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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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Comments: ( Back to comment list | You must be logged in to post comments.)
re: non-computer exploration of parts iii, iv & bonusi | Comment 3 of 5 |
(In reply to non-computer exploration of parts iii, iv & bonusi by Dej Mar)

In parts i and ii, the words must be at least 5 and 4 letters respectively. 

Firstly: my program didn't list words that were as short as the minimum length or the next few possible lengths--only enough to cover the longest and second-longest words, in case the longest were ruled out. Thus, for example, your stuts would beat out empurpled as the last alphabetically in that category.

Second: The 3-letter words are too short.

 


  Posted by Charlie on 2012-02-11 11:31:46
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