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.

Largest words satisfying parts i and ii:

part ia
accoutred
adjourned
begloomed
bemuzzled
blossomed
centupled
chorussed
cistronic
empurpled

part ib
peccadillos
pokeberry
solfeggio
soliloquy
wolfberry
zecchinos

part iia
abhorred
accessed
accoutre
acentric
acervuli
acetonic
acetylic
achillea
achromic
affirmed
agrypnia
airspeed
allotted
allottee
annulled
beefwood
befitted
befogged
befooled
befouled
begulfed
behowled
belonged
bemuzzle
bentwood
benzylic
biopsied
biosolid
biotypic
bistroic
bottomed
censured
censused
centroid
centuple
cesspool
chivvied
chortled
chorused
closured
clotured
coryphee
costumed
cottoned
deerweed
defogged
deformed
degummed
dehorned
deloused
demurred
dioptric
disyoked
effulged
empurple
fissured
fortuned
gossypol
inputted
instroke
inturned
knotweed
notturni

part iib
oddballs
oomiacks
peccadillo
peebeens
picachos
picadors
piedfort
pleaders
pledgors
pollacks
rollmops
shebeens
shedders
skidders
skiddoos
sledders
smidgins
sniffily
solacers
solecist
solfeggi
solfeggios
solidest
solidity
speeders
speedily
spiffily
splicers
spondees
spongily
spongins
spoonbills
tiebacks
tobaccos
tolidins
tombacks
tonicity
treaders
tribades
tribally
trochils
trollops
trollopy
unhallow
unifaces
unmellow
volcanos
woodbins
zecchino
zecchins

When it comes to the bonus for these two parts, just eliminate words with double letters, except when the double letter is in the middle of even-length words.

Posted by Charlie on 2012-02-11 00:27:31