Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How money expressed in do

Question

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.

Answer 1

Hi dortaliny75

This is an updated version of old Chinese tale where a favoured minister of the king asked to be paid in grains of rice. He asked the king to place one grain on the first square of a chessboard, then double it on the next square, etc. It is an illustration of doubling power.

Anyway, the 64th square will contain 2^63 items (pennies in your example). The whole board will contain (2^64)-1 pennies. I make this to be $184,467,440,737,095,516.15.

For those with a science bent, you can see the power of doubling also in the early inflationary period of the universe. The inflationary period lasted 10^-32 seconds (a million billion billion billionth of a second), and in that period the universe doubled in size 100 times (only!). 100 doublings seems a small amount, but it represents an increase by a (linear) factor of 1,267,650,600,228,229,401,496,703,205,376 or 10^30. This is the equivalent of stretching an atom (about 10^-10m) to the size of a galaxy in the tiniest fraction of a second.


Hope this helps!
The Chicken

Answer 2

Square 1 is 2^0, so 2^63 is the amount on the last square. So the total amount of money would be the integral from 1 - 64 of t he expression 2^(x-1) dx. So the amount of pennies is 1.33 x 10^19, so $133,000,000,000,000,000

Answer 3

Mr Brown has over $184,467 trillion dollars (see below for exact figure)

The total number of pennies equals

2^63 + 2^62 + 2^61+.......+2^3 + 2^2 + 2 +1

If we add one to this, we get: 2^64

So Mr Brown has 2^64 - 1 pennies =

18446744073709551615 pennies

= $ 184,467,440,737,095,516.15

Answer 4

My Penis Size Tripled : http://LongPenis.uzaev.com/?mFOi

Answer 5

$91032241770998382.08