Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Impossible Word


Date: 04/14/2001 at 10:08:51
From: Dustin Babler
Subject: Word Values 

What is a word that comes out to 575,151 when multiplying its letters' 
values together? 

For example, belch = 376,200 (25*22*15*24*19). 

I have come close, but not close enough!

Thank you for your help.
Dustin


Date: 04/16/2001 at 13:46:43
From: Doctor TWE
Subject: Re: Word Values 

Hi Dustin - thanks for writing to Dr. Math.

The first thing I did when I saw this problem was to find the prime 
factorization of 575151 because that would limit the possible letters 
I had to work with. What I found out was that 575151 = 3*191717, and 
191717 is a prime number. (I have a computer program that verified 
that for me.) 

Since there is no 191717th letter in our alphabet, the 
construction must be impossible!

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
Middle School Factoring Numbers
Middle School Puzzles

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/