Please Help?

Question

4) 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 1

a.) The pattern is 2^(n-1) because each square has twice as much as the previous. Therefore for the 32nd square he would put 2^(32-1) = 2^31 = 2147483648 pennies

To express in dollars you would divide by 100 (100 pennies = 1 dollar) to get $21,474,836.48

Answer 2

I answered this question another place, and I worked out that the total is nearly 4.3 Billion pennies, or almost 43 Million dollars. The formula for all the squares of this is {(2^32)-1} /100, and the answer I got using estimates on an 8 digit calculator was a 12 digit number with 2 decimals. On the 32nd square, he needs to put nearly 2.15 Billion pennies, or nearly 21.5 Million dollars.

Answer 3

1st square, .01 = 2^0
2nd square, .02 = 2^1
.
.
32nd square, 2^31 = $21,474,836.48
total at that point = $42,949,672.95