reached the 39th square of the chessboard they approached the king and told him that they had emptied the entire royal granary and had only reached the 39th square.  The king was quite shocked.  He asked how much more rice would be needed, and the royal astronomer said that he had calculated that it was far more rice than had ever been produced in the entire world.

Have fun!

Megan x