# Can You Help Me Figure This Out?

Okay, I  have a math problem.  I’m pretty sure it’s a simple algebraic formula or something, but my right brain is working against my left right now.  It doesn’t help that it is a “Word Problem,” either. 😛

I’m stuck.

Here’s the problem:

Fred buys a Coke on day 1 and for the next 9 days he gives 1 new Coke to someone new.
Each person who receives a Coke from Fred gives a new Coke to someone new each day after receiving one.
Each person who receives a new Coke follows the same pattern.  (Giving a new Coke to someone new each day)
At the end of 10 days (including the day Fred bought his first Coke), all of the leftover Coke cans are gathered together.

How many Coke cans are there in all?

I need the answer and the formula that’s used to figure this out.

## 5 thoughts on “Can You Help Me Figure This Out?”

1. Tim says:

(Sum 2^10)-1=1023 cans on the 10th day. You are searching for the sum of a geometric progression or series.

• Tim, we keep getting 512 (doubling each day)… Approx. half of that. What did I miss?

You genius, you. 🙂

• Tim says:

Johnny, it does double, so that on the tenth day, 512 cans of Coke are distributed; however, don’t forget to ADD the total of all cans for the ten days. Therefore, the series is: 1,2,4,8,16,32,64,128,256,and 512 over the ten days, and the total of all of these added is 1023 (ergo, the sum of 2 to the 10th power less the fact that the first day only had 1 can distributed). BTW, this also has undertones of computing, if you look closely: it’s why we refer to “16GB” of RAM, or “256MB” of storage (old school), since computing is all about binary digits (“bits”) and the geometric doubling of those bits to form banks of memory.

2. “Tim Crowder’s a GENius. Your death therapy cured me, you GENius!” (as sung by Bob in “What About Bob?”) 😀

Thanks Tim! You’ve cured my left brain atrophy!

• Tim says:

My pleasure, my friend. Next time we meet up, we’ll share a can of Coke. 🙂