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Words Equal to a Dollar

Date: 10/11/2001 at 21:55:32
From: Marc
Subject: Words equal to a dollar

I need some help with some one dollar words. You know, if a=1, b=2, 
c=3... z=26.  I would like a list of words that equals 100 (a.k.a. a 
dollar).  

Thank you very much.


Date: 10/12/2001 at 09:33:46
From: Doctor Ian
Subject: Re: Words equal to a dollar

Hi Marc,

The only way a sane person would approach this problem is with a 
computer program. The program would work this way: Start with a word, 
and convert each letter to its corresponding value; add up the values; 
if the sum is 100, print out the word.  

If you run a program like that on the dictionary that comes standard 
with Red Hat Linux, you get the following list:

  abatements acceptors accumulate acknowledge acolytes acquitted
  activates addressing adiabatically adulthood affectation Afghanistan
  airdrops alienation alternated amusedly analysis Anglophobia
  animately annually answerable anterior appertain applying appointed
  apropos archaicness arrests arrivals asbestos atonally attitude
  attunes augments automated Aventino Avernus avocation awfully
  backslashes backtracking Balkanizes bandwagons Bayreuth bedazzles
  bedposts beginnings benediction Berlinize Bernardino bettering
  bewitching bipartite Blackwells blasphemes blissful bolstered
  Bontempo borrowed botanist boulevard boundary boycott bronchus
  Burnett burnished buzzy cannibalized carpenter centipedes cherishing
  chimpanzee choppers chromium clinically clockwise clotting coarsest
  coasters colleagues collecting colonials cometary companion
  congenital congress conjunct Connelly connivance consigns contented
  corridor costumed courses courter cousins coverlet crankiest
  cruising crusts Cubanizes culture Culvers cutout declarative
  decouples decrypted defections deliberates delineating delivery
  demodulate denominate denounces denumerable depletion deploring
  designers destuffs deterring diagonally digestive dinginess
  discernible discipline discredited disjoint disjunct divinely
  dominates doubleheader draftsmen drizzle dualities Edmonton
  electives elephants elsewhere emasculate embodiment emptily encrust
  encumbers Englewood enlivens ensurer envoys equalized espouse
  eventual evolute evolves excavates excellent excerpted explains
  explodes extracted falseness ferments filtering finitely flurry
  forewarn forsaking fountain freshest friendlier generating
  geographer glimpses glittered glorifies godparent governs Granville
  grappling guttered gypsies harmonics healthily Hellenized hemoglobin
  Henrietta highways Hiroshima hitchhikes hobbyist Hollandaise
  Honduras honeycomb honoring hospital hotness humblest hungrier
  identifies immature impaction imported impotence inadequacy
  inapplicable incubating inefficient infernos inferring inflation
  ingrown innately innovate inoculate insecticide intellect Intelsat
  interfaces interfere irritate isolates jostles judiciary Jurassic
  keyboards kissers Koppers Kristin Kronecker landscaping languished
  largeness Latinized liberator lightest lightning likelihood lowlands
  lubricant luckiest Luftwaffe mailboxes maintains Marjory martingale
  matchless maximize McLaughlin measurer Melampus mercantile mercurial
  merrily midpoint Milwaukee minuter mirrored mittens moderates
  molecular Mongolian motors mourns nastily negotiated neoclassic
  nestling nostalgic operetta orients ornament oscillated outlined
  outset overboard pairwise Pakistani Pasteur pasture Paulette
  percents performed permits personage personal perturb piggybacks
  pistachio pitying plastered plebiscite plummet plunging pocketing
  Pollux Portland posting pounding pouring powders practicing
  Precambrian predicates preludes Presley presser prevent primary
  printer probings problems procured producer profiles profuse progeny
  publicly pumpkin pursue pussy putter quadrangle Quantico quarry
  quarter quicklime raincoats receptor reciprocal recompiled
  recreating redesigns Redstone referring refinery refuting regimented
  regressed regroup remedying renovate repress reprint reprobate
  repulsed reputable reschedule researcher resents residues resolved
  responded restore resumes retiring reversal revives rewound
  ridicules rituals riverbank roadster roomful roommate rulings
  runtime sagebrush saintly savory schematics scoreboard Scripps
  sculpted scuttle secreting selective semaphore services session
  settles setups shadowing shakedown sharpens shattered Sheraton
  shibboleth shipyard shivers shooter shovels shrieking sightly
  simulate skewers slenderer slumps smitten smokers snobbery socialism
  Socrates soother sources spenders spirited splashy spooler spouted
  squares squint standards stanzas starfish starling status steamers
  stemming stoves strains strangled straws stress striding striker
  styles subnets subsume sucrose suffocated Sumerian surcharge surely
  Suzanne sweetened swifter swimmer swollen syndicate tabernacles
  Tallahatchie tangents tattooed Taurus telegrams telephone telescope
  temperance temporal tensely therefore thirty thorny threatened
  toilets tolerated towards towers Treadwell trembling triplet Tropez
  tropics truism turkey twisted Tyburn unaltered unavailable unbounded
  unbroken underdone undress unequaled unlinks unmodified unprimed
  unrelated upsets useless utensil variety verbalize Victrola violins
  voyaging washings Watergate weariest Wednesday whenever whirling
  whiskey whisking whistled wholesale wizards wriggles writing Yankton

