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Cent mille milliards de poemes


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 
answer but I've had no luck.

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


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.  
  
THEOREM: If Raymond Queneau had published ten Limericks instead of
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/   
    
Associated Topics:
High School Permutations and Combinations

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