Bob Crabb Posted December 25, 2007 Share Posted December 25, 2007 file Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted December 25, 2007 Share Posted December 25, 2007 fill Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted December 25, 2007 Author Share Posted December 25, 2007 hill Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 2, 2008 Share Posted January 2, 2008 hall Quote Link to comment Share on other sites More sharing options...
TCH-Vivek Posted January 2, 2008 Share Posted January 2, 2008 halt Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 2, 2008 Share Posted January 2, 2008 hilt Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 2, 2008 Author Share Posted January 2, 2008 tilt Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 2, 2008 Share Posted January 2, 2008 milt Quote Link to comment Share on other sites More sharing options...
TCH-Vivek Posted January 3, 2008 Share Posted January 3, 2008 malt Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 3, 2008 Author Share Posted January 3, 2008 mall Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 3, 2008 Share Posted January 3, 2008 mull Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 3, 2008 Author Share Posted January 3, 2008 pull Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 3, 2008 Share Posted January 3, 2008 hull Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 4, 2008 Author Share Posted January 4, 2008 hall Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 4, 2008 Share Posted January 4, 2008 pall Quote Link to comment Share on other sites More sharing options...
TCH-James Posted January 4, 2008 Share Posted January 4, 2008 pull Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 4, 2008 Share Posted January 4, 2008 full Quote Link to comment Share on other sites More sharing options...
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TCH-Thomas Posted January 4, 2008 Share Posted January 4, 2008 fall Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 4, 2008 Share Posted January 4, 2008 fail Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 4, 2008 Author Share Posted January 4, 2008 hail Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 4, 2008 Share Posted January 4, 2008 mail Quote Link to comment Share on other sites More sharing options...
btrfld Posted January 6, 2008 Share Posted January 6, 2008 rail Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 6, 2008 Share Posted January 6, 2008 bail Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 6, 2008 Share Posted January 6, 2008 (edited) bait  Trivia: In N-Word Space, say in some Unabridged Dictionary what is the answer to the following questions:  1) What is the distribution of letters? Is is sparse or dense? 1a) Related questions: what does the word distribution look like as a function of length of word? 2) Given the answer to 1a - what number of letters would allow the most flexibility with the fewest repeated words for this game? 3) For a given length word (in this game four), can all possible four letters words be gotten to given the rules?  Next post will include these answers - I already have them (from an Unabridged Dictionary I used to use for, well... black hat purposes... in another life. ) These are interesting questions though (to lovers of language and syntax anyway...)  Cheers,  Patrick Edited January 6, 2008 by pagoda Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 6, 2008 Author Share Posted January 6, 2008 wait Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 6, 2008 Share Posted January 6, 2008 (edited) wail  More correctly, I should have said that I have some of the answers, but not all... Those I do have are shown below.  #1) What does the distribution of letters in the Unabridged Dictionary look like?  The Letter a Appears 184697 Times The Letter b Appears 36966 Times The Letter c Appears 96102 Times The Letter d Appears 63378 Times The Letter e Appears 217977 Times The Letter f Appears 21933 Times The Letter g Appears 43713 Times The Letter h Appears 59952 Times The Letter i Appears 188408 Times The Letter j Appears 2717 Times The Letter k Appears 14630 Times The Letter l Appears 121765 Times The Letter m Appears 65693 Times The Letter n Appears 148412 Times The Letter o Appears 159708 Times The Letter p Appears 73194 Times The Letter q Appears 3394 Times The Letter r Appears 149137 Times The Letter s Appears 130612 Times The Letter t Appears 141357 Times The Letter u Appears 81553 Times The Letter v Appears 18515 Times The Letter w Appears 12406 Times The Letter x Appears 6385 Times The Letter y Appears 48375 Times The Letter z Appears 8122 Times  The Total Number of Letter in the Unabridged Dictionary Is: 2099101  #1a) What is the distribution of words in the Unabridged Dictionary as a function of word length?  My Unabridged Dictionary contains 213,583 words. Each individual letter in the English alphabet is considered a "word" even though we don't normally think of all of them in that manner. To be sure, some of them we do (such as "a"), but not the majority of them.  Number of Words of Length [ 1]: 26 Number of Words of Length [ 2]: 61 Number of Words of Length [ 3]: 627 Number of Words of Length [ 4]: 2988 Number of Words of Length [ 5]: 7198 Number of Words of Length [ 6]: 14163 Number of Words of Length [ 7]: 20452 Number of Words of Length [ 8]: 27015 Number of Words of Length [ 9]: 29824 Number of Words of Length [10]: 29220 Number of Words of Length [11]: 25021 Number of Words of Length [12]: 19966 Number of Words of Length [13]: 14683 Number of Words of Length [14]: 9672 Number of Words of Length [15]: 5890 Number of Words of Length [16]: 3363 Number of Words of Length [17]: 1808 Number of Words of Length [18]: 838 Number of Words of Length [19]: 428 Number of Words of Length [20]: 197 Number of Words of Length [21]: 81 Number of Words of Length [22]: 40 Number of Words of Length [23]: 17 Number of Words of Length [24]: 5  This is a near Gaussian distribution. In the context of this Scrabble game, it shows that there are 2,988 possible four letter words.  