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### Egg Doubling Problem; UK & US: Naming Large Numbers

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Date: 5/6/96 at 19:39:11
From: Roy Cole
Subject: Egg  doubling problem

Dear Dr. Math,

If you have rectangles that are twenty-three by eighty-nine, you have
one egg. The first time you double you have two eggs. The second time
you have four eggs. The third you have eight. The sixtieth time you
have a lot of eggs!

How many rectangles would they fill if each egg is one unit?

Nightvid
```

```
Date: 10/24/96 at 10:13:17
From: Doctor Lynn
Subject: Re: Egg doubling problem

Hi Roy -

After n doublings, you have 2^n eggs.  On the 60th time you have
2^60 eggs.  As each box holds 23 * 89 = 2097 eggs, the number of
filled boxes is 2^60 divided by 2097.

This can probably be solved analytically, especially since
2097 = 2^11-1, but it is much easier to use a clever computer program
which can handle big numbers.  This shows that in fact
549,795,662,664,209 or 550 million million boxes are filled, with 703
eggs left in another unfilled box.

Which is a lot of egg.

-Doctor Lynn,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```

```
Date: 10/24/96 at 10:22:2
From: Doctor Ken
Subject: Re: Egg doubling problem

Hi Roy-

I just wanted to point out something that might be a little confusing

Doctor Lynn said that there were 550 million million boxes filled, and
you may be wondering why he didn't just say 550 trillion boxes.  Well,
he's from the UK, and they actually have different names for the
numbers over there.  So to him the number 549,795,662,664,209 is about
550 billion, while to Americans it's about 550 trillion.

You can see a more complete discussion on the naming of numbers at

http://mathforum.org/dr.math/problems/large_numbers.html

and at

http://mathforum.org/dr.math/problems/1plus_eleven_zeros.html

-Doctor Ken,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Large Numbers
Elementary Word Problems