Every letter of the alphabet is given a nonzero numerical value which need not be an integer. The value of a word is the product of the values of its letters. For example, if c=2, a=4, and t=3, then "cat" has the value 2*4*3=24.

Suppose that every pair of homophones has equal values (thus, ate=eight, implying a=igh).

Show that every letter of the alphabet has value 1.

(In reply to Homonym verification by David Shin)

I removed the reference to dictionary.com for several reasons. First, dictionary.com is merely a tool that searches many different online dictionaries, and will return multiple pronunciations and/or definitions for any given word. Mainly, though, we have abstained in the past from specifying problem constraints so specifically in the problem text themselves (favoring reference to "common English words," for example, than linking to the online Scrabble dictionary). That not only makes the problem easier to approach just from general knowledge and common sense. Also, problems that link to outside resources, be it a word list, a dictionary, a grid for a problem, even an outside image, are discouraged because then the reliability of this site depends on that of others. Sorry if you missed the discussion on the subject, but for something as generally accepted as word pronunciation, an outside resource is not really needed, particularly one as inconsistent itself as the myriad texts at dicionary.com.

Posted by DJ on 2005-01-19 19:24:47