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 Ascension II (Posted on 2012-02-10)
This is a variation of Ascension.

(i) What is the longest word in the English language having an odd number (2n+1, with n ≥ 2) of letters in which the first n letters (reading left to right) are arranged in alphabetical order and the next n+1 letters are arranged in reverse alphabetical order? How about the longest word with the first n letters (reading left to right) are arranged in reverse alphabetical order and the next n+1 letters are arranged in alphabetical order?

(ii) What is the longest word in the English language having an even number (2n, with n ≥ 2) of letters in which the first n letters (reading left to right) are arranged in alphabetical order and the next n letters are arranged in reverse alphabetical order? How about the longest word with the first n letters (reading left to right) being arranged in reverse alphabetical order and the next n letters being arranged in alphabetical order?

(iii) What is the last word alphabetically that satisfies all the conditions (i)(a) ? What is the first word alphabetically that satisfies all the conditions of (i)(b)?

(iv) What is the last word alphabetically that satisfies all the conditions (ii)(a) ? What is the first word alphabetically that satisfies all the conditions of (ii)(b)?

Bonus Question:

Work out each of (i), (ii), (iii) and (iv) replacing the term "alphabetical order" with "strictly alphabetical order" and replacing "reverse alphabetical order" with "strictly reverse alphabetical order".

Note: Palindromes, proper nouns and abbreviations are not allowed. Also, hyphenated words like A-bomb, X-rays are not permissible.

 No Solution Yet Submitted by K Sengupta No Rating

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 non-computer exploration of parts iii, iv & bonusi | Comment 2 of 5 |
(In reply to computer exploration of parts i and ii by Charlie)

Borrowing from Charlie's extensive and assumedly thourough list to fill in the blanks:

(iii)(a) empurpled - (v.) colored purple
(iii)(b) peccadillos - (n., pl.) slight offenses
(iv)(a) notturni - (n., pl.) musical compositions appropriate for the night or evening
(iv)(b) solfeggios - (n., pl.) vocal exercises using the sol-fa syllables

BONUS:
(i)(a) empurpled
(i)(b) soliloquy - (n.) the act of talking while or as if alone
(ii)(a) any of the following 8-letter words:
acentric, acervuli, acetonic, acetylic, achromic,
agrypnia, befooled, befouled, begulfed, behowled,
belonged, benzylic, biopsied, biosolid, biotypic,
bistroic, censured, censused, centroid, centuple,
chivvied, chortled, chorused, closured, clotured,
costumed, deformed, dehorned, deloused, dioptric,
disyoked, empurple, fortuned, instroke, inturned

(ii)(b) any of the following 8-letter words:
solacers, solecist, solidest, solidity, spiffily,
splicers,  spongily, spongins, tiebacks, tolidins,
trollops, trollopy, unifaces, volcanos

(iii)(a) empurpled
(iii)(b) soliloquy
(iv)(a) inturned - (adj.) curved or turned inward around an axis or fixed point
(iv)(b)
Though listed among the words in Charlie's list for (ii)(b), I found no online dictionary or reference that indicated picachos was an English word. The only references I found indicated it to be a Spanish plural (adjectival) noun meaning "peaks", thus I offer the next word satisfying the conditions:
picadors - (n.) a horseman who pricks the bull in the early stages of bullfighting to goad and weaken it

As inferred from Charlie's comment, the term "strictly" can be interpretted as no repetition of letters of the subset of letters of the word - yet, another interpretation can be that the  order of the letter subset are also alphabetically consecutive in their sequence. From this second interpretation, I offer the following as possible solutions:

(i)(a) abuts - (v.) adjoins, touches or borders on at one end
(i)(b) none found
(ii)(a) any of the following 4-letter words:
abed, abut, efts, hied, hits, nots,
oped, opts, sted, stut, tuba, tuts
(ii)(b) any of the following 4-letter words:
bade, bagh, balm, bars, bast, fers,
jist, onde, post, poxy, vugh
(iii)(a) abuts
(iii)(b) none found
(iv)(a) tuts - (n.; v.; interj.) tut-tut
(iv)(b) bade - (v.) past tense of bid

Edited on February 12, 2012, 2:26 am
 Posted by Dej Mar on 2012-02-11 06:53:53

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