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- Xref: bloom-picayune.mit.edu rec.puzzles:18143 news.answers:3074
- Newsgroups: rec.puzzles,news.answers
- Path: bloom-picayune.mit.edu!enterpoop.mit.edu!snorkelwacker.mit.edu!usc!wupost!cs.utexas.edu!uunet!questrel!chris
- From: uunet!questrel!chris (Chris Cole)
- Subject: rec.puzzles FAQ, part 7 of 15
- Message-ID: <puzzles-faq-7_717034101@questrel.com>
- Followup-To: rec.puzzles
- Summary: This posting contains a list of
- Frequently Asked Questions (and their answers).
- It should be read by anyone who wishes to
- post to the rec.puzzles newsgroup.
- Sender: chris@questrel.com (Chris Cole)
- Reply-To: uunet!questrel!faql-comment
- Organization: Questrel, Inc.
- References: <puzzles-faq-1_717034101@questrel.com>
- Date: Mon, 21 Sep 1992 00:09:02 GMT
- Approved: news-answers-request@MIT.Edu
- Expires: Sat, 3 Apr 1993 00:08:21 GMT
- Lines: 1217
-
- Archive-name: puzzles-faq/part07
- Last-modified: 1992/09/20
- Version: 3
-
- ==> english/records/spelling/single.words.s <==
- Word Records from Webster's Third
-
- Spelling
-
- Letter Patterns
-
- Entire Word
- longest word trinitrophenylmethylnitramine (29,1)
- longest palindrome kinnikinnik (11,1)
- longest beginning with a palindrome adinida (7,1)
- longest beginning with b palindrome boob (4,1)
- longest beginning with c palindrome carac civic (5,2)
- longest beginning with d palindrome deified devoved (7,2)
- longest beginning with e palindrome ecce esse (4,2)
- longest beginning with f palindrome f (1,1)
- longest beginning with g palindrome goog (4,1)
- longest beginning with h palindrome hagigah halalah (7,2)
- longest beginning with i palindrome igigi imami (5,2)
- longest beginning with j palindrome j (1,1)
- longest beginning with k palindrome kinnikinnik (11,1)
- longest beginning with l palindrome lemel level lysyl (5,3)
- longest beginning with m palindrome malayalam (9,1)
- longest beginning with n palindrome nauruan (7,1)
- longest beginning with o palindrome oppo otto (4,2)
- longest beginning with p palindrome peeweep (7,1)
- longest beginning with q palindrome qazaq (5,1)
- longest beginning with r palindrome reviver rotator (7,2)
- longest beginning with s palindrome sawbwas seesees seities sememes (7,4)
- longest beginning with t palindrome terret tibbit tippit (6,3)
- longest beginning with u palindrome uku ulu utu (3,3)
- longest beginning with v palindrome vav (3,1)
- longest beginning with w palindrome waw wow (3,2)
- longest beginning with x palindrome x (1,1)
- longest beginning with y palindrome yaray (5,1)
- longest beginning with z palindrome z (1,1)
- longest with middle a palindrome halalah rotator (7,2)
- longest with middle b palindrome sawbwas (7,1)
- longest with middle c palindrome soccos succus (6,2)
- longest with middle d palindrome murdrum (7,1)
- longest with middle e palindrome sememes (7,1)
- longest with middle f palindrome deified (7,1)
- longest with middle g palindrome degged (6,1)
- longest with middle h palindrome aha ihi oho (3,3)
- longest with middle i palindrome hagigah reviver (7,2)
- longest with middle j palindrome kajak (5,1)
- longest with middle k palindrome kinnikinnik (11,1)
- longest with middle l palindrome hallah selles (6,2)
- longest with middle m palindrome sammas (6,1)
- longest with middle n palindrome adinida (7,1)
- longest with middle o palindrome devoved (7,1)
- longest with middle p palindrome tippit (6,1)
- longest with middle q palindrome q (1,1)
- longest with middle r palindrome nauruan (7,1)
- longest with middle s palindrome seesees (7,1)
- longest with middle t palindrome seities (7,1)
- longest with middle u palindrome alula arura (5,2)
- longest with middle v palindrome civic level rever tevet (5,4)
- longest with middle w palindrome peeweep (7,1)
- longest with middle x palindrome sexes (5,1)
- longest with middle y palindrome malayalam (9,1)
- longest with middle z palindrome kazak qazaq (5,2)
- longest tautonym tangantangan (12,1)
- longest beginning with a tautonym akeake atlatl (6,2)
- longest beginning with b tautonym bellabella (10,1)
- longest beginning with c tautonym caracara chowchow couscous (8,3)
- longest beginning with d tautonym dugdug dumdum (6,2)
- longest beginning with e tautonym ee (2,1)
- longest beginning with f tautonym froufrou (8,1)
- longest beginning with g tautonym ganggang greegree guitguit (8,3)
- longest beginning with h tautonym hotshots (8,0) ?
- longest beginning with i tautonym ipilipil (8,1)
- longest beginning with j tautonym juju (4,1)
- longest beginning with k tautonym kavakava kawakawa khuskhus kohekohe kouskous kukukuku (8,6)
- longest beginning with l tautonym lapulapu lavalava lomilomi (8,3)
- longest beginning with m tautonym mahimahi makomako matamata murumuru (8,4)
- longest beginning with n tautonym nagnag (6,1)
- longest beginning with o tautonym oo (2,1)
- longest beginning with p tautonym palapala pioupiou piripiri poroporo (8,4)
- longest beginning with q tautonym quiaquia (8,1)
- longest beginning with r tautonym riroriro (8,1)
- longest beginning with s tautonym sweeswee (8,1)
- longest beginning with t tautonym tangantangan (12,1)
- longest beginning with u tautonym ulaula (6,1)
- longest beginning with v tautonym valval verver (6,2)
- longest beginning with w tautonym wallawalla (10,1)
- longest beginning with x tautonym ? (0,0) ?
- longest beginning with y tautonym yariyari (8,1)
- longest beginning with z tautonym zoozoo (6,1)
- longest head 'n' tail einsteins muckamuck okeydokey overcover pungapung tarantara trinitrin (9,7)
- longest with middle a head 'n' tail muckamuck pungapung (9,2)
- longest with middle b head 'n' tail aba (3,1)
- longest with middle c head 'n' tail overcover (9,1)
- longest with middle d head 'n' tail okeydokey (9,1)
- longest with middle e head 'n' tail arear caeca (5,2)
- longest with middle f head 'n' tail efe ofo (3,2)
- longest with middle g head 'n' tail aggag algal edged magma (5,4)
- longest with middle h head 'n' tail outshouts (9,0) ?