The question of sparseness or denseness is really more relevant to words than letter. So, how many possible combinations are there for each letter?  For Words of Length 1 There Are: 26 Combinations For Words of Length 2 There Are: 676 Combinations For Words of Length 3 There Are: 17576 Combinations For Words of Length 4 There Are: 456976 Combinations For Words of Length 5 There Are: 11881376 Combinations For Words of Length 6 There Are: 308915776 Combinations For Words of Length 7 There Are: 8031810176 Combinations For Words of Length 8 There Are: 208827064576 Combinations For Words of Length 9 There Are: 5429503678976 Combinations For Words of Length 10 There Are: 141167095653376 Combinations For Words of Length 11 There Are: 3.67034448698778e+15 Combinations For Words of Length 12 There Are: 9.54289566616822e+16 Combinations For Words of Length 13 There Are: 2.48115287320374e+18 Combinations For Words of Length 14 There Are: 6.45099747032972e+19 Combinations For Words of Length 15 There Are: 1.67725934228573e+21 Combinations For Words of Length 16 There Are: 4.36087428994289e+22 Combinations For Words of Length 17 There Are: 1.13382731538515e+24 Combinations For Words of Length 18 There Are: 2.94795102000139e+25 Combinations For Words of Length 19 There Are: 7.66467265200362e+26 Combinations For Words of Length 20 There Are: 1.99281488952094e+28 Combinations For Words of Length 21 There Are: 5.18131871275445e+29 Combinations For Words of Length 22 There Are: 1.34714286531616e+31 Combinations For Words of Length 23 There Are: 3.50257144982201e+32 Combinations For Words of Length 24 There Are: 9.10668576953721e+33 Combinations  In other words, the set of words that we actually use in our language is VERY sparse when compared with the number of possible combinations. Anyone know why this is so? (There is a good argument as to why this is the way things are the way they are with respect to our language. Yes, it's partly that our lexicon cannot contain so many words (we could not remember them all) but it's deeper than just that answer...)  #2) Given the answer in #1a what length of initial word would allow the most flexibility in terms of not repeating words (as has been done many times in the four letter version)?  I don't know the answer since I do not know how sparse the words are in relation to one another. Since the rules of the game allow for the changing of only one letter per turn, we would need to know the word length that has the most densely packed set of words each of which has another word of distance one letter from one another using some path to get to another word (i.e. to go from "tail" to "fail" changes the first letter of the word, so these words differ by one letter, but are not near neighbors in an alphabetical list - thus, they are near in the sense that they differ by one letter.) That said, one would guess that the game would have many more possible answers (i.e. playable words) using words of length 8, 9, 10 or 11. However, the initial word choice would determine the space of possible playable words.  #3) It is sufficient to answer this question by finding an example in which a word or small set of words is self contained - that is, cannot be expanded to create a new word by the changing of one letter. So - is there either a single word or a small cycle of words of length four that cannot be reached given the starting point chosen for this game of Scrabble? I don't know the answer to this either. However, both this problem and the above problem should be solvable, but the answers are not obvious to me right now. You can bet I will keep looking. After all, what better way to waste time...  Cheers,  Pagoda Edited January 6, 2008 by pagoda Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 6, 2008 Author Share Posted January 6, 2008 wall  Patrick, you have way too much time on your hands! Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 7, 2008 Share Posted January 7, 2008 pall  Yup - no argument there...  I'll take that hit and eat it since it is much deserved.  Patrick Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 7, 2008 Share Posted January 7, 2008 poll Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 7, 2008 Share Posted January 7, 2008 poil  (a yarn or thread made from silk, used for ribbon, velvet, and as the core of gold, silver and tinsel yarn) Quote Link to comment Share on other sites More sharing options...
TCH-Vivek Posted January 7, 2008 Share Posted January 7, 2008 soil Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 7, 2008 Share Posted January 7, 2008 boil Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 7, 2008 Author Share Posted January 7, 2008 toil Quote Link to comment Share on other sites More sharing options...
Bob Crabb Posted January 7, 2008 Share Posted January 7, 2008 toll Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 7, 2008 Share Posted January 7, 2008 boll Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 7, 2008 Author Share Posted January 7, 2008 bowl Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 7, 2008 Share Posted January 7, 2008 bawl Quote Link to comment Share on other sites More sharing options...
Bob Crabb Posted January 8, 2008 Share Posted January 8, 2008 ball Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 8, 2008 Author Share Posted January 8, 2008 bell Quote Link to comment Share on other sites More sharing options...
