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Question 65064: I am so lost on this. Please help....
CLASSIC PROBLEM - 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 and 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 on the first square. Then place two 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 of 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?
Answer:
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b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer:
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c) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How money expressed in dollars would the farmer need to give the salesman?
Answer:
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Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a) How much money expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer:
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The 1st square has 2^0=1 cent
The 2nd square has 2^1=2 cents
So, the 32nd square has 2^31 cents
2^31=$21,474,836.48
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b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer:
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1+2+4+8+...+2^31
S(n)=(n/2)(1st term + last term)
S(32)=(32/2)(1+2147483648)=$34,359,7383.80
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c) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How money expressed in dollars would the farmer need to give the salesman?
Answer:
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1+2+4+....+2^63
S(64)=(64/2)(1+2^63)
=$2.951479052x10^18
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Cheers,
Stan H.
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