The Value of a WordDate: 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/ |
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