But suppose you don't want to do that? 

The next best thing would be to come up with a bunch of prefixes and 
suffixes, and figure out the points for those. For example, the suffix 
'ing' is worth 9 + 14 + 7 = 30 points, so if you can come up with 
other words that are worth 70 points, you can stick 'ing' on the end.  

There are lots of common suffixes like this: 'ed', 'er', 'ers', and so 
on. 

There are lots of common prefixes, too:  'un', 're', 'pre', 'inter', 
'con', and so on. 

The idea here is to break down a large problem into smaller problems 
that are more easily solved.  

Another time-honored, real-world technique is to see if someone else 
has already solved your problem - or at least part of your problem.  
For example, if you go to http://www.google.com/    and search on the 
phrase 'dollar words', you'll find sites like 

  Dollar Words - Balmoral Software
  http://www.balmoralsoftware.com/dollar.htm   

which will let you type in a word and will return its value. You may 
be able to find other sites where people have listed words that 
they've come up with.  

But note that strategies like using a computer, or finding someone 
else to do the work for you, suffer from one serious drawback. The 
_point_ of the exercise is to give you a lot of practice adding up 
numbers. So having someone else give you the words, or even add up the 
scores for your guesses, is a little like asking someone else to take 
batting practice for you. It's not going to do you much good. 

I hope this helps. Write back if you'd like to talk about this some 
more, or if you have any other questions. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/   
    

Date: 12/05/2002 at 20:57:52
From: Stephen
Subject: 100 dollar words with a=26

Dr.Math,

     I found a puzzle that asks to find 100 dollar words that have a 
equalling 26, b=25 so on and so forth. I would like to know how many 
possible solutions there are and what they are. 

Thank you very much.

Date: 12/06/2002 at 13:39:52
From: Doctor Ian
Subject: 100 dollar words with a=26

Hi Stephen,

I've generalized the program that I used earlier to allow any mapping at all.
Here is the actual Perl code, which should run just about anywhere with 
trivial changes (e.g., the location of the dictionary):

    #!/usr/local/bin/perl -w

    use strict;

    # Find 'dollar words' with an arbitrary mapping of letters to values.

    #                a   b   c   d   e   f   g   h   i   j   k   l   m
    my @mapping = ( 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14,
                    13, 12, 11, 10,  9,  8,  7,  6,  5,  4,  3,  2,  1 );
    #                n   o   p   q   r   s   t   u   v   w   x   y   z

    open( WORDS, "< /usr/share/dict/words" );

    while( my $word =  ) {
        chomp( $word );
        if ( word_score( $word ) == 100 ) {
            print "$word ";
        }
    }

    close( WORDS );


    sub word_score {
        # Return the score for a given word.

        my $word = lc( shift );           
        $word =~ s/[^a-z]//g;             

        my @chars = split( '', $word );   
        my $score = 0;

        foreach my $c ( @chars ) {
            $score += letter_score( $c );
        }

        return $score;
    }


    sub letter_score {
        # Return the score for a given letter.

        my $letter = shift;
        return $mapping[ ord( $letter ) - ord( 'a' ) ];
    }

