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### Cent mille milliards de poemes

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Date: 02/12/2000 at 23:55:53
From: Sarah
Subject: Cent mille milliards de poemes

Hello. I have this problem and I've been doing research to find the

The French poet, Raymond Queneau, once published a book entitled _Cent
mille milliards de poemes_, which consisted of a sonnet on each of ten
pages. The claim to fame of this book is that it actually contained
10^14 (ten to the 14th power) poems, which is a really huge number.
How was Queneau able to do this on only ten pages?

Thank you.
Sarah
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Date: 02/13/2000 at 02:45:50
From: Doctor Mike
Subject: Re: Cent mille milliards de poemes

Sarah,

You may have read a poem by Shakespeare that begins "Shall I compare
thee to a summer's day?"  It is a Sonnet, and all sonnets have exactly
14 lines. Monsieur Queneau published a book with 10 sonnets, but each
page was cut into horizontal strips so that one line was on each
strip. By folding back different combinations of strips, one can form
various different sonnets with lines chosen from the original ten. For
instance:

First line is the first line from Queneau's sonnet #1
Second line is the second line from Queneau's sonnet #9
Third line is the third line from Queneau's sonnet #3
Fourth line is the fourth line from Queneau's sonnet #3
Fifth line is the fifth line from Queneau's sonnet #3
Sixth line is the sixth line from Queneau's sonnet #10
...................
14th line is the 14th line from Queneau's sonnet #7

Since there is a total of 10 original sonnets, there are exactly 10
possibilities to choose for each line of your constructed new sonnet.
For each of the 10 choices for line 1, there are 10 choices for line
2. Hence there are 100 (10 squared) choices for the first 2 lines.
For each of the 100 choices for the first 2 lines, there are 10
choices for line 3. Hence there are 1000 (10 cubed) choices for the
first 3 lines.

Since there are 14 lines in a sonnet, there are 10 to the 14th power
different ways to construct the new sonnet. The number "10 to the 14"
is written "100,000,000,000,000" and pronounced (in American English)
as "100 trillion," or "100 thousand billion". The French use "cent"
for 100, "mille" for thousand, and "milliard" for billion, hence the
title for Queneau's publication.

I will close with a Theorem, whose proof is left to the reader; and I
will give the hint that all Limerick poems have exactly five (5)
lines.

ten sonnets, he would have had to call it "Cent mille de poemes."

I hope this clears things up for you.

- Doctor Mike, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Permutations and Combinations

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