Egg Doubling Problem; UK & US: Naming Large NumbersDate: 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/ |
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