When I run this on the dictionary that comes with Mac OS X, I get 
the following list of 'dollar words':

    abaze abbey Abram abrook acca acher acold acrid acronym action actuary
    adati Adonis aftosa agistor agnize Agnostus agoge agrah agroof agrope
    Agrotis agruif Aimak aimful ajava Alexas alimony alumna amaas amatol
    ambar amlong amongst amrita amsath amtman anatomy aneurysm Ankoli
    annuent antitax aplome apolysis apoplex aporose apostasy Arains arche
    ardent Argive arming arnotta arolium arrowroot ascent Asellus asself
    assertum assever asthma asystole Ateles atheous atomize atonic
    atwitter aurorium austere autology averter Avertin avidya axised
    axweed baboo bacon Bajau bakery bakli balas ballot balsa banco barie
    barkey barrer barways basal basify basote bassist Batak batten bauch
    bazzite bebay beboss bedusk befog begat behorn beira belter beman
    bepart bequest berapt bergylt berith besoil betag betrap betters
    bhikku bilge bilic billywix bimasty bingey bismar blissom bobfly
    boltwork bonbon booger bootee bopyrid border bourdon bovinity boxthorn
    boyology brack brehon bromism Brotula bryozoan bucket Buduma bugdom
    bullan bumpee bunkie burled burring bushful busked buttyman Caca
    cahoot caird calumny calves canary canel Canopus carid carolus caseum
    castra catch cation cautel cavish cawquaw ceder cedre centuply cered
    cernuous chain chalk chantry chare charuk cheepy Chera chewer Chian
    china choreus Chouan chough chouser chrome chukar chunter chymify
    citric cittern citydom clamor Clara clawer clean climax Cneorum coater
    codify coenurus coiler collotypy colmar colyone conger conuzee corneum
    cornic corsite cosmic counsel countess courier couscous cowardy cowled
    cowyard Coyotero creed cresset crimsony critic crocin crowing cruller
    crustosis Cucumis culturist cumber cumbre cumular curiously Cursorius
    cushion cuttyhunk cyclar Cygnid Cynara cynology Cynosura Cypseli
    cytopyge cytozoic czarism daric dartrous Datisi daunton dawkin dehull
    demal demast demote dennet detritus devoter diasyrm diatom digitus
    diluter dimmer dinitro dinmont dinnery dipetto diptote Dirca diswood
    disworth dithery doblon dodge dollar domba dossier dotard dotting
    downwith drably draff draggy draper drawstop dromic drunkery ducker
    Ducula dullify dunnish durenol dustbin earthly ebrious ecotype Edgar
    edgrew effuse egghot Elbert elfic elide Elohim eloign embolo emotive
    emulously endyma enquire entirety envelop environs enwisen eponymous
    epopee epulosis erbia erogeny eruptive escarp espial Etamin eternity
    ethenyl euaster Eudeve eulysite euonymin eupnea evisite examen exilic
    existent exostome expressly extrusive facet falter fanam fatuism
    feckly fegary Ferae Fesapo ficary fifie filler Filosa fipenny firetop
    fissive flake flaxen flecky flight flobby floorer fluidly flusher
    fluting fluxile foeish fogyish footstep foppish fopship foresay
    foreuse forever forgrown forkful formazyl formee forrad forsooth
    forthgo Fossores fostell frappe frasco Freddy fretwork friarly fribby
    fruitworm Funkia furiant furiosa galley gallows galosh gamma ganzie
    garish Gaspar geotonus gercrow germen gestion gibel gigful Gileno
    Glitnir glittery Gloria glorious gloryful glossary goober goofily
    gormed Gothic grade grasset grievous gripper Grissel gropple groundly
    grubroot grudge grummel grumness Grusian gummosis gunnies gunsman
    gunyang gustfully hallex halma Hamal hamal hanbury hange harbor
    Hattize haywire hazelly heartly hefter hekteus hemmer hence hennery
    henpen heptal hermitry heroess hestern hickory Hippuris Hirundo hocket
    hogget holder holewort holotype honeywort hookwormy Hoosier hopbush
    hopvine hordary horopito hueless Hughoc humane Humean humorism hurling
    Hurrian hurtfully husking Hyades Hyblan hydrone hydrosol hydrotomy
    hydrula hymnwise hyperoon hyponasty hypospray Iberis Iliad illustre
    image immerd immound impact implume impostrix imposure improver inaja
