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Frequently Asked Questions (FAQS);faqs.463 ==> 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.