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Transcript of SESSA'S WHEAT
Once upon a time there was a small kingdom at the edge of a desert. A greedy king ruled the kingdom. He was so greedy that if any of his subjects invented anything new he would get to see it and use it first.
One day, an inventor named Sessa created the game of chess. Sessa hoped that the game of chess could take away the boredom and sadness that most of the citizens of the kingdom felt. Hearing of this new game, however, the king sent for Sessa and his new game board. Sessa brought the game
board to the king and taught him how to play the game of chess. The king was so
delighted with this new game that he decided to give Sessa a reward!
Sessa immediately asked for the kingdom as a whole to be given more food but the greedy
king said no. The reward was for Sessa and Sessa only. Sessa told the king that he would need one week to decide what his reward should be. Sessa spent hours and
hours trying to figure out a reward that would be beneficial to him and the other people in the kingdom. On the last day, Sessa, who had still not been able to decide what he wanted to do decided to play a game of chess with his son. In the middle of
the chess game Sessa stopped and looked at his chessboard. That evening, Sessa went to the palace and told the king he had decided what he wanted. Sessa presented the king his chessboard and told him that he would want a reward in grains of wheat
But he had a special number in mind. He told the king that he would first want one piece of wheat, for the first square on the chessboard. Then he would
want two pieces on the third square, and then double that on the fourth square and so on and so fourth. The king eagerly agreed, thinking that he had cheated Sessa out of a much larger reward. The king called his royal mathematicians and asked them to calculate the amount of wheat needed to fill Sessa’s demands. The mathematicians believed that they could quickly calculate the amount of wheat
needed by hand so they drew a giant chessboard on the ground. They made sure that the board had 64 squares just like Sessa’s did.
On the first square they placed 1
grain of wheat, on the second square they placed two grains of wheat. When they got to the third square they placed 4 grains of wheat. Then they reached the fifth
square and placed 8 grains of wheat. They then reached the sixth square and placed 16 grains of wheat. After that they placed 32 grains of wheat on the 7th Finally they reached the end of the first row and placed 64 grains of wheat on the 8th square. The King started to feel anxious; this was already the amount of wheat that would fill a bag, how much more would Sessa end up with?
The number of grains of wheat kept growing and growing. Before the mathematicians were even half way through the board, the king’s supply of wheat was gone. The king begged Sessa to think of another reward. The king would loose all of the wheat that he had saved up for himself if Sessa refused. Sessa agreed to change his reward ONLY if the King would allow him to choose a reward that would benefit the kingdom. The King readily agreed.
Sessa asked the king to take his supply of wheat and feed the entire kingdom, instead of keeping it to himself. The king agreed to Sessa’s demands, knowing that even though he would lose much of his supply of wheat, he would lose even more if he denied Sessa. The Kingdom was soon well fed and happy :)
........A few months after this event occurred, the citizens of the kingdom were healthy enough to overthrow the greedy king and in his place they put Sessa on the throne
The kingdom lived in happiness and harmony for many years to come, all thanks to Sessa and his chessboard. Although it has been hundreds and hundreds of years, mathematicians are still trying to solve the exact number of grains of wheat that Sessa would have received. We have calculated it and now know the number. Heres how we found it :
Total # of grains:
Grain of wheat: (http://www.bakeinfo.co.nz/Facts/Wheat-Milling/Wheat/Wheat-grain)
length: 5-9 mm (we went with 7 mm)
A=38.5mm^2 or .0385 m^2
The area of each grain of wheat: .0385 m^2
After finding the area of each grain of wheat, we multiplied the total # of grains by the area of each grain.
18,446,744,073,709,551,615 * .0385m^2 = 7.101996468*10^17 m^2
Total area of all grains:
216,000 ft^2 or 20,100 m^2
We assumed that each seat takes up
10,167 * .5 m^2 = 5083.5 m^2
We also took into account lights, basketball hoops, and scoreboards
lights: ~ 30m^2
basketball hoops: 2 * 5m^2 = 10m^2
scoreboards: 2 * 10m^2 = 20m^2
20,100 m^2 - 5083.5m^2 - 30m^2 - 10m^2 - 20m^2 = 14,956.5 m^2
Area of Gampel after taking out space taken up from seats, lights, hoops, and scoreboards: 14,956.5 m^2
(7.101996468 * 10^17 m^2) / 14,956.5 m^2 = 4.748434773 * 10^13
Total # of Gampels that would be filled by Sessa’s wheat: