Let us define an x-pandigital word, where A=1,B=2,C=3, etc., as an English word such that the concatenated digits 0 to x of the positional letter-values are used exactly once. In order for a word to be a true x-pandigital word all digits between 0 and x, and only digits 0 to x, must be used exactly once.
What are the shortest and longest x-pandigital words*?

A zeroless x-pandigital word is a word with the same constraints as an x-pandigital word, but excludes the digit 0. What are the shortest and longest zeroless x-pandigital words?

*More than one possible word may exist for both shortest and longest. The length of an x-pandigital word can be less or equal to length x. As such, an x-pandigital word that uses more digits is considered longer for words otherwise of the same length.
You may provide as many x-pandigital words you find, even those that are neither the smallest or largest. An example of an x-pandigital word where x=5 is CENT {C=3, E=5, N=14, T=20}. The concatenated value of CENT is 351420, composed of the digits (not numbers) 0 thru 5.

(In reply to computer solutions by Charlie)

I'm impressed as to the expanse of your dictionary, yet your list found more than x-pandigital words as defined:
"In order for a word to be a true x-pandigital word all digits between 0 and x, and only digits 0 to x, must be used exactly once."
The list should be much, much smaller, as each digit is to be used only once in each word.

From your list, only the following are true x-pandigital words:
    len
x wrd num word and numeric value
2  2   3  at   120
2  2   3  ta   201
3  3   4  act  1320
3  3   4  cat  3120
5  4   6  cent 351420

From your list, only the following are true zeroless x-pandigital words:
    len
x wrd num word and numeric value
1  1   1  a    1
2  2   2  ab   12
2  2   2  ba   21
3  2   3  aw   123
3  3   3  cab  312
4  3   4  cud  3214
4  3   4  daw  4123
4  3   4  wad  2314
5  3   5  cox  31524
5  3   5  dow  41523
5  3   5  new  14523
5  3   5  wen  23514

There is at least one longer valid true x-pandigital word.
As to the zeroless true x-pandigital words, there is one longer word. Though it is found in a modern dictionary, it is considered Scottish, archaic, thus some would argue as to its validity. 

Edited on November 8, 2012, 4:41 am

Posted by Dej Mar on 2012-11-08 01:25:56