    inblown incubus incurse infill Ingram inkhorn inkless inmate inoscopy
    insane inspoke insurant intrine invivid iodite Ionian isogamy isospore
    isotypic Jahvist Jaina jassid jawless jessed jocker jocosity jogger
    Johann jointist jollify Jordan jordan Josiah juggle juicily Juletta
    kande kaolin Kartvel kasher Kassak kemple Kerria Khamti kiack kilerg
    kilovolt kinkle kinless kipskin kirimon kirkify kittock knead knotted
    kolinsky konjak koolah krausen kuchen Kuroshio laang lacily lagan
    lagna lamish lammer lampas Lance lance larigo larkspur lassoer lathery
    lazyship legion leisure Lenca Lepomis leprously lewisson ligula liking
    limoid linder Linotype linotype lipase lipothymy lipped lithify loggat
    logman Logria longways loofie lopping lornness lounder lovably lovage
    lovingly loweite loxocosm Lucile lufbery lustrate lutanist luxation
    luxuriously lyomerous lyriform macco Magism magma Mahdi Malope Manatus
    mankin manual margin marlpit marrowsky martlet masted matless maumetry
    Maximon maybush mazzard medal Medize meeten megilp meiosis Menkar
    mercer Mergulus metochy Miaotze millpost mimotype mincer misjoin
    misled mislive mismarry mistless miswrite mitotic Mizraim moistify
    moloker moltenly monkish monology monotic moorburn Moorman moorman
    moquette Morcote mordent moronism mortally Mosaism motherly mottled
    mouthful mugient muirburn Muphrid muteness myoneure myriare myristic
    mysticity naked nakong Nambe naology Naskhi natator nerving netbush
    Nettapus netting neuroses neutrino newsless newsman newsworthy noggen
    nomology nonhero nonstress nonunion nonvinous notably notaeum novelist
    nubbin Numenius Numida Nyamwezi nymphal nymphid oarless oarman
    obliquus octene octuplex Ocypete odontist Oedipus Ogboni ogived Ohioan
    oilskin okonite ominously onsetter oophoron opacity operant Opilia
    opinant organum orgiast oriency orthotropy oscular osmometry osteitis
    ostiate otectomy otoplasty ouenite outflung outgate outname outpaint
    outporch outrooper outscore outsonnet outstreet outtrail outvictor
    overawe overflow overfoot overlap overmount overpast overrule oversee
    overslip oversourly overtoil overwise oviculum ovigerm oysterroot
    palea paletot pandour panisc pannel papacy papyral paraxon parsec
    partite paussid pebbly pedee Peking Pelias Pelusios pentite peoplet
    periplus perjurous permuter peropod perrier pertness phallus Philyra
    phobist Phyllium Physeter physicky phytology phytosaur picaro picker
    Picumnus pietic pietose piggin pilular pinbush pinned pinolin pintano
    pismire pistolet pityroid plague plainly planar plasma plastery
    platurous playpen plumbet plutean plutology podder poduran poisonous
    polarity Polyborus polycotyl polygam Polyodon polyoecy polyprism
    polysomous polyspast pongee poringly portsman possessory posticum
    postoral postward potboil potifer powerful preally premious preopen
    prepink preprint pressful prestore prevoid prewound primsie prioral
    proline pronate propene prorata protean proustite provide psaltery
    Psephurus Psoroptes puddle pulicous pulingly Pullman punctuist
    punitive puriform purpureous puruloid putation pygmoid pyloritis
    pyoureter pyritoid pyrocoll pyrolytic pyronine pyroxonium pyrrolic
    quadra quaestor quartful quartic Quatsino queerer querying quinine
    quinoid quintant quintroon quoilers rache railway rammel Ramona ramsch
    rathely reach realtor rebia rebuke rechew recoat recoil recurse redeye
    reeker reetam refill refloor reflush refuge reinter relator relime
    repick reputed resawer rescuer respoke restrive reswear retame
    reverist reviler revival revivify revuette rewayle rewriter rhinal
    rhizine rhizoid Rhoecus riches rikshaw rimmed rimosely rindle ripping
    Rissian ritling rivage rivality rivingly rizzomed roberd romancy
    rondino roomless Rosales rostrate roughdry roulette roundel rugged
    ruinator rumbler rushbush ruthfully Rutiodon Sabal sabulum sacrist
    saithe salomon saltee saltern samovar sarlak sarpler satang Savara