- longest with middle i head 'n' tail trinitrin (9,1)
- longest with middle j head 'n' tail anjan (5,1)
- longest with middle k head 'n' tail arkar kokko (5,2)
- longest with middle l head 'n' tail ingling khalkha (7,2)
- longest with middle m head 'n' tail bamba bombo mamma pampa (5,4)
- longest with middle n head 'n' tail tarantara (9,1)
- longest with middle o head 'n' tail ingoing mesomes (7,2)
- longest with middle p head 'n' tail apa (3,1)
- longest with middle q head 'n' tail q (1,1)
- longest with middle r head 'n' tail adrad kurku ugrug verve (5,4)
- longest with middle s head 'n' tail hotshot (7,1)
- longest with middle t head 'n' tail einsteins (9,1)
- longest with middle u head 'n' tail mauma shush siusi veuve (5,4)
- longest with middle v head 'n' tail ava eve (3,2)
- longest with middle w head 'n' tail abwab (5,1)
- longest with middle x head 'n' tail manxman (7,1)
- longest with middle y head 'n' tail calycal (7,1)
- longest with middle z head 'n' tail z (1,1)
-
- Subset of Word
- longest internal palindrome kinnikinniks sensuousness sensuousnesses (11,3)
- longest internal tautonym anhydrohydroxyprogesterone anhydrohydroxyprogesterones kinnikinnick kinnikinnicks kinnikinnics kinnikinniks magnetophotophoresis methylethylpyridine micromicrofarad neuroneuronal trimethylethylene (10,11)
- longest repeated prefix kinnikinnick kinnikinnicks kinnikinnics kinnikinniks micromicrofarad neuroneuronal (10,6)
- most consecutive doubled letters bookkeeper bookkeeping (3,2)
- most doubled letters possessionlessness possessionlessnesses successlessness successlessnesses (4,4)
- longest two cadence humuhumunukunukuapuaa humuhumunukunukuapuaas (8,2)
- longest three cadence effervescence effervescences extendednesses neglectednesses pervertednesses redheadednesses reflectednesses unexpectednesses vallabhacharya vallabhacharyas (5,10)
- longest four cadence alveolopalatal coproporphyrinuria coproporphyrinurias distributivities gastroschisises humuhumunukunukuapuaa humuhumunukunukuapuaas inevitabilities roentgenometries somesthesises stresslessness stresslessnesses (4,12)
- longest five cadence indecipherablenesses recollectivenesses (4,2)
-
- Letter Counts
-
- Lipograms
- longest letters from first half hamamelidaceae (14,1)
- longest letters from second half nonsupports (11,0) ?
- longest without ab hydroxydesoxycorticosterone (27,1)
- longest without abcd philoprogenitivenesses (22,1)
- longest without a to h supposititiously (16,1)
- longest without a to k monotonously synonymously tumultuously voluptuously (12,4)
- longest without a to n prototropy zoosporous (10,2)
- longest without a to q susurrus (8,1)
- longest without a to s tutty (5,1)
- longest without e humuhumunukunukuapuaas macracanthorhynchiasis phonocardiographically prorhipidoglossomorpha supradiaphragmatically (22,5)
- longest without et humuhumunukunukuapuaas phonocardiographically prorhipidoglossomorpha (22,3)
- longest without eta coccidioidomycosis (18,1)
- longest without etai phyllospondylous (16,1)
- longest without etain chlorophyllous chromosomology chrysochlorous phyllomorphous polymorphously scolopophorous (14,6)
- longest without etains promorphology (13,1)
-
- Letter Choices
-
- Vowels
- longest all vowels aiee ieie (4,2)
- longest each vowel once entwicklungsroman (17,1)
- longest each vowel & y once cylindrocellular phosphuranylites ventriculography (16,3)
- shortest each vowel once eulogia eutocia eutopia isourea sequoia (7,5)
- shortest each vowel & y once oxyuridae (9,1)
- shortest vowels in order caesious (8,1)
- shortest vowels & y in order facetiously (11,1)
- longest vowels in order abstentious (11,1)
- longest vowels & y in order abstemiously (12,1)
- shortest vowels in reverse order muroidea (8,1)
- shortest vowels & y in reverse order ? (80,0) ?
- longest vowels in reverse order subcontinental (14,1)
- longest vowels & y in reverse order ? (0,0) ?
- longest one vowel strengths (9,1)
- longest two vowels schwartzbrots (13,1)
- longest containing a univocalic tathagatagarbhas (16,1)
- longest containing e univocalic strengthlessnesses (18,1)
- longest containing i univocalic instinctivistic (15,1)
- longest containing o univocalic loxolophodonts (14,1)
- longest containing u univocalic struldbrugs (11,1)
- longest containing y univocalic glycyls gypsyfy khlysts khlysty phytyls pyrryls qyrghyz rhythms styryls thymyls tyddyns (7,11)
- longest alternating vowel-consonant hypovitaminosises (17,1)
- longest alternating vowel-consonant excluding y aluminosilicates diketopiperazine epicoracohumeral (16,3)
-
- Consonants
- longest consonant string bergschrund bergschrunds catchphrase eschscholtzia eschscholtzias festschrift festschriften festschrifts goldschmidtine goldschmidtines goldschmidtite goldschmidtites lachsschinken lachsschinkens latchstring mischsprache mischsprachen nachschlag nachschlage nachschlags promptscript veldtschoen weltschmerz weltschmerzes (6,24)
- longest one consonant assessees coccaceae (9,2)
- longest two consonant nauseousnesses sensuousnesses (14,2)
-
- Isograms
- longest isogram dermatoglyphics (15,1)
- longest pair isogram scintillescent (14,1)
- longest trio isogram deeded (6,1)
- longest tetrad isogram kukukuku (8,1)
- longest polygram unprosperousnesses (18,0) ?
- longest pyramid chachalaca deadheaded disseisees evennesses keennesses kinnikinic rememberer sassanians sereneness sleeveless susurruses (10,11)
- most repeated letters dihydroxycholecalciferol hydroxydesoxycorticosterone hysterosalpingographies methyldihydromorphinone microspectrophotometrically octamethylpyrophosphoramide phosphatidylethanolamine pseudohermaphroditism tetrabromophenolphthalein tetraiodophenolphthalein trinitrophenylmethylnitramine (9,11)
- highest containing a repeated palaeacanthocephala tathagatagarbha tathagatagarbhas (6,3)
- highest containing b repeated bubbybush flibbertigibbet flibbertigibbets flibbertigibbety (4,4)
- highest containing c repeated chroococcaceae chroococcaceous circumcrescence circumcrescences echinococcic micrococcaceae (5,6)
- highest containing d repeated condiddled dadded deadheaded dendrodendritic diddered diddled diddledees didodecahedron disbudded dodded doddered doddled driddled dunderheaded dunderheadedness dunderheadednesses dyakisdodecahedral dyakisdodecahedron dyakisdodecahedrons fiddledeedee fiddleheaded granddaddy lepidodendrid lepidodendrids lepidodendroid muddleheaded muddleheadedness muddleheadednesses muddyheaded puddingheaded skedaddled woodshedded (4,32)
- highest containing e repeated ethylenediaminetetraacetate (7,1)
- highest containing f repeated chiffchaff chiffchaffs giffgaff giffgaffed giffgaffing giffgaffs riffraff (4,7)
- highest containing g repeated aggregating aggreging chugalugging gagging gaggling ganggang ganggangs gigging giggling gigglingly glugging goggling grigging grogging guggling lallygagging lollygagging zigzagging (4,18)
- highest containing h repeated ichthyophthiriasis ichthyophthirius ichthyophthiriuses rhamphorhynchid rhamphorhynchids rhamphorhynchoid rhamphorhynchus (4,7)
- highest containing i repeated dirigibilities discriminabilities distinguishabilities divisibilities ignitibilities indiscernibilities indiscerptibilities indistinguishability indivisibility infinitesimalities intelligibilities invincibilities (6,12)
- highest containing j repeated ajonjoli ajonjolis avijja avijjas djokjakarta gastrojejunal gastrojejunostomy hajj hajjes hajji hajjis jajman jajmani jajmans jajoba jejuna jejunal jejune jejunely jejuneness jejunenesses jejunities jejunity jejunostomies jejunostomy jejunum jeremejevite jeremejevites jimberjawed jimjams jinglejangle jinglejangles jinjili jinjilis jipijapa jipijapas jirajara jirajaras jiujitsu jiujitsus jiujutsu jiujutsus jogjakarta jojoba jujitsu jujitsus juju jujube jujubes jujus jujut
-
-
- highest containing k repeated kakkak kakkaks knickknack knickknackatories knickknackatory knickknackeries knickknackery knickknacky kukukuku kukukukus (4,10)
- highest containing l repeated allochlorophyll allochlorophylls alloplastically intellectualistically lillypillies lillypilly polysyllabically (5,7)
- highest containing m repeated dynamometamorphism hamamelidanthemum immunocompromised mammatocumulus mammectomies mammectomy mammiform mammilliform mammogram mammonism mammonisms mesembryanthemum mesembryanthemums meshummadim mohammedanism mohammedanisms muhammadanism muhammadanisms mummiform tetramethylammonium thermometamorphism zamzummim zamzummims (4,23)
- highest containing n repeated inconvenientness inconvenientnesses nannoplankton nannoplanktonic nondenominational nondenominationalism nonentanglement nonintervention noninterventionist syngenesiotransplantation unconvincingness unconvincingnesses (5,12)
- highest containing o repeated monogonoporous pseudomonocotyledonous (6,2)
- highest containing p repeated aplopappus haplopappus hyperleptoprosopic hyperleptoprosopy snippersnapper whippersnapper (4,6)
- highest containing q repeated qaraqalpaq qaraqalpaqs (3,2)
- highest containing r repeated ferriprotoporphyrin ferroprotoporphyrin (5,2)
- highest containing s repeated possessionlessnesses (9,1)
- highest containing t repeated ethylenediaminetetraacetate tetrasubstituted throttlebottom totipotentiality yttrotantalite (5,5)
- highest containing u repeated humuhumunukunukuapuaa humuhumunukunukuapuaas (9,2)
- highest containing v repeated overconservative ovoviviparity ovoviviparous ovoviviparously ovoviviparousness vulvovaginitis (3,6)
- highest containing w repeated bowwow bowwows powwow powwowed powwowing powwows swallowwort whillywhaw whillywhaws whitlowwort williwaw williwaws willowware willowweed willowworm willywaw willywaws (3,17)
- highest containing x repeated dextropropoxyphene executrix executrixes exlex exlexes exonarthex exotoxic exotoxin hexachlorocyclohexane hexahydroxy hexaxon hexoxide hydroxydeoxycorticosterone hydroxydesoxycorticosterone maxixe maxixes myxoxanthin oxyhexactine oxyhexaster paxwax paxwaxes paxywaxies paxywaxy saxifrax saxifraxes saxitoxin sextuplex xanthotoxin xanthoxenite xanthoxenites xanthoxylaceae xanthoxyletin xanthoxyletins xanthoxylin xanthoxylins xanthoxylum xanthoxylums (2,37)
- highest containing y repeated acetylphenylhydrazine acetylphenylhydrazines anhydrohydroxyprogesterone anhydrohydroxyprogesterones brachydactyly chylophylly cryptozygy cystopyelography cytophysiologically cytophysiology dacryocystorhinostomy dactylosymphysis dihydroxyphenylalanine dyssynergy glycolytically gypsyfy gypsyfying hydrodynamically hydronymy hydroxydeoxycorticosterone hydroxydesoxycorticosterone hydroxyethyl hydroxyethylation hydroxyethylations hydroxylysine hydroxymethyl hydroxymethylation
-
-
- highest containing z repeated pizzazz pizzazzes razzmatazz razzmatazzes (4,4)
- most different letters blepharoconjunctivitis pseudolamellibranchiata pseudolamellibranchiate psychogalvanometric (16,4)
- highest ratio length/letters kukukuku (400,1)
- highest ratio length/letters (no tautonyms) senselessnesses (375,1)
- lowest length 16 ratio length/letters ventriculography (106,1)
- lowest length 17 ratio length/letters entwicklungsroman hydrobasaluminite pterygomandibular (113,3)
- lowest length 18 ratio length/letters carboxyhemoglobins entwicklungsromane hyperglobulinemias psychogalvanometer ventriculographies (120,5)
- lowest length 19 ratio length/letters psychogalvanometric (118,1)
- lowest length 20 ratio length/letters brachycephalizations dimethyltubocurarine encephalomyocarditis magnetofluiddynamics moschellandsbergites (133,5)
- lowest length 21 ratio length/letters diphenylthiocarbazone pseudolamellibranchia sphygmomanometrically (140,3)
- lowest length 22 ratio length/letters blepharoconjunctivitis (137,1)
- lowest length 23 ratio length/letters pseudolamellibranchiata pseudolamellibranchiate (143,2)
- lowest length 24 ratio length/letters diphenylaminechlorarsine laryngotracheobronchitis meningoencephalomyelitis (171,3)
- lowest length 25 ratio length/letters spectroheliokinematograph (166,1)
-
- Letter Appearance
- longest narrow letters (ACEMNORSUVWXZ) erroneousnesses verrucosenesses (15,2)
- longest tall letters (BDFGHIJKLPQTY) lighttight lillypilly (10,2)
- longest vertical-symmetry letters (AHIMOTUVWXY) homotaxia thymomata (9,2)
- longest horizontal-symmetry letters (BCDEHIKOX) checkbook checkhook chookchie (9,3)
- highest ratio of dotted letters (IJ) jinjili (71,1)
-
- Typewriter
- longest top row proprietory proterotype rupturewort (11,3)
- longest middle row shakalshas (10,1)
- longest in order wettish (7,1)
- longest in reverse order bourree chapote chappie chappow gouttee (7,5)
- longest left hand tesseradecades (14,0) ?
- longest right hand hypolimnion kinnikinnik (11,2)
- longest alternating hands leucocytozoans (14,1)
- longest one finger deeded humhum hummum muhuhu muumuu (6,5)
- longest adjacent keys assessees redresser redresses seeresses sweeswees (9,5)
-
- Puzzle
- longest formed with chemical symbols nonrepresentationalism (22,1)
- longest formed with US postal codes convallarias (12,1)
- longest formed with compass points newnesses sweeswees (9,2)
- longest formed with piano notes cabbaged fabaceae fagaceae (8,3)
-
- Letter Order
-
- Alphabetical
- longest letters in order aegilops (8,1)
- longest letters in order with repeats aegilops (8,1)
- longest letters in reverse order sponged wronged (7,2)
- longest letters in reverse order with repeats trollied (8,1)
- longest roller-coaster decriminalizations provincializations (18,2)
- longest no letters in place trinitrophenylmethylnitramine (29,1)
- most letters in place abudefduf agammaglobulinemias archencephalon archetypical archetypically syngenesiotransplantation (5,6)
- most letters in place shifted cooperatively daughterlinesses definitivenesses gymnoplast gymnoplasts inoperative inoperativeness inopportunely intraoperatively neighborlinesses operatively postoperatively preoperatively undefendablenesses unoperative unspiritually (6,16)
- most consecutive letters in order consecutively bierstube bierstuben bierstubes gymnopaedia gymnopaedias gymnopaedic gymnopedia gymnopedias gymnophiona gymnoplast gymnoplasts klavierstuck limnopithecus limnoplankton limnoplanktonic overstudy overstuff overstuffed semnopithecus semnopitheque semnopitheques thamnophile thamnophiles thamnophiline thamnophilus thamnophis understudy (4,27)
- most consecutive letters in order aborticide aborticides abscinded absconded abscondence abscondences alimentotherapy aluminographies aluminography aluminotype aluminotypes ambuscade ambuscaded ambuscades helminthosporia helminthosporin helminthosporins helminthosporium helminthosporiums helminthosporoid laminograph laminographic laminographies laminography laminosioptes limnograph limnopithecus limnoplankton limnoplanktonic luminophor luminophors luminoscope opaquers reconstructive reconstructively
-
-
- most consecutive letters appropinquates appropinquations appropinquities equiponderates equiponderations perquisition perquisitions preconquest propinquities quadruplications sesquiterpenoid sesquiterpenoids (8,12)
- highest ratio of consecutive letters to length klompen (85,1)
-
- ==> english/repeat.p <==
- What is a sentence containing the most repeated words, without:
- using quotation marks,
- using proper names,
- using a language other than English,
- anything else distasteful.
