Would like someone to help. have figured several times and different each time.?

Question

I am looking for someone to try this problem to see what anwer they get. I have gotten several different answers . don't know if calulating wrong or what. thanks. here is the problem.. copied it form homework for you to read.

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:
Show work in this space




b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer:
Show work in this space




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:
Show work in this space

Answer 1

a) How much money expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer:
Show work in this space

it is a geometric sequence 2^0,2^1,2^2......2^n-1
t32=2^31
so he would have placed 2^31 pennies in the 32ndsquare
b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer21474836.48 dollars
Show work in this space
t32=2^31
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:92233720368547758.08dollars
Show work in this space
t64=2^63

Answer 2

a) How much money expressed in dollars would Mr. Brown have to put on the 32nd square?

The number of pennies placed on square n is 2^(n-1). So for square 32 the number of pennies is 2^(32-1) = 2^31. The amount of money in dollars is 2^31/100.

b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?

The number of pennies is:
S = 2^0 + 2^1 + 2^2 + ... + 2^31 = 2^32 - 1
The amount of money expressed in dollars is: (2^32 - 1)/100

c) How much money expressed in dollars would the traveling salesman receive in total to fill the whole checkerboard (64 squares)?

The number of pennies is:
S = 2^0 + 2^1 + 2^2 + ... + 2^63 = 2^64 - 1
The amount of money expressed in dollars is: (2^64 - 1)/100

Answer 3

First any number raised to the zero power equals 1

Second we are doubling for each square so that is base 2. This is binary, the number system computers use to count.

so for the first square to be equal to 1 penny you have
2^0 (the ^ means raised to a power)
which is 2 to the zero power which equals 1
The next square is 2^1 = 2 ect...

since we are starting the cound for which square we are on you have to start counting at zero not one.

You have ten fingers numbered 1 to 10 OR starting at zero numbered 0 to 9

The total amount of money is the sum of all 64 squares.


You can add up all 64 squares the hard way OR use the formula

total = (2^(n+1))-1

Finally remember we are taking about pennies and teh answer is supposed to be in dollars so divide the total pennies by 100

Answer 4

Here is what I would do. Look for a pattern:
day 1 1 cent
day 2 2 cents, total 3 cents
day 3 4 cents, total 7 cents
day 4 8 cents, total 15 cents

notice that the total is always one less than twice the number of cents that day

Also notice that the amount each day is 2 to the power of the day number minus one

So on day 32, 2 to the 31st power cents (divide by 100 to get dollars) would go on the 32nd square, and the total would be that number times 2 - 1 (then divide by 100 again)

Answer 5

Hi To get an idea of how great this number is, use you computer to calculate 2 ^ 64, 2 ^ 32. The number is huge, and the salesman will never get his money. But he could marry the daughter and be happy!

Answer 6

the money on the Nth square will be 2^(n-1) cents.
on N squares the total will be 2^N -1

on the 32nd square this will be 2^31=$21,474,836.48

on 32 squares, the total will be 2^32 -1=$42,949,672.95

on all 64 squares he would need
2^64 -1=$184,467,440,737,095,516.15

This is aprox 15,372. times the US GDP