CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock?

Question

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

Answer 1

a) $21,474,836.48 on the 32nd square
b) $42,949,672.95 total if there was only 32 squares

a) Look at the first few numbers in the sequence
square 1: 1 pennies 2^0
square 2: 2 pennies 2^1
square 3: 4 pennies 2^2
square 4: 8 pennies 2^3
Note how it's 2 raise to the square number -1
So square n: 2^(n-1)
For Square 32 2^31 = 2147483648 pennies
adjust it for dollars
$21474836.48 dollars

b) Look at the same thing for the series
total pennies on squares
square 1: 1 pennies 2^1 - 1
square 2: 3 pennies 2^2 -1
square 3: 7 pennies 2^3 -1
square 4: 15 pennies 2^4 - 1

note that the sum is one less than 2 to the square number
square n: (2^n)-1 pennies
square 32 42,949,67295 pennies
$42,949,672.95 dollars

Answer 2

classic answer

1,2,4,8.....

the nth term of that sequence can be expressed:

2^(n-1)

so

2^(64-1)=2^63=9223372036854775808

2^(32-1)=

you have to divide by 100 to get the answer in dollars instead of cents

Answer 3

a) $21474836.48
b) $42941672.95
I leave the work for you to show.

Answer 4

I'm disappointed. I thought this was going to be a dirty joke.