All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 X-pandigital Words (Posted on 2012-11-07)
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.

 See The Solution Submitted by Dej Mar No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solutions | Comment 1 of 3

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))) = 1
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

finds 2120 x-pandigital words for the various values of x.

An abbreviated list (sorted) follows to show shortest and longest, with sufficient margin to allow you to judge whether a given word is "common" enough to be allowed:

With zeroes:

`    lenx wrd num word and numeric value2  2  3 at 1202  2  3 ta 2012  2  4 ut 21202  3  4 bat 21202  3  4 jab 10122  3  4 tab 2012...2  5  9 butut 2212021202  5  9 taluk 2011221112  5  9 vault 2212112202  6  8 albata 112212012  6  8 atabal 120121122  6  8 balata 211212012  6  9 ablaut 1212121202  6 10 atlatl 12012120122  6 10 taluka 20112211112  6 10 valuta 22112212012  7 11 abuttal 122120201122  7 11 bullbat 22112122120`
`3  3  4 act 13203  3  4 cat 31203  3  5 cut 321203  3  5 jaw 101233  3  5 mat 131203  3  5 tam 201133  3  5 taw 20123...3  7 10 catcall 31203112123  7 10 catclaw 31203121233  7 10 cutback 32120213113  7 10 tambala 20113211213  7 11 catwalk 312023112113  7 11 tactual 201320211123  7 12 jumbuck 1021132213113  8 12 backtalk 2131120112113  9 13 blackjack 21213111013113  9 13 matambala 1312011321121`
`4  4  6 cant 3114204  4  6 dawt 4123204  4  6 duct 4213204  4  7 **** 32114204  4  7 want 2311420...4  8 11 amadavat 113141221204  8 12 tamandua 2011311442114  8 13 ambulant 11322112114204  8 14 autumnal 121202113141124  8 14 tantalum 201142011221134  9 14 attackman 12020131113114`
`5  4  6 cent 3514205  4  7 newt 14523205  4  7 went 23514205  4  8 nowt 141523205  4  8 town 201523145  4  8 wont 23151420...5 13 20 nonattendance 141514120205144114355 13 20 unaccountable 211413315211420121255 13 21 mononucleated 1315141514213125120545 13 21 unaccountably 2114133152114201212255 13 23 monocotyledon 131514153152025125415145 14 21 unaccommodated 2114133151313154120545 14 22 nonaccountable 14151413315211420121255 14 23 malcontentedly 13112315142051420541225`
`6  6  8 wafted 231620546  6  9 except 5243516206  6  9 expect 5241653206  6  9 pecten 1653205146  6  9 tamped 2011316546  6  9 temped 2051316546  6 10 exempt 52451316206  6 10 fantom 61142015136  6 10 foment 61513514206  6 10 jumped 10211316546  6 10 tumped 20211316546  6 11 potman 161520131146  6 11 potmen 161520135146  6 11 tampon 201131615146  6 11 tympan 202513161146  6 11 unwept 211423516206  6 12 uptown 211620152314...6 13 19 nonacceptance 14151413351620114356 13 21 bamboozlement 2113215152612513514206 13 21 developmental 4522512151613514201126 13 21 fundamentally 6211441135142011212256 13 22 nonconceptual 14151431514351620211126 13 23 pneumonectomy 161452113151453201513256 13 24 nonemployment 1415145131612152513514206 14 23 uncontemplated 211431514205131612120546 14 24 nondevelopment 1415144522512151613514206 15 25 developmentally 4522512151613514201121225`
`7  9 13 genuflect 75142161253207 10 15 neglectful 1457125320621127 10 16 engulfment 51472112613514207 10 16 zygodactyl 26257154132025127 11 15 genuflected 7514216125320547 12 19 neglectfully 14571253206211212257 12 21 pneumatology 161452113120151215725 (this is the complete list for x=7) `
`8  8 12 fragment 618171351420 8  9 14 pentagram 16514201718113...8 20 30 electroencephalogram 5125320181551435168112157181138 21 31 electroencephalograph 51253201815514351681121571811688 22 33 electroencephalography 5125320181551435168112157181168258 23 34 electroencephalographer 5125320181551435168112157181168518`
`9  8 10 fetching 65203891479  8 14 tromping 201815131691479  9 12 fletching 6125203891479  9 12 refecting 1856532091479  9 13 carpeting 31181652091479  9 13 factoring 61320151891479  9 13 fathoming 61208151391479  9 13 preacting 16185132091479  9 14 fragments 618171351420199  9 14 sceptring 193516201891479  9 14 tampering 201131651891479  9 14 tempering 205131651891479  9 15 frowsting 6181523192091479  9 15 importing 9131615182091479  9 15 permuting 1651813212091479  9 16 promoting 16181513152091479  9 16 prompting 1618151316209147...9 21 30 electrocardiographies 5125320181531184915718116895199 21 30 meningoencephalitides 1351491471551435168112920945199 21 32 antiferromagnetically 114209651818151317145209311212259 21 32 clinicopathologically 312914931516120815121579311212259 21 32 electroencephalograms 512532018155143516811215718113199 21 32 electroretinographies 512532018151852091415718116895199 21 33 overintellectualizing 1522518914205121253202111292691479 21 33 straightforwardnesses 1920181978206151823118414519195199 22 33 electroencephalographs 5125320181551435168112157181168199 23 33 electroencephalographic 5125320181551435168112157181168939 24 35 electrocardiographically 512532018153118491571811689311212259 24 35 electroencephalographies 512532018155143516811215718116895199 24 36 electroencephalographers 512532018155143516811215718116851819`

