Million Point Word PuzzleDate: 05/18/2005 at 11:13:04 From: Stephanie Subject: (no subject) If a = 1, b = 2, ... , z = 26, is there a word that when the values of the letters are multiplied will make a product of one million? For example, BAD = (2)(1)(4) = 8. It is hard for me to think logically of words and numbers together. Date: 05/18/2005 at 11:22:27 From: Doctor Ian Subject: Re: Hi Stephanie, This is a variation on the "dollar word" problem that we hear about every so often: Words Equal to a Dollar http://mathforum.org/library/drmath/view/56834.html With a slight modification to the program there (basically, it has to multiply 1 by the scores for the letters, rather than adding them to zero; and the target score is a million instead of 100), I asked it to look at every word in the dictionary, and found NO words for which the product is a million. There are lots of words where the letters multiply to MORE than a million. But if you're looking for exactly a million, I think someone has sent you on a wild goose chase. In fact, let's stop and think about this for a minute. Suppose we DID find some letters whose product is a million. Since a million is a power of 10, these could ONLY be letters whose prime factors are 2 or 5 or both: 2, 4, 8, 16, 5, 10, 20, 25 b d h p e j t y So those are the only letters we could possilby use. Any OTHER letter would introduce a prime factor that isn't 2 or 5. I think you can tell just by looking at those that there's very little chance that you'd ever be able to find a "million point" word. And perhaps that's the point of the question--for you to figure out WHY you shouldn't expect to find one. On the other hand, if we change things so that a=2, b=3, and so on, it turns out that there _is_ a word that works: http://dictionary.reference.com/search?q=ixodid Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 1/25/2010 at 11:22:27 From: Steve Macke Subject: Re: But there is a word... using just those letters you put up. It is a 5 letter word, not a common word. Those were the hints I received: http://www.merriam-webster.com/dictionary/typey I have been confounded by this problem since high school algebra (20 years ago). My problem was finding a word with 2 y's in it. I found a word jumble solver site too: http://www.zachwordunscrambler.com/ This helped a lot to solve this problem for me. Thanks, Steve |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994-2015 The Math Forum
http://mathforum.org/dr.math/