ppp: The Sum of Its Parts (Reader Comments and Addenda)

Joe Robins points out that though "Sadie" is a proper noun and thus slightly imperfect, its anagram "aside" is perfectly valid and thus validly perfect. I've now added that to the list. I was amused to see that another anagram, ideas, was already on the list; clearly I didn't try anagramming most of the words on the list.

Mark Schnitzius wrote a computer program to find all perfect words in an extensive word list that includes many very obscure words. The longest perfect word his program found is "Dayabhaga"; it's defined at a Hindu Web site as "law of inheritance." Note that Mark's list is not complete, because it doesn't include inflected forms of words.

Mark also suggests an elaboration on the perfect-words game: finding words in which the highest letter value is equal to the product, rather than the sum, of the other letter values. Most of the words he turned up consist of some number of As and some number of one other letter, like gag or Anna. (I'd call those "prime words" rather than product-perfect; they contain no "divisors" other than A (1) and the highest-valued letter.) But there are a few gems that don't fit that pattern and are common words. You can look at his list or try to come up with some on your own.

Dan Tilque provides some "trivial" perfect words: aa, BB, ee, and oo.

Jacob Mattison points out that "a lot of the common two-letter groupings are at the end of the alphabet. So you can't [often] use TR, ST, PR, SN, SP, WR, SL," and so on. Dan adds that no perfect word can contain more than two letters in the second half of the alphabet.

(Last updated: 6 August 1999)

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