Question 29877: I have searched this site for a certain word problem that I am stumped on. I have seen similar problems but I still do not understand how to solve. Would someone be kind enough to help me with this? Thank you so much!
A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Crane came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Crane insisted on giving the man an award for his heroism.
So, the salesman said, “If you insist, I do not want much. Get your checkerboard and place one grain of wheat on the first square. Then place two grains of wheat on the next square. Then place four grains on the third square. Continue this until all 64 squares are covered with grains of wheat.” As he had just harvested his wheat, Mr. Crane did not consider this much of an award, but he soon realized he made a miscalculation on the amount of wheat involved.
a) How much wheat would Mr. Brown have to put on the 24nd square?
b) How much total grain would the traveling salesman receive if the checkerboard only had 24 squares?
c)Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman?
I've attempted the first question and here is what I have:
24= 1x2^24-1
= 2^23
=8,388,608
Please help. Thanks.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Well, you certainly have the right answer to the first question.
As for the second question...the total number of grains if the checkerboard had only 24 squares?
This would amount to  = 16,777,216-1 = 16,777,215 grains of wheat.
On a regular checkerboard having 64 squares, the number of grains would be:
 = 18,446,744,073,709,551,615 grains of wheat.
I'm no farmer, but, from what I have read, one can assume that a bushel of wheat contains about 5,000,000 grains, so one would need about 4,000 billion bushels of wheat to cover this award.
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