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Ascension II (Posted on 2012-02-10) Difficulty: 4 of 5
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    
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Some Thoughts computer assisted parts iii and iv Comment 5 of 5 |

From a modification of my computer program:

In parts iii:a and iv:a start at the bottom of the list and go upward until you reach a word that's acceptably common.  In iii:b and iv:b start at the top and go downward.

part iiia
uvula
wyled
wyted
part iiib
baals
babel
babes
baboo
backs
baddy
badly
part iva
typo
typp
tyre
tyro
uvea
wyle
wynd
wynn
wyte
part ivb
aahs
aals
baal
baas
babe
babu
baby

  Posted by Charlie on 2012-02-12 13:35:48
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