-
- ==> english/repeat.s <==
- Five "had"s in a row:
-
- The parents were unable to conceive, so they hired someone else to
- be a surrogate.
-
- The parents had had a surrogate have their child.
-
- The parents had had had their child.
-
- The child had had no breakfast.
-
- The child whose parents had had had had had no breakfast.
-
- ==> english/repeated.words.p <==
- What is a sentence with the same word several times repeated?
-
- ==> english/repeated.words.s <==
- It is true for all that, that that that that that that signifies, is not
- the one to which I refer.
-
- Here are some steps to understanding the entire sentence:
- That is not the one to which I refer.
- That (that that that signifies) is not the one to which I refer.
- That that that that that that signifies, is not the one to which I refer.
-
- In Annamite:
- Ba ba ba ba.
- (Three ladies gave a box on the ear to the favorite of the Prince.)
-
- ==> english/rhyme.p <==
- What English words are hard to rhyme?
-
- "Rhyme is the identity in sound of an accented vowel in a word...and
- of all consonantal and vowel sounds following it; with a difference in
- the sound of the consonant immediately preceding the accented vowel."
- (From The Complete Rhyming Dictionary by Clement Wood). Appropriately
- Wood says a couple of pages later, "If a poet commences, 'October is
- the wildest month' he has estopped himself from any rhyme; since
- "month" has no rhyme in English."
-
- ==> english/rhyme.s <==
- NI3 = Merriam-Webster's Third New International Dictionary
- NI2 = Merriam-Webster's New International Dictionary, Second Edition
- RHD = Random House Unabridged Dictionary
- + means slang, foreign, obsolete, dialectical, etc.
-
- Word Rhyme Assonance
- --------------- --------------------------------------- --------------------
- aitch brache (NI2+), taich (NI2+) naish
- angry unangry (NI2+) aggry
- angst lanx
- beards weirds
- breadth death
- bulb pulp
- carpet charpit
- chimney timne, polymny (NI2+)
- cusp wusp (NI2) bust
- depth stepped
- eighth faith
- else belts
- exit direxit (RHD+) sexist
- fiends teinds, piends
- filched hilched (NI3+), milched (NI2) zilch
- filth spilth, tilth
- fifth drift
- film pilm (NI3+) kiln
- fluxed luxed (NI3+), muxed (NI3+) ducked
- glimpsed rinsed
- gospel hostile
- gulf pulse
- jinxed outminxed (?) blinked
- leashed niched, tweesht (NI2+)
- liquid wicked
- mollusk smallest
- mouthed southed
- month grumph
- mulcts bulks
- mulched gulched (NI3+) bulged
- ninth pint
- oblige bides
- oomph sumph (NI3+)
- orange sporange
- pint jint (NI2+) bind
- poem phloem, proem
- pregnant regnant
- purple curple (NI3+), hirple (NI3+)
- puss schuss
- rhythm smitham
- scalds balds, caulds (NI3+), faulds (NI3+)
- scarce clairce (NI2), hairse (NI2+) cares
- sculpts gulps
- silver chilver (NI3+)
- sixth kicks
- spirit squiret (NI2+)
- tenth nth bent
- tsetse baronetcy, intermezzi, theetsee
- tuft yuft
- twelfth health
- widow kiddo
- width bridge
- window indo, lindo
- wolf bulls
-
- ==> english/self.ref.letters.p <==
- Construct a true sentence of the form: "This sentence contains _ a's, _ b's,
- _ c's, ...," where the numbers filling in the blanks are spelled out.
-
- ==> english/self.ref.letters.s <==
- A little history of the problem, culled from the pages of _Metamagical
- Themas_, Hofstadter's collection of his _Scientific American_ columns.
- First mention of it is in the Jan. '82 column, a followup to one on self-
- referential sentences. Lee Sallows opened the field with a sentence that
- began "Only the fool would take trouble to verify that his sentence was
- composed of ten a's ...." etc.
-
- Then in the addendum to the Jan.'83 column on viral sentences, Hofstadter
- quotes Sallows describing his Pangram Machine, "a clock-driven cascade of
- sixteen Johnson-counters," to tackle the problem. An early success was:
- "This pangram tallies five a's, one b, one c, two d's, twenty-
- eight e's, eight f's, six g's, eight h's, thirteen i's, one j,
- one k, three l's, two m's, eighteen n's, fifteen o's, two p's,
- one q, seven r's, twenty-five s's, twenty-two t's, four u's, four
- v's, nine w's, two x's, four y's, and one z."
-
- Sallows wagered ten guilders that no-one could create a perfect self-
- documenting sentence beginning, "This computer-generated pangram contains
- ...." within ten years.
-
- It was solved very quickly, after Sallows' challenge appeared in Dewdny's
- Oct. '84 SA column. Larry Tesler solved it by a method Hofstadter calls
- "Robinsonizing," which involves starting with an arbitrary set of values
- for each letter, getting the true values when the sentence is made, and
- plugging the new values back in, making a feedback loop. Eventually, you
- can zero in on a set of values that work. Tesler's sentence:
- This computer-generated pangram contains six a's, one b, three
- c's, three d's, thirty-seven e's, six f's, three g's, nine h's,
- twelve i's, one j, one k, two l's, three m's, twenty-two n's,
- thirteen o's, three p's, one q, fourteen r's, twenty-nine s's,
- twenty-four t's, five u's, six v's, seven w's, four x's, five
- y's, and one z.
-
- The method of solution (called "Robinsonizing," after the logician Raphael
- Robinson) is as follows:
- 1) Fix the count of a's.
- 2) Fix the count of b's.
- 3) Fix the count of c's.
- ...
- 26) Fix the count of z's.
- Then, if the sentence is still wrong, go back to step 1.
-
- Most attempts will fall into long loops (what Hofstadter calls attractive
- orbits), but with a good computer program, it's not too hard to find a
- Robinsonizing sequence that zeros in on a fixed set of values.
-
- The February and May 1992 _Word Ways_ have articles on this subject,
- titled "In Quest of a Pangram, (Part 1)" by Lee Sallows. It tells of his
- search for a self-referential pangram of the form, "This pangram
- contains _ a's, ..., and one z." (He built special hardware to search
- for them.) Two such pangrams given in the article are:
-
- This pangram lists four a's, one b, one c, two d's,
- twenty-nine e's, eight f's, three g's, five h's, eleven i's,
- one j, one k, three l's, two m's twenty-two n's, fifteen o's,
- two p's, one q, seven r's, twenty-six s's, nineteen t's, four
- u's, five v's, nine w's, two x's, four y's, and one z.
-
- This pangram contains four a's, one b, two c's, one d, thirty
- e's, six f's, five g's, seven h's, eleven i's, one j, one k,
- two l's, two m's eighteen n's, fifteen o's, two p's, one q,
- five r's, twenty-seven s's, eighteen t's, two u's, seven v's,
- eight w's, two x's, three y's, & one z.
