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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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 computer exploration of parts i and ii | Comment 1 of 5

Largest words satisfying parts i and ii:

`part iaaccoutredadjournedbegloomedbemuzzledblossomedcentupledchorussedcistronicempurpled`
`part ibpeccadillospokeberrysolfeggiosoliloquywolfberryzecchinos`
`part iiaabhorredaccessedaccoutreacentricacervuliacetonicacetylicachilleaachromicaffirmedagrypniaairspeedallottedallotteeannulledbeefwoodbefittedbefoggedbefooledbefouledbegulfedbehowledbelongedbemuzzlebentwoodbenzylicbiopsiedbiosolidbiotypicbistroicbottomedcensuredcensusedcentroidcentuplecesspoolchivviedchortledchorusedclosuredcloturedcorypheecostumedcottoneddeerweeddefoggeddeformeddegummeddehorneddelouseddemurreddioptricdisyokedeffulgedempurplefissuredfortunedgossypolinputtedinstrokeinturnedknotweednotturni`
`part iiboddballsoomiackspeccadillopeebeenspicachospicadorspiedfortpleaderspledgorspollacksrollmopsshebeenssheddersskiddersskiddoossledderssmidginssniffilysolacerssolecistsolfeggisolfeggiossolidestsolidityspeedersspeedilyspiffilysplicersspondeesspongilysponginsspoonbillstiebackstobaccostolidinstombackstonicitytreaderstribadestriballytrochilstrollopstrollopyunhallowunifacesunmellowvolcanoswoodbinszecchinozecchins`

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

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