Bob Crabb Posted January 8, 2008 Share Posted January 8, 2008 sell Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 8, 2008 Share Posted January 8, 2008 sill Quote Link to comment Share on other sites More sharing options...
TCH-Vivek Posted January 9, 2008 Share Posted January 9, 2008 silk Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 9, 2008 Share Posted January 9, 2008 bilk Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 9, 2008 Author Share Posted January 9, 2008 balk Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 9, 2008 Share Posted January 9, 2008 talk Quote Link to comment Share on other sites More sharing options...
Bob Crabb Posted January 9, 2008 Share Posted January 9, 2008 tack Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 9, 2008 Author Share Posted January 9, 2008 sack Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 10, 2008 Share Posted January 10, 2008 rack Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 10, 2008 Share Posted January 10, 2008 lack Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 10, 2008 Author Share Posted January 10, 2008 lark Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 10, 2008 Share Posted January 10, 2008 lurk  (What I am not doing so much of these days on the TCH forums ) Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 10, 2008 Author Share Posted January 10, 2008 lure Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 10, 2008 Share Posted January 10, 2008 sure Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 11, 2008 Share Posted January 11, 2008 sire Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 11, 2008 Share Posted January 11, 2008 fire Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 11, 2008 Share Posted January 11, 2008 fare Quote Link to comment Share on other sites More sharing options...
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TCH-Bruce Posted January 12, 2008 Author Share Posted January 12, 2008 fire Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 12, 2008 Share Posted January 12, 2008 file Quote Link to comment Share on other sites More sharing options...
Bob Crabb Posted January 13, 2008 Share Posted January 13, 2008 film Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 13, 2008 Author Share Posted January 13, 2008 fill Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 13, 2008 Share Posted January 13, 2008 till Quote Link to comment Share on other sites More sharing options...
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TCH-Bruce Posted January 14, 2008 Author Share Posted January 14, 2008 kiln Quote Link to comment Share on other sites More sharing options...
Bob Crabb Posted January 14, 2008 Share Posted January 14, 2008 kilt Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 15, 2008 Share Posted January 15, 2008 tilt Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 15, 2008 Author Share Posted January 15, 2008 silt Quote Link to comment Share on other sites More sharing options...
Bob Crabb Posted January 15, 2008 Share Posted January 15, 2008 salt Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 17, 2008 Share Posted January 17, 2008 halt Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 17, 2008 Author Share Posted January 17, 2008 hall Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 18, 2008 Share Posted January 18, 2008 hill Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 19, 2008 Share Posted January 19, 2008 pill Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 19, 2008 Author Share Posted January 19, 2008 pile Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 20, 2008 Share Posted January 20, 2008 pale Quote Link to comment Share on other sites More sharing options...
Bob Crabb Posted January 20, 2008 Share Posted January 20, 2008 sale Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 20, 2008 Author Share Posted January 20, 2008 bale Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 20, 2008 Share Posted January 20, 2008 kale Quote Link to comment Share on other sites More sharing options...
Bob Crabb Posted January 20, 2008 Share Posted January 20, 2008 kyle Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 20, 2008 Author Share Posted January 20, 2008 kyte Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 22, 2008 Share Posted January 22, 2008 kite Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 22, 2008 Author Share Posted January 22, 2008 bite Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 23, 2008 Share Posted January 23, 2008 site Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 23, 2008 Share Posted January 23, 2008 TCH-Thomas said: Â site To which I respond: cite Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 23, 2008 Share Posted January 23, 2008 (I'm not responding to my own post - I just didn't get this edit in fast enough - ignore this post in the context of the game...)  Bruce:  kyte  That a great one! My unabridged dictionary says the following:  kyte: the paunch; stomach; belly  Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 23, 2008 Author Share Posted January 23, 2008 city  (Thanks Patrick ) Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 23, 2008 Share Posted January 23, 2008 pity Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 23, 2008 Author Share Posted January 23, 2008 pits Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 23, 2008 Share Posted January 23, 2008 nits Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 26, 2008 Author Share Posted January 26, 2008 nuts Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 27, 2008 Share Posted January 27, 2008 puts Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 27, 2008 Author Share Posted January 27, 2008 pots Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 27, 2008 Share Posted January 27, 2008 sots  Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 27, 2008 Author Share Posted January 27, 2008 sits Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 27, 2008 Share Posted January 27, 2008 kits Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 27, 2008 Author Share Posted January 27, 2008 kiss Quote Link to comment Share on other sites More sharing options...
pagoda Posted January 27, 2008 Share Posted January 27, 2008 hiss Quote Link to comment Share on other sites More sharing options...
TCH-Thomas Posted January 28, 2008 Share Posted January 28, 2008 miss  (hiss means elevator/lift in swedish) Quote Link to comment Share on other sites More sharing options...
TCH-Bruce Posted January 28, 2008 Author Share Posted January 28, 2008 mist Quote Link to comment Share on other sites More sharing options...
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