    sawmill scaff scavel scenery scenist sclere Scorpii scrape screel
    screeny scriptory scrobe scullog scutate sealet secant secpar securer
    sedulous seethe seizing sellie semihot semistory sensuously Serean
    Serena serfism seriously serology serpigo serumal sesame setulose
    Shaker shaker shandry shansa shattery Shaula sheikly shelver shicer
    Shilluh shimal shiplet shoeboy shortish sicca siding sienna signal
    signify silently silicyl Simblum simility Sinology sinuate Sirione
    sixfold skivvies sleekly slewing slifter slimish slipknot slipover
    slipstep slithery slitted slitwise slodge slotting slowpoke slugger
    slugwood smutproof snapper snorting snuffer snuggery somatist somital
    sonorant soothful soulfully southerly spacer Spartan spence spoach
    spoolful sportless spraints sprittie spuilyie spuriae spurling
    squeezer stagworm stairway stammer stance stannery starnel starved
    stelae stepaunt stepwise sternal sternmost stertorous stewpond stibic
    stifler stilted stiltish stimpart stionic stipular stolidly stomata
    stomatous stopping stowbord strangury stremma Strongylus strontia
    struthious stupidity subitem subjee subruler subsect substant
    substruct subsystem success suckler sudoric Suecism sugarer Sulides
    sulphurous superunit supplier surpriser Susanna swearer swingle
    swooning swordlet syconid sylphish syncytia synthete syntomia syringes
    systatic tabic Tagula taimen taking Takitumu talitol talpid talpify
    tamein tankert Tanzine Tarasc tarbush tardily tarnish tarrier tartness
    tartronyl tashie tautotype teachy teaish teamer tearpit teasel teevee
    teioid telesis tellurous temerous tenesmus tenoroon terrine tertiary
    testatory tetterous Teutonist thalli thixotropy thrombus thrummer
    Thursday ticken Timuquan tinkler tinselly tinstone toftman tolling
    tombic tonality tonsured townfolk toxemic treble tribal tribune
    trifoil trinkle triseme trishna trisporous tritorium trophic tropology
    trostera troublous troweler trudgen trumpless truncal tuberin Tullian
    turbine turgidly Turkishly tutorial twaddly twifold twigger twinned
    typhlosis Ulyssean umbones unbase unborne unbreezy uncalk unclose
    unforgot ungotten unhand unharsh unholily unhonest unhumbly unific
    unleaky unmaid unmussed unnuzzled unpetal unplank unpleat unpopulous
    unpromptly unquizzed unrazed unritual unroyally unsettle unsinful
    unsiphon unsmartly unsorted unsquare unstack unstored unstrain
    unsupped unsutured untaxed unthank unthrift untoward unvoice unvulgar
    unwitted unwonted unwotting unyoking uparise upbend upeygan upflood
    upflower upgale upgorge uppermost upplough upraise upspeak upstaff
    upstage uratoma ureide urinator usninic uveitic vapidly vaporary
    vapulary varnishy Vaudism ventless verdurous vibrion vicine villosity
    vinasse virginly virgultum viridity visitee vitrean volage volition
    voluble volutate votation wagwag wairch Wanapum wangle warluck wartime
    waterway waterwort waxberry wayaka wedger whappet whitepot whitetop
    whizgig willies willowwort winged wirepull wiriness wishing wishness
    wombed wrastler wrathily wrongful xenocryst Xiphosurus yeastily
    yellowtop yeomanry Yeshiva Yurucari zaffer zamang zebrule zincuret
    zoccolo Zoharist zooperist zootomic

Note that it makes a difference what dictionary you use!  I ran the 
standard mapping on this dictionary, and here are the first words it 
comes up with:

    abactinally abrogative absinthol acclimation accumulate acenaphthene
    achroous acknowledge acriflavine acromegaly Acronycta acronyx
    actinocarp acuminose acurative acylation adelocodonic ademonist
    adiabatically adipopexia adsessor adulthood adventual aeriality
    aerometer aetosaur affectation affricative Africanist aftercareer

Compare this with the previous list.  For example, this dictionary contains
'abatement' (not a dollar word), but not 'abatements' (a dollar word). 

I hope this helps. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/   
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