Impossible WordDate: 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/ |
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