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Sunday, October 16, 2005 

Problem of the Week #4: The Penny Problem

Suppose you put 1 penny in your piggy bank on the first day of the month. On the second day, you put 2 pennies in, 4 pennies on the third day, etc. Each day double the previous day’s amount.
How much would you have saved after 31 days?

Allright.... This is a huge number:

2,147,483,647 pennies
or
21,474,836.47 dollars

I doubled the amount of pennies that were put into the piggy bank up to day 31. Then, I added all of my numbers together to get the total amount of pennies inside the piggy bank.

After 31 days I would haved saved 21,424,836.47 dollars, in pennies that 2,147,483,647 pennies. How I got that was I doubled the amount of the pennies each day to the previous day up to the 31 day. After that I added them all up and got the total number of pennies in the piggy bank.

We got 2,147,483,648 pennies. $21474836.48

2 * x = xPennies

that is the formula we used to find out the solution.

Cursti & Meghan
Period 6

i doubled the number of pennies for eachday and i ended up with
1073741824 Pennies or $10737418.24

if i did that for 31 days i would end up with 2,147,483,647 pennies in dollars that would be $21,474,836.47

Ok I got this I doubled the pennies until day 31 and added up all my numbers.My final answer 2,147,483,648 pennies or $21474836 dollars.I tried to make up a equation but... I hope this is right.

The answer I came up with was $10,737,418.24 or 1,073,741,824 pennies. I multiplied every number [or day] I got by 2 [or doubled it] till I got up to the 31st day. That's a lot of pennies!

Chao!

I went 1+1+2+4+8+16+32, and on till day 31, i double each number and i went all the way till 2,147,483,647 pennies!

Each day I multiplied the previous days # of pennies by 2 untill on the 31 day I had $10,737,418.24 or 1,073,741,824 pennies. Good grief, why would anyone only collect in pennies!?

If i did that for 31 days total i would end up with 2,147,483,647 pennies. That's a lot of money!

2,147,483,648 = how many pennies you would save over 31 days
2 times x=pennies is what i used

2,147,483,648 = how many pennies you would save over 31 days
2 times x=pennies is what i used

2,147,483,648 = how many pennies you would save over 31 days
2 times x=pennies is what i used

At first i got 1073741824 pennies on day 31, but then that would be how many pennies i added to my piggy bank on that day so then i added up all the numbers and i got the biggest number i have ever calculated : 2,757,464,127

The correct answer for this POW is $21,474,836.47. Become a millionare in 1 month!

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