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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 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 iiiauvulawyledwyted`
`part iiibbaalsbabelbabesbaboobacksbaddybadly`
`part ivatypotypptyretyrouveawylewyndwynnwyte`
`part ivbaahsaalsbaalbaasbabebabubaby`

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

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