The Value of a Word

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.

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/