What is the full representation of Godel's G in TNT (Typographical Number Theory)?
85527
I "Googled" for it but couldn't find where anyone had actually written it all out and posted it.  This seems to come close:\n\nAN ALGEBRAIC EQUATION FOR THE HALTING PROBABILITY\nhttp://www.cs.auckland.ac.nz/CDMTCS/chaitin/berlin.pdf\n\n"The result is an exponential Diophantine equation with the parameter n and the property that it has infinitely many solutions if and only if the nth bit of Ω is a 1."\n\n"It takes the compiler only a few minutes to convert the 300-line Lisp interpreter into a 200-page 17,000-variable universal exponential Diophantine equation."
176413
Great puzzle, took me awhile to make it to f=1, g=4. The letters are from a-i: 9,8,7,2,6,1,4,5,3.\n\nPlugged in this is: (9 * 87 + 2/6) / (14 + 5/3) or (783 + 1/3) / (15 + 2/3) which equals 50.\n\nAnswer logged Sunday, March 12th, 3:20 pm with no other valid answers yet. Sorry to have to write that, but I've seen people change their answers too many times in the past.
752902
-\nglyf - Glyf Data\n\nThis table contains information that describes the glyphs in the font in the TrueType outline format. Information regarding the rasterizer (scaler) refers to the TrueType rasterizer.\n\nEach glyph begins with the following header:\n\nType Name Description\nSHORT numberOfContours If the number of contours is greater than or equal to zero, this is a single glyph; if negative, this is a composite glyph.\nSHORT xMin Minimum x for coordinate data.\nSHORT yMin Minimum y for coordinate data.\nSHORT xMax Maximum x for coordinate data.\nSHORT yMax Maximum y for coordinate data.\n\nNote that the bounding rectangle from each character is defined as the rectangle with a lower left corner of (xMin, yMin) and an upper right corner of (xMax, yMax).\n\nNote: The scaler will perform better if the glyph coordinates have been created such that the xMin is equal to the lsb. For example, if the lsb is 123, then xMin for the glyph should be 123. If the lsb is -12 then the xMin should be -12. If the lsb is 0 then xMin is 0. If all glyphs are done like this, set bit 1 of flags field in the 'head' table.\n\n\nSimple Glyph Description\n\nThis is the table information needed if numberOfContours is greater than zero, that is, a glyph is not a composite.\n\nType Name Description\nUSHORT endPtsOfContours[n] Array of last points of each contour; n is the number of contours.\nUSHORT instructionLength Total number of bytes for instructions.\nBYTE instructions[n] Array of instructions for each glyph; n is the number of instructions.\nBYTE flags[n] Array of flags for each coordinate in outline; n is the number of flags.\nBYTE or SHORT xCoordinates[ ] First coordinates relative to (0,0); others are relative to previous point.\nBYTE or SHORT yCoordinates[ ] First coordinates relative to (0,0); others are relative to previous point.\n\nNote: In the glyf table, the position of a point is not stored in absolute terms but as a vector relative to the previous point. The delta-x and delta-y vectors represent these (often small) changes in position.\n\nEach flag is a single byte. Their meanings are shown below.\n\nFlags Bit Description\nOn Curve 0 If set, the point is on the curve; otherwise, it is off the curve.\nx-Short Vector 1 If set, the corresponding x-coordinate is 1 byte long. If not set, 2 bytes.\ny-Short Vector 2 If set, the corresponding y-coordinate is 1 byte long. If