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### Working Backward

```
Date: 11/30/1999 at 21:04:03
From: Shannon
Subject: Math Riddle

A woman is selling eggs.
She sells 1/2 her eggs and 1/2 an egg to Peter.
Later on, she sells 1/2 her eggs again and 1/2 an egg to John.
Later on, she sells 1/2 her eggs again and 1/2 an egg to Stacey.
Later on, she sells 1/2 her eggs again and 1/2 an egg to Mary.
Later on, she sells 1/2 her eggs again and 1/2 an egg to Jason.
Later on, she sells 1/2 her eggs again and 1/2 an egg to Mark.
Finally the woman is only left with one egg.

How many eggs did she start with, if she never broke an egg in half or
added more eggs after the first purchase?
```

```
Date: 12/02/1999 at 11:24:57
From: Doctor Schwa
Subject: Re: Math Riddle

This is a great problem for working backward.

She is left with one egg. Just before that, she sold 1/2 her eggs and
1/2 an egg to Mark. Therefore how many eggs did she have then? You
could solve the equation

x - (1/2 x + 1/2) = 1

or you could probably figure it out by common sense. Keep working
backward -- you may notice a pattern as you go - and eventually you'll
know how many eggs she had at the beginning.

- Doctor Schwa, The Math Forum
http://mathforum.org/dr.math/
```
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Middle School Puzzles
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