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| X-pandigital Words (Posted on 2012-11-07) |
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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.
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Submitted by Dej Mar
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Solution:
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The smallest possible x-pandigital word would be J (10), the tenth letter of Latin/English alphabet and modern slang for joint (cannabis) or Air Jordan shoes. Neither slang term has yet to appear in a major dictionary and letters generally are not considered valid words, thus the smallest x-pandigital words are AT (1|20) and TA (20|1).
The largest x-pandigital word is FETCHING. (6|5|20|3|8|9|14|7).
Other x-pandigital words are:
ACT (1|3|20),
ACTED (1|3|20|5|4),
CAT (3|1|20),
CADET (3|1|4|5|20), and
CENT (3|5|14|20).
The following are zeroless x-pandigital words:
x
1 A
2 AB a muscle of the abdomen
BA variant of baa, the bleat of a sheep
BA (Egyptian mythology) the soul
U (British, informal) [adjective] characteristic of or appropriate to the upper class; [pronoun] variant spelling of 'you'
3 AW interjection used for disappointment or sympathy
BAC (archaic) a broad, flat-bottomed ferryboat
CAB
4 CUD
DAW common black-and-gray Eurasian bird
WAD
5 AWED
COX helmsman, coxswain; act as a coxswain
CUED
DOW (chiefly Scottish) to be able or capable
DUCE a leader or commander, a chief
NEW
WADE
WEN 1. a harmless cyst; 2. variant of wynn
6 DOWF (Scottish, archaic) dull, listless
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