-
- It also contains one in Dutch by Rudy Kousbroek:
-
- Dit pangram bevat vijf a's, twee b's, twee c's, drie d's,
- zesenveertig e's, vijf f's, vier g's, twee h's, vijftien i's,
- vier j's, een k, twee l's, twee m's, zeventien n's, een o,
- twee p's, een q, zeven r's, vierentwintig s's, zestien t's,
- een u, elf v's, acht w's, een x, een y, and zes z's.
-
- References:
- Dewdney, A.K. Scientific American, Oct. 1984, pp 18-22.
- Sallows, L.C.F. Abacus, Vol.2, No.3, Spring 1985, pp 22-40.
- Sallows, L.C.F. Word Ways, Feb. & May 1992
- Hofstadter, D. Scientific American, Jan. 1982, pp 12-17.
-
- ==> english/self.ref.numbers.p <==
- What true sentence has the form: "There are _ 0's, _ 1's, _ 2's, ...,
- in this sentence"?
-
- ==> english/self.ref.numbers.s <==
- There are 1 0's, 7 1's, 3 2's, 2 3's, 1 4's, 1 5's, 1 6's, 2 7's, 1 8's,
- and 1 9's in this sentence.
-
- There are 1 0's, 11 1's, 2 2's, 1 3's, 1 4's, 1 5's, 1 6's, 1 7's, 1 8's
- and 1 9's in this sentence.
-
- ==> english/self.ref.words.p <==
- What sentence describes its own word, syllable and letter count?
-
- ==> english/self.ref.words.s <==
- This sentence contains ten words, eighteen syllables, and sixty-four letters.
-
- ==> english/sentence.p <==
- Find a sentence with words beginning with the letters of the alphabet, in order.
-
- ==> english/sentence.s <==
- After boxes containing dynamite exploded furiously
- generating hellish inferno jet killing laboring miners,
- novice operator, paralyzed, quickly refuses surgical treatment
- until veteran workers x-ray youth zealously.
-
- A big cuddly dog emitted fierce growls happily ignoring joyful kids licking
- minute nuts on pretty queer rotten smelly toadstalls underneath vampires
- who x-rayed young zombies.
-
- ==> english/snowball.p <==
- Construct the longest coherent sentence you can such that the nth
- word is n letters long.
-
- ==> english/snowball.s <==
- I
- do
- not
- know
- where
- family
- doctors
- acquired
- illegibly
- perplexing
- handwriting;
- nevertheless,
- extraordinary
- pharmaceutical
- intellectuality,
- counterbalancing
- indecipherability,
- transcendentalizes
- intercommunications'
- incomprehensibleness.
-
- ==> english/spoonerisms.p <==
- List some exceptional spoonerisms.
-
- ==> english/spoonerisms.s <==
- Original by Spooner himself:
-
- I am afraid you have tasted the whole worm, and must
- therefore take the next town drain.
-
- Some years ago in the Parliament, a certain member known for his quick and
- rapier wit, cut across a certain other member who was trying to make some
- bad joke. He called him a "Shining Wit" then apologized for making a
- Spoonerism.
-
- Another famous broadcast fluff was on the Canadian Broadcasting
- Corporation, which an announcer identified as the "Canadian
- Broadcorping Castration."
-
- Oh yes, another radio announcer one that has sort of crept into
- common English usage is "one swell foop".
-
- A friend of mine had just eaten dinner in the school
- cafeteria, and he didn't look very happy. Another of
- my friends said, "John, what's wrong?" Knowing exactly
- what he was saying, he said, "It's the bound grief I
- had for dinner!"
-
- A radio announcer, talking about a royal visit (or some such) said the
- visitor would be greeted with a "twenty one sun galoot".
-
- There are several fractured fables based on spoonerisms, such as:
-
- A king on a desert island was so beloved by his people, they decided to
- give him a very special gift for the anniversary of his coronation. So
- after much thought, they decided to make him a throne out of seashells,
- which were plentiful on the island. And when it was finished, they
- presented it to the king, who loved it. But he soon discovered it was
- very uncomfortable to sit on. So he told his subjects it was too
- special to use everyday (so as not to hurt their feelings) and put it in
- the attic of his palace (which was, of course, a hut like all the other
- dwellings on the island), planning to use it just for special occasions.
- But that night, it fell through the ceiling of his bedroom and landed
- on top of him, killing him instantly. And the moral of the story is:
- Those who live in grass houses shouldn't stow thrones!
-
- ==> english/states.p <==
- What long words have all bigrams either a postal state code or its reverse?
-
- ==> english/states.s <==
- 10 paramarine
- 10 indentment
- 10 cacocnemia
- 9 amendment
- 9 paramimia
- 9 paramenia
- 9 paralinin
- 9 paralalia
- 9 palilalia
- 9 palapalai
- 8 scalawag
- 8 memorial
-
- Disallowing reversals of state codes the longest common ones are:
-
- 8 malarial
- 7 malaria
- 6 scalar
- 6 marine
- 5 flaky
-
- Terry Donahue
-
- ==> english/telegrams.p <==
- Since telegrams cost by the word, phonetically similar messages can be cheaper.
- See if you can decipher these extreme cases:
-
- UTICA CHANSON MIGRATE INVENTION ANNUAL KNOBBY SORRY IN FACTUAL BEEN CLOVER.
-
- WEED LICHEN ICE CHEST FOREARM OTHER DISGUISE DELIMIT.
-
- CANCEL MYOCARDIA ITS INFORMAL FUNCTION.
-
- YEARN AFFIX, LOST UKASE, UGANDA JAIL, CONSERVE TENURES YACHT APPEAL.
-
- EYELET SHEILA INDIA HOUSE SHEILAS TURKEY.
-
- BOB STILT SEA, CANTANKEROUS BOAT, HUMUS GOAD IMMORTAL DECOS GUARD.
-
- MARY SINBAD SHEER TOURNEY AUGUSTA WIND NOCTURNE TOOTHBRUSH.
-
- WHINE YOSEMITE NAMES SOY CAN PHILATELIST.
-
- ALBEIT DETRACT UNIVERSE EDIFY MUSTAFA TICKET TICKET IN.
-
- ==> english/telegrams.s <==
- These are from an old "Games" magazine:
-
- UTICA CHANSON MIGRATE INVENTION ANNUAL KNOBBY SORRY IN FACTUAL BEEN CLOVER.
- You take a chance on my great invention and you'll not be sorry.
- In fact, you'll be in clover.
-
- WEED LICHEN ICE CHEST FOREARM OTHER DISGUISE DELIMIT.
- We'd like a nice chest for our mother; the sky's the limit.
-
- CANCEL MYOCARDIA ITS INFORMAL FUNCTION.
- Can't sell my ol' car dear; it's in for malfunction.
-
- YEARN AFFIX, LOST UKASE, UGANDA JAIL, CONSERVE TENURES YACHT APPEAL.
- You're in a fix. Lost your case. You goin' to jail.
- Can serve ten years. You ought to appeal.
-
- EYELET SHEILA INDIA HOUSE SHEILAS TURKEY.
- I let Sheila in their house; she lost her key.
-
- BOB STILT SEA, CANTANKEROUS BOAT, HUMUS GOAD IMMORTAL DECOS GUARD.
- Bob's still at sea; can't anchor his boat. You must go to him
- or tell the coast guard.
