 
A young lady named Mildred* was negotiating her allowance with her father. The devious parent new something she didn't, and made her this offer: "You can have $50 cash at the end of the month. Or you can have whatever is on the last square of this checkerboard. There's one cent on the first square, two cents on the second square, four cents on the third square, and the amount on each square will double every day."*Name changed to protect the innocent The young lady thought for few minutes. Despite knowing that pennies were no longer legal tender in Canada, but wisely refraining from pointing that out to her impatiently waiting father, she decided not to fall for the obvious fake, and chose the $50 cash. That's when I stepped in. Once more, knowing a little math saved the day. I pointed out to the young lady that the original one cent on the first square would have doubled 63 times by the time money was placed on the last square. Working in dollars, with one cent being $0.01, after 63 doubles, there would be: $0.01 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = $0.01 x 263 = $92,233,720,368,547,758.08 ... or over 92 quadrillion dollars. For reference, this is about a thousand times all the money in the world! I suggested she tell her father she'd settle for the 92 quadrillion dollars and he could keep the extra, including the eight cents! He wasn't amused. It wasn't Mildred's fault, of course, as she'd not yet learned about exponents or exponential growth. And now that she knew how sneaky her father was, we imagine she negotiated a much more substantial allowance than a mere $50! |