Suppose A=1, B=2, C=3, ..., Z=26. Then, ETUDE is an interesting word. It has 5 letters, it starts and ends with the 5th letter of the alphabet, and E+T+U+D+E=5+20+21+4+5=55. What other words both start and end with the Xth letter of the alphabet and add up to XX, where X is the number of letters in the word and XX is X concatenated with X? (For ETUDE, X=5.)

In addition to the given noun ETUDE [a short composition featuring a point of technique], the following English words may be considered interesting:

• EXILE (noun) the act of expelling a person from their native land; a person so expelled; (verb) to expel from a country
• ENVIE [obsolete] (verb) to vie; to emulate; to strive
• GASTING [obsolete] present participle of GAST (verb) to terrify or frighten
• GAWPING [chiefly U.K.] present particple of GAWP (verb) to gawk
• GLOMING [archaic spelling of GLOMMING] present partiple of GLOM (verb) to take by theft
• GORGING present particple of GORGE (verb) to consume greedily; to stuff to capacity
• GRIMING present particple of GRIME (verb) to cover with dirt; to soil
• HYACINTH (noun) a bulbous perennial herb with small sweet-smelling flowers; (noun) a red transparent zircon gemstone

The total value of each 'E'-word -- ENVIE, ETUDE, EXILE -- is 55; the total value of each 'G'-word -- GASTING, GAWPING, GLOMING, GORGING and GRIMING -- is 77; and the total value of the 'H'-word -- HYACINTH -- is 88. 

Hypothetically, if at least one vowel is required, the shortest interesting word spelled in the modern English alphabet would be DOUD, DUOD, DYKD or DKYD (none of which is found in any standard English dictionary, though the first two are defined in the web-based Urban Dictionary of slang words). I found no 'F'-words (with total value of 66). And, though several 'I'-words (with a total value of 99) can be found, none are English words. All 'A'-, 'B'- and 'C'- words have "bookend"-letter values that are two small to permit a word value equal to the sum of the letters in the word, and words "bookended" with any letter with a value greater than 9 have a word-letter value too great to be matched with the sum of the letter values.

Posted by Dej Mar on 2011-11-04 14:51:23