-
- MARY SINBAD SHEER TOURNEY AUGUSTA WIND NOCTURNE TOOTHBRUSH.
- Mary's in bed; she hurt her knee. A gust of wind
- knocked her into the brush.
-
- WHINE YOSEMITE NAMES SOY CAN PHILATELIST.
- Why don't you (why'n'ya) send me the names, so I can
- fill out a list.
-
- ALBEIT DETRACT UNIVERSE EDIFY MUSTAFA TICKET TICKET IN.
- I'll be at the track and I have a receipt if I must have a ticket to
- get in.
-
- ==> english/trivial.p <==
- Consider the free non-abelian group on the twenty-six letters of the
- alphabet with all relations of the form <word1> = <word2>, where <word1>
- and <word2> are homophones (i.e. they sound alike but are spelled
- differently). Show that every letter is trivial.
-
- For example, be = bee, so e is trivial.
-
- ==> english/trivial.s <==
- be = bee ==> e is trivial;
- ail = ale ==> i is trivial;
- week = weak ==> a is trivial;
- lie = lye ==> y is trivial;
- to = too ==> o is trivial;
- two = to ==> w is trivial;
- hour = our ==> h is trivial;
- faggot = fagot ==> g is trivial;
- bowl = boll ==> l is trivial;
- gell = jel ==> j is trivial;
- you = ewe ==> u is trivial;
- damn = dam ==> n is trivial;
- limb = limn ==> b is trivial;
- bass = base ==> s is trivial;
- cede = seed ==> c is trivial;
- knead = need ==> k is trivial;
- add = ad ==> d is trivial;
- awful = offal ==> f is trivial;
- gram = gramme ==> m is trivial;
- grip = grippe ==> p is trivial;
- cue = queue ==> q is trivial;
- carrel = carol ==> r is trivial;
- butt = but ==> t is trivial;
- lox = locks ==> x is trivial;
- tsar = czar ==> z is trivial;
- vlei = flay ==> v is trivial.
-
- For a related problem, see _The Jimmy's Book_ (_The American Mathematical
- Monthly_, Vol. 93, Num. 8 (Oct. 1986), p. 637):
-
- Consider the free group on twenty-six letters A, ..., Z. Mod out by
- the relation that defines two words to be equivalent if (a) one is a
- permutation of the other and (b) each appears as a legitimate English
- word in the dictionary. Identify the center of this group.
-
- -- clong@remus.rutgers.edu (Chris Long)
-
- ==> english/weird.p <==
- Make a sentence containing only words that violate the "i before e" rule.
-
- ==> english/weird.s <==
- From the May, 1990 _Word Ways_:
-
- That is IE - Or, Is That EI?
-
- by Paul Leopold
- Stockholm, Sweden
-
- "Seeing wherein neither weirdly-veiled sovereign deigned
- agreeing, their feisty heirs, leisurely eyeing eight heinous
- deity-freightened reindeer sleighs, counterfeited spontaneity,
- freeing rein (reveille, neighing!); forfeited obeisance,
- fleeing neighborhood. Kaleidoscopically-veined foreign
- heights being seized, either reigned, sleight surfeited,
- therein; reinvented skein-dyeing; reiteratedly inveighed,
- feigning weighty seismological reinforcement."
-
- The above passage appears in a book on the ecological conservation
- measures of the enlightened plutocracies of antiquity, Ancient
- Financier Aristocracies' Conscientious Scientific Species Policies,
- by Creighton Leigh Peirce and Keith Leiceister Reid. . . .
-
- Any beings decreeing such ogreish, albeit nonpareil,
- homogeneity must be nucleic protein-deficient from sauteing
- pharmacopoeial caffeine and codeine!
-
- From an 'fgrep cie /usr/dict/words', with similiar words removed.
- ancient coefficient concierge conscience conscientious deficient efficient
- financier glacier hacienda Muncie omniscient proficient science
- Societe(?) society species sufficient
-
- A search through Webster's on-line dictionary produced the following exceptions:
-
- Word: *cie*
- Possible matches are:
- 1. -facient 2. abortifacient 3. ancien regime
- 4. ancient 5. ancientry 6. boccie
- 7. cenospecies 8. christian science 9. coefficient
- 10. concierge 11. conscience 12. conscience money
- 13. conscientious 14. conscientious objector15. deficiency
- 16. deficiency disease 17. deficient 18. domestic science
- 19. earth science 20. ecospecies 21. efficiency
- 22. efficiency engineer 23. efficient 24. facies
- 25. fancier 26. financier 27. genospecies
- 28. geoscience 29. glacier 30. glacier theory
- 31. habeas corpus ad subjiciendum32. hacienda 33. inconscient
- 34. inefficiency 35. inefficient 36. insufficience
- 37. insufficiency 38. insufficient 39. international scientific vocabulary
- 40. library science 41. liquefacient 42. mental deficiency
- 43. mutafacient 44. natural science 45. nescience
- 46. omniscience 47. omniscient 48. physical science
- 49. political science 50. precieux 51. prescience
- 52. prescientific 53. prima facie 54. proficiency
- 55. proficient 56. pseudoscience 57. rubefacient
- 58. science 59. science fiction 60. scient
- 61. sciential 62. scientific 63. scientific method
- 64. scientism 65. scientist 66. scientistic
- 67. secret society 68. self-sufficiency 69. self-sufficient
- 70. social science 71. social scientist 72. societal
- 73. society 74. society verse 75. somnifacient
- 76. specie 77. species 78. stupefacient
- 79. sub specie aeternitatis80. subspecies 81. sufficiency
- 82. sufficient 83. sufficient condition 84. superficies
- 85. type species 86. unscientific 87. valenciennes
- 88. vers de societe
-
- ==> english/word.boundaries.p <==
- List some sentences that can be radically altered by changing word boundaries
- and punctuation.
-
- ==> english/word.boundaries.s <==
- Issues topping our mail: manslaughter.
- Is Sue stopping our mailman's laughter?
-
- The real ways I saw it.
- There always is a wit.
-
- You read evil tomes, Tim, at Ed's issue.
- "You're a devil, Tom!" estimated sis Sue.
-
- ==> english/word.torture.p <==
- What is the longest word all of whose contiguous subsequences are words?
-
- ==> english/word.torture.s <==
- This problem was discussed in _Word Ways_ in 1974-5. In August 1974,
- Ralph Beaman, in an article titled "Word Torture", offered the word
- SHADES, from which one obtains HADES, SHADE; ADES, HADE, SHAD; DES, ADE,
- HAD, SHA; ES, DE, AD, HA, SH; S, E, D, A, H. All of these are words
- given in Webster's Third.
-
- Since that time, a serious search has been launched for a seven-letter
- word. The near misses so far are:
- Date Person Word Missing
- Aug 74 Ralph Beaman GAMINES INES, GAMI, NES, INE
- Nov 74 Dmitri Borgmann ABASHED INE, NES, ABASHE, BASHE, ASHE (all in OED)
- May 75 David Robinson GUNITES GU, GUNIT (using Webster's Second)
- May 75 David Robinson ETAMINE ETAMI, TAMI (using Webster's Second)
- May 75 Ralph Beaman MORALES RAL (using Webster's Second)
- Aug 75 Tom Pulliam SHEAVES EAV (using Webster's Second)
-
- Webster's Second has been used for most of the attempts since it
- contains so many more words than Webster's Third. The seven-letter
- plateau remains to be achieved.
-
- ==> games/chess/knight.control.p <==
- How many knights does it take to attack or control the board?