Without zeroes (using a slightly different program, finding 2420 words in all):

` `
`1  1  1 a 11  2  2 aa 111  2  3 ka 1111  4  6 kaka 111111 (this is the complete list for x=1) 2  2  2 ab 12 2  2  2 ba 212  2  3 al 1122  2  3 la 1212  3  3 aba 1212  3  3 baa 2112  3  4 aal 11122  3  4 ala 11212  3  4 alb 11222  3  4 ava 1221...2  7  9 kabbala 1112211212  7 10 baklava 21111212212  7 12 valvula 2211222211212  8 12 kavakava 1112211112212  8 12 lavalava 121221121221`
`3  2  3 aw 1233  2  4 mu 13213  2  4 um 21133  3  3 cab 3123  3  4 awa 12313  3  4 bam 21133  3  4 caw 31233  3  4 cub 32123  3  4 lac 12133  3  4 vac 22133  3  4 wab 23123  3  5 amu 113213  3  5 awl 123123  3  5 bum 221133  3  5 cum 321133  3  5 cwm 323133  3  5 lam 121133  3  5 law 121233  3  5 maw 131233  3  5 vaw 221233  3  5 waw 231233  3  6 lum 1221133  3  6 mum 1321133  3  6 umm 211313...3  8 10 maccabaw 13133121233  8 11 callback 311212213113  8 14 muckluck 132131112213113  9 12 balaclava 2112131212213  9 13 blackball 21213112112123  9 15 muckamuck 132131111321311`
` `
`4  3  4 cud 32144  3  4 daw 41234  3  4 wad 23144  3  5 awn 123144  3  5 max 131244  3  5 mud 132144  3  5 naw 141234  3  5 wan 231144  3  5 wax 231244  3  5 wud 232144  3  6 mun 132114...4  8 11 backland 213111211444  8 12 labdanum 1212411421134  8 13 duckwalk 42131123112114  8 13 laudanum 12121411421134  9 12 balmacaan 2112131311144  9 13 blackland 2121311121144`
` `
`5  3  5 cox 315245  3  5 dow 415235  3  5 new 145235  3  5 wen 235145  3  6 now 1415235  3  6 own 1523145  3  6 won 2315145  3  6 wyn 232514...5 12 18 cannonballed 3114141514211212545 12 18 downloadable 4152314121514121255 12 19 mollycoddled 13151212253154412545 12 19 nonmalleable 14151413112125121255 13 19 noncancelable 1415143114351212125`
` `
`6  5  7 fancy 61143256  5  7 fumed 62113546  5  7 mazed 13126546  5  7 pawed 16123546  5  8 cozen 315265146  5  8 fawny 612314256  5  8 umped 21131654...6 12 16 backpedalled 21311165411212546 12 17 codependency 315451651445143256 12 19 compoundable 31513161521144121256 12 19 confoundedly 31514615211445412256 12 19 nonflammable 14151461211313121256 12 19 pneumococcal 16145211315315331126 12 19 unconfounded 21143151461521144546 12 20 uncompounded 211431513161521144546 12 20 unemployable 21145131612152512125`
`7  6  8 gawped 712316547  7 10 flagmen 61217135147  7 10 pawnage 16123141757  7 11 pygmean 162571351147  7 12 zymogen 262513157514...7 11 15 camouflaged 3113152161217547 11 18 campanology 311316114151215725`
` `
`8  7 11 grumped 718211316548  7 12 gumdrop 7211341815168  7 13 grownup 71815231421168  7 13 upgrown 21167181523148  8 14 wrongful 23181514762112...8 14 20 encephalograph 514351681121571811688 14 23 overprogrammed 152251816181571811313548 14 23 unprogrammable 211416181571811313121258 14 24 gynandromorphy 7251411441815131518168258 15 22 encephalography 51435168112157181168258 15 22 unchoreographed 21143815185157181168548 15 26 lymphogranuloma 122513168157181142112151318 17 28 neuropharmacology 1452118151681181313151215725`
` `
`9  8 10 grecized 71853926549  8 11 wafering 231651891479  8 11 wheeping 238551691479  8 11 wheezing 238552691479  8 12 cognizer 3157149265189  8 12 forewing 6151852391479  8 12 pouching 1615213891479  8 12 psyching 1619253891479  8 12 whelping 2385121691479  8 12 whoofing 2381515691479  8 12 zorching 2615183891479  8 13 frowning 61815231491479  8 13 impugner 91316217145189  8 13 powering 16152351891479  8 13 whomping 23815131691479  8 13 whooping 23815151691479  8 13 whopping 23815161691479  8 14 gumdrops 721134181516199  8 14 prowling 161815231291479  8 15 grownups 718152314211619...9 18 26 videoconferencings 229451531514651851439147199 18 27 lymphangiographies 1225131681147915718116895199 18 28 neuropharmacologic 14521181516811813131512157939 18 29 neurophysiological 145211815168251991512157931129 18 29 neuropsychological 145211815161925381512157931129 18 29 phenomenologically 168514151351415121579311212259 18 31 uncompromisingness 21143151316181513919914714519199 19 29 overcommercializing 152251831513135183911292691479 19 30 neuropharmacologies 1452118151681181313151215795199 20 31 neuropharmacological 14521181516811813131512157931129 20 33 neurophysiologically 1452118151682519915121579311212259 20 34 uncompromisingnesses 21143151316181513919914714519195199 21 31 phosphoglyceraldehyde 16815191681571225351811245825459 22 33 phosphoglyceraldehydes 168151916815712253518112458254519`

 Posted by Charlie on 2012-11-07 14:53:32

 Search: Search body:
Forums (0)