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### Stack of Oranges

```
Date: 9 Jan 1995 11:25:34 -0500
From: Bahar Zaker
Subject: (none)

A stack of oranges is compactly arranged so the bottom layer consists
of  oranges in an equilateral triangle with n oranges on a side. The layer
next to the bottom consists of n - 1 oranges on a side. This pattern
continues upward with one orange on the top. How many oranges are
there?

I thought that any amount of oranges would satisfy that, for example,
4,3,2,1, but when I try to picture it,  I guess that's wrong. Any help
would be appreciated.

Thanks,
Bahar Zaker
```

```
Date: 9 Jan 1995 12:41:44 -0500
From: Dr. Ken

Hello there!

I think that all that may be required here is for me to clarify the question
for you.  I was confused about the wording here, too.  When they ask how
many oranges there are, they want the answer in terms of n.  In other words,
come up with and prove a formula that, when given the number (n) of oranges
on one side of the bottom layer, will output the total number of oranges.
Hint: what is 1 + 2 + 3 + ... + n?

I'll let you handle it from here.

-Ken "Dr." Math
```
Associated Topics:
High School Puzzles

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