Egg Doubling Problem; UK & US: Naming Large Numbers

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 
in the answer you just received from us.  

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/