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### The Value of a Word

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Date: 08/25/98 at 21:10:19
From: Jonathan Gordon
Subject: Advanced prealgebra

Our teacher told us to think of a word that equals to one dollar. The
key was: a=.01, b=.02, c=.03, .... I have brainstormed all night, and
still can't come up with one. Help, please.
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Date: 08/27/98 at 16:56:21
From: Doctor Peterson
Subject: Re: Advanced prealgebra

Hi, Jonathan.

Interesting question - it's not exactly math, but makes you use a lot
of it to come up with an answer. I played with it for a while, and have
a few ideas on how to search for an answer, but when I finally found
two good ones, it wasn't by using any of the techniques I'd thought of!
I just thought of a word, found that it worked, and then tried one it
reminded me of and found that that worked too. I hope I'm late enough
so that you will already have found one.

You can get started easily enough by just trying a few words and
finding some that are about the right size. You should quickly get a
feel for what makes the value of a word larger or smaller - more
letters or higher letters will both increase the value, so that both
YYYY and 100 A's would be worth a dollar (if they were words). Try
adding prefixes or suffixes or other combining forms to make it bigger
(as in "telephone"), or making plurals or past tenses to make smaller
changes (as in "elephants"). The more similar a word is to the last
one you tried, the less work it takes to calculate its value.

Then I would try modifying a promising word by adding small letters
(like an E to increase the value by 5) or replacing letters (like
changing P to T to add 4) to make it closer to the right value. If you
find a word that's near the right value, think about what letters you
could change to make it right - then how you could rearrange those
letters to make a real word.

To have fun with this, I wrote a little computer program so I could
type in any word and see its value. That let me experiment all I wanted
without costing too much time. (I didn't cheat and run a dictionary
through my program, but only because I don't have one I could use that
way.) If you can't do that, I would certainly make a list of the value
of each letter in the alphabet, so I could easily calculate the value
of a word. Any technique that speeds up the process of guessing can
help.

So do you want to know what my words were? I've hidden them somewhere
in my answer.

- Doctor Peterson, The Math Forum
Check out our web site! http://mathforum.org/dr.math/
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Associated Topics:
High School Puzzles
Middle School Puzzles
Middle School Word Problems

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