-
- ==> games/chess/knight.control.s <==
- Fourteen knights are required to attack every square:
-
- 1 2 3 4 5 6 7 8
- ___ ___ ___ ___ ___ ___ ___ ___
- h | | | | | | | | |
- --- --- --- --- --- --- --- ---
- g | | | N | N | N | N | | |
- --- --- --- --- --- --- --- ---
- f | | | | | | | | |
- --- --- --- --- --- --- --- ---
- e | | N | N | | | N | N | |
- --- --- --- --- --- --- --- ---
- d | | | | | | | | |
- --- --- --- --- --- --- --- ---
- c | | N | N | N | N | N | N | |
- --- --- --- --- --- --- --- ---
- b | | | | | | | | |
- --- --- --- --- --- --- --- ---
- a | | | | | | | | |
- --- --- --- --- --- --- --- ---
-
- Three knights are needed to attack h1, g2, and a8; two more for b1, a2,
- and b3, and another two for h7, g8, and f7.
-
- The only alternative pattern is:
-
- 1 2 3 4 5 6 7 8
- ___ ___ ___ ___ ___ ___ ___ ___
- h | | | | | | | | |
- --- --- --- --- --- --- --- ---
- g | | | N | | | N | | |
- --- --- --- --- --- --- --- ---
- f | | | N | N | N | N | | |
- --- --- --- --- --- --- --- ---
- e | | | | | | | | |
- --- --- --- --- --- --- --- ---
- d | | | N | N | N | N | | |
- --- --- --- --- --- --- --- ---
- c | | N | N | | | N | N | |
- --- --- --- --- --- --- --- ---
- b | | | | | | | | |
- --- --- --- --- --- --- --- ---
- a | | | | | | | | |
- --- --- --- --- --- --- --- ---
-
- Twelve knights are needed to control (attack or occupy) the board:
-
- 1 2 3 4 5 6 7 8
- ___ ___ ___ ___ ___ ___ ___ ___
- a | | | | | | | | |
- --- --- --- --- --- --- --- ---
- b | | | N | | | | | |
- --- --- --- --- --- --- --- ---
- c | | | N | N | | N | N | |
- --- --- --- --- --- --- --- ---
- d | | | | | | N | | |
- --- --- --- --- --- --- --- ---
- e | | | N | | | | | |
- --- --- --- --- --- --- --- ---
- f | | N | N | | N | N | | |
- --- --- --- --- --- --- --- ---
- g | | | | | | N | | |
- --- --- --- --- --- --- --- ---
- h | | | | | | | | |
- --- --- --- --- --- --- --- ---
-
- Each knight can control at most one of the twelve squares a1, b1, b2,
- h1, g1, g2, a8, b8, b7, h8, g8, g7. This position is unique up to
- reflection.
-
- References
- Martin Gardner, _Mathematical Magic Show_.
-
- ==> games/chess/mutual.check.p <==
- What position is a stalemate for both sides and is reachable in a legal game
- (including the requirement to prevent check)?
-
- ==> games/chess/mutual.check.s <==
- Put the following configuration in one corner:
-
- |
- | x
- | P x
- |B P P
- |K R B
- +---------
-
- ("x" is a Black pawn), and the same with colors reversed in the h8
- corner.
-
- --Noam D. Elkies (elkies@zariski.harvard.edu)
- Dept. of Mathematics, Harvard University
-
- ==> games/chess/mutual.stalemate.p <==
- What's the minimal number of pieces in a legal mutual stalemate?
-
- ==> games/chess/mutual.stalemate.s <==
- 6.
-
- W Kh8 e6 f7 h7 B Kf8 e7
- W Kb1 B Ka3 b2 b3 b4 a4
- W Kf1 B Kh1 Bg1 f2 f3 h2
-
- ==> games/chess/queens.p <==
- How many ways can eight queens be placed so that they control the board?
-
- ==> games/chess/queens.s <==
- 92. The following program uses a backtracking algorithm to count positions:
-
- #include <stdio.h>
-
- static int count = 0;
-
- void try(int row, int left, int right) {
- int poss, place;
- if (row == 0xFF) ++count;
- else {
- poss = ~(row|left|right) & 0xFF;
- while (poss != 0) {
- place = poss & -poss;
- try(row|place, (left|place)<<1, (right|place)>>1);
- poss &= ~place;
- }
- }
- }
-
- void main() {
- try(0,0,0);
- printf("There are %d solutions.\n", count);
- }
- --
- Tony Lezard IS tony@mantis.co.uk OR tony%mantis.co.uk@uknet.ac.uk
- OR EVEN arl10@phx.cam.ac.uk if all else fails.
-
- ==> games/chess/size.of.game.tree.p <==
- How many different positions are there in the game tree of chess?
-
- ==> games/chess/size.of.game.tree.s <==
- Consider the following assignment of bit strings to square states:
-
- Square State Bit String
- ------ ----- --- ------
-
- Empty 0
- White Pawn 100
- Black Pawn 101
- White Rook 11111
- Black Rook 11110
- White Knight 11101
- Black Knight 11100
- White Bishop 11011
- Black Bishop 11010
- White Queen 110011
- Black Queen 110010
- White King 110001
- Black King 110000
-
- Record a position by listing the bit string for each of the 64 squares.
- For a position with all the pieces still on the board, this will take
- 164 bits. As pieces are captured, the number of bits needed goes down.
- As pawns promote, the number of bits go up. For positions where a King
- and Rook are in position to castle if castling is legal, we will need
- a bit to indicate if in fact castling is legal. Same for positions
- where an en-passant capture may be possible. I'm going to ignore these
- on the grounds that a more clever encoding of a position than the one
- that I am proposing could probably save as many bits as I need for these
- considerations, and thus conjecture that 164 bits is enough to encode a
- chess position.
-
- This gives an upper bound of 2^164 positions, or 2.3x10^49 positions.
-
- Jurg Nievergelt, of ETH Zurich, quoted the number 2^70 (or about 10^21) in
- e-mail, and referred to his paper "Information content of chess positions",
- ACM SIGART Newsletter 62, 13-14, April 1977, to be reprinted in "Machine
- Intelligence" (ed Michie), to appear 1990.
-
- Note that this latest estimate, 10^21, is not too intractable:
- 10^7 computers running at 10^7 positions per second could scan those
- in 10^7 seconds, which is less than 6 months.
-
- In fact, suppose there is a winning strategy in chess for white. Suppose
- further that the strategy starts from a strong book opening, proceeds through
- middle game with only moves that DT would pick using the singular
- extension technique, and finally ends in an endgame that DT can analyze
- completely. The book opening might take you ten moves into the game and
- DT has demonstarted its ability to analyze mates-in-20, so how many nodes
- would DT really have to visit? I suggest that by using external storage
- such a optical WORM memory, you could easily build up a transposition
- table for such a midgame. If DT did not find a mate, you could progressively
- expand the width of the search window and add to the table until it did.
- Of course there would be no guarantee of success, but the table built
- would be useful regardless. Also, you could change the book opening and
- add to the table. This project could continue indefinitely until finally
- it must solve the game (possibly using denser and denser storage media as
- technology advances).
-
- What do you think?
-
- -------
-
- I think you are a little bit too optimistic about the feasibility. Solving
- mate-in-19 when the moves are forcing is one thing, but solving mate-in-19
- when the moves are not forcing is another. Of course, human beings are no
- better at the latter task. But to solve the game in the way you described
- would seem to require the ability to handle the latter task. Anyway, we
- cannot really think about doing the sort of thing you described; DT is just a
- poor man's chess machine project (relatively speaking).
- --Hsu
-
- i dont think that you understand the numbers involved.
- the size of the tree is still VERY large compared to all
- the advances that you cite. (speed of DT, size of worms,
- endgame projects, etc) even starting a project will probably
- be a waste of time since the next advance will overtake it
- rather than augment it. (if you start on a journey to the
- stars today, you will be met there by humans)
- ken
-
- ==> games/cigarettes.p <==
- The game of cigarettes is played as follows:
- Two players take turns placing a cigarette on a circular table. The cigarettes
- can be placed upright (on end) or lying flat, but not so that it touches any
- other cigarette on the table. This continues until one person looses by not
- having a valid position on the table to place a cigarette.
-
- Is there a way for either of the players to guarantee a win?
-
- ==> games/cigarettes.s <==
- The first person wins by placing a cigarette at the center of the table,
- and then placing each of his cigarettes in a position symmetric (with
- respect to the center) to the place the second player just moved. If the
- second player could move, then symmetrically, so can the first player.
-
- ==> games/connect.four.p <==
- Is there a winning strategy for Connect Four?
-
- ==> games/connect.four.s <==
- An AI program has solved Connect Four for the standard 7 x 6 board.
- The conclusion: White wins, was confirmed by the brute force check made by
- James D. Allen, which has been published in rec.games.programmer.
-
- The program called VICTOR consists of a pure knowledge-based evaluation
- function which can give three values to a position:
- 1 won by white,
- 0 still unclear.
- -1 at least a draw for Black,
-
- This evaluation function is based on 9 strategic rules concerning the game,
- which all nine have been (mathematically) proven to be correct.
- This means that a claim made about the game-theoretical value of a position
- by VICTOR, is correct, although no search tree is built.
- If the result 1 or -1 is given, the program outputs a set of rules applied,
- indicating the way the result can be achieved.
- This way one evaluation can be used to play the game to the end without any
- extra calculation (unless the position was still unclear, of course).
-
- Using the evaluation function alone, it has been shown that Black can at least
- draw the game on any 6 x (2n) board. VICTOR found an easy strategy for
- these boardsizes, which can be taught to anyone within 5 minutes. Nevertheless,
- this strategy had not been encountered before by any humans, as far as I know.
-
- For 7 x (2n) boards a similar strategy was found, in case White does not
- start the game in the middle column. In these cases Black can therefore at
- least draw the game.
-
- Furthermore, VICTOR needed only to check a few dozen positions to show
- that Black can at least draw the game on the 7 x 4 board.
-
- Evaluation of a position on a 7 x 4 or 7 x 6 board costs between 0.01 and 10
- CPU seconds on a Sun4.
-
- For the 7 x 6 board too many positions were unclear. For that reason a
- combination of Conspiracy-Number Search and Depth First Search was used
- to determine the game-theoretical value. This took several hundreds of hours
- on a Sun4.
-
- The main reason for the large amount of search needed, was the fact that in
- many variations, the win for White was very difficult to achieve.
- This caused many positions to be unclear for the evaluation function.
-
- Using the results of the search, a database will be constructed
- of roughly 500.000 positions with their game-theoretical value.
- Using this datebase, VICTOR can play against humans or other programs,
- winning all the time (playing White). The average move takes less
- than a second of calculation (search in the database or evaluation
- of the position by the evaluation function).
-
- Some variations are given below (columns and rows are numbered as is customary
- in chess):
-
- 1. d1, .. The only winning move.
-
- After 1. .., a1 wins 2. e1. Other second moves for White has not been
- checked yet.
- After 1. .., b1 wins 2. f1. Other second moves for White has not been
- checked yet.
- After 1. .., c1 wins 2. f1. Only 2 g1 has not been checked yet. All other
- second moves for White give Black at least a draw.
- After 1. .., d2 wins 2. d3. All other second moves for White give black
- at least a draw.
-
- A nice example of the difficulty White has to win:
-
- 1. d1, d2
- 2. d3, d4
- 3. d5, b1
- 4. b2!
-
- The first three moves for White are forced, while alternatives at the
- fourth moves of White are not checked yet.
-
- A variation which took much time to check and eventually turned out
- to be at least a draw for Black, was:
-
- 1. d1, c1
- 2. c2?, .. f1 wins, while c2 does not.
- 2. .., c3 Only move which gives Black the draw.
- 3. c4, .. White's best chance.
- 3. .., g1!! Only 3 .., d2 has not been checked completely, while all
- other third moves for Black have been shown to lose.
-
- The project has been described in my 'doctoraalscriptie' (Master thesis)
- which has been supervised by Prof.Dr H.J. van den Herik of the
- Rijksuniversiteit Limburg (The Netherlands).
-
- I will give more details if requested.
-
- Victor Allis.
- Vrije Universiteit van Amsterdam.
- The Netherlands.
- victor@cs.vu.nl
-
- ==> games/craps.p <==
- What are the odds in craps?
-
- ==> games/craps.s <==
- The game of craps:
- There is a person who rolls the two dice, and then there is the house.
- 1) On the first roll, if a 7 or 11 comes up, the roller wins.
- If a 2, 3, or 12 comes up the house wins.
- Anything else is a POINT, and more rolling is necessary, as per rule 2.
- 2) If a POINT appears on the first roll, keep rolling the dice.
- At each roll, if the POINT appears again, the roller wins.
- At each roll, if a 7 comes up, the house wins.
- Keep rolling until the POINT or a 7 comes up.
-
- Then there are the players, and they are allowed to place their bets with
- either the roller or with the house.
-
- -----
- My computations:
-
-
-
-
-
- On the first roll, P.roller.trial(1) = 2/9, and P.house.trial(1) = 1/9.
- Let P(x) stand for the probability of a 4,5,6,8,9,10 appearing.
- Then on the second and onwards rolls, the probability is:
-
- Roller:
- --- (i - 2)
- P.roller.trial(i) = \ P(x) * ((5/6 - P(x)) * P(x)
- (i > 1) /
- ---
- x = 4,5,6,8,9,10
-
- House:
- --- (i - 2)
- P.house.trial(i) = \ P(x) * ((5/6 - P(x)) * 1/6
- (i > 1) /
- ---
- x = 4,5,6,8,9,10
-
- Reasoning (roller): For the roller to win on the ith trial, a POINT
- should have appeared on the first trial (the first P(x) term), and the
- same POINT should appear on the ith trial (the last P(x) term). All the in
- between trials should come up with a number other than 7 or the POINT
- (hence the (5/6 - P(x)) term).
- Similar reasoning holds for the house.
-
- The numbers are:
- P.roller.trial(i) (i > 1) =
-
- (i-1) (i-1) (i-1)
- 1/72 * (27/36) + 2/81 * (26/36) + 25/648 * (25/36)
-
-
- P.house.trial(i) (i > 1) =
-
- (i-1) (i-1) (i-1)
- 2/72 * (27/36) + 3/81 * (26/36) + 30/648 * (25/36)
-
-
- -------------------------------------------------
- The total probability comes to:
- P.roller = 2/9 + (1/18 + 4/45 + 25/198) = 0.4929292929292929..
- P.house = 1/9 + (1/9 + 2/15 + 15/99) = 0.5070707070707070..
-
- which is not even.
- ===========================================================================
-
- ==
- Avinash Chopde (with standard disclaimer)
- abc@unhcs.unh.edu, abc@unh.unh.edu {.....}!uunet!unh!abc
-
- ==> games/crosswords/cryptic/clues.p <==
- What are some clues (indicators) used in cryptics?
-
-