SOLUTION: 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 ou

Question 64421: 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 Brown came out gratefully thanked the traveling salesman for saving his daughter's life. Mr. Brown 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 penny of the first square. Then place teo pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies." As he'd been saving pennies for over 25 years, Mr. Brown did not consider this much an award, but soon realized he made a miscalculation on the amount of money involved.
a) How much money expressed in dollars would Mr. Brown have to put on the 32nd square?
b)How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
c) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How much money expressed in dollars would the farmer need to give the salesman?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Consider the following:
Let n = the number of the square.
For n = 1 (the first square), the number of pennies is = = 1
For n = 2, the number of pennies is = = 2
For n = 3, the number of pennies is = = 4
...and so on.
For the 32nd square, n = 32, so the number of pennies on this square is and
Change this to dollars by diving by 100 (100 pennies to the dollar) and you get:
$21,474,836.48 Just on the 32nd square.
To find the total number of pennies when all 64 squares are filled in this fashion, it's Note here, that the 1 is subtracted after raising 2 to the 64th power. The resulting number is too large for most calculators to display, but here is the result: pennies.
In dollars, that's: $184,467,440,737,095,516.15

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