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
re: computer solutions by Dej Mar)
Here's the revised list, where each digit appears only once in each numeric value:
(sequence of each line is x, word length, number length, 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
5 5 6 acted 132054
5 5 6 cadet 314520
9 8 10 fetching 6520389147
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
5 4 5 awed 12354
5 4 5 cued 32154
5 4 5 duce 42135
5 4 5 wade 23145
revised first program (second program--no zeros--similar):
OPEN "\words\words.txt" FOR INPUT AS #1
OPEN "xpandigw.txt" FOR OUTPUT AS #2
DO
INPUT #1, w$
good = 1: n$ = ""
FOR i = 1 TO LEN(w$)
p = INSTR("abcdefghijklmnopqrstuvwxyz", MID$(w$, i, 1))
IF p = 0 THEN good = 0: EXIT FOR
n$ = n$ + LTRIM$(STR$(p))
NEXT
IF good THEN
REDIM used(9)
FOR i = 1 TO LEN(n$)
used(VAL(MID$(n$, i, 1))) = used(VAL(MID$(n$, i, 1))) + 1
IF used(VAL(MID$(n$, i, 1))) > 1 THEN good = 0
NEXT
IF used(0) = 0 THEN good = 0
flag = 1
FOR i = 0 TO 9
IF used(i) = 0 THEN flag = 0
IF used(i) = 1 AND flag = 0 THEN good = 0: EXIT FOR
NEXT
IF good THEN
x = 9
FOR i = 0 TO 9
IF used(i) = 0 THEN x = i - 1: EXIT FOR
NEXT
PRINT w$, x
PRINT #2, USING "# ## ## & &"; x; LEN(w$); LEN(n$); w$; n$
IF LEN(w$) > LEN(longest$) THEN
longlen = LEN(w$)
longxval = x
longest$ = w$
ln$ = n$
END IF
END IF
END IF
LOOP UNTIL EOF(1)
PRINT
PRINT longest$, longlen, longxval, ln$
CLOSE
|
|
Posted by Charlie
on 2012-11-08 09:52:23 |
re(2): computer solutions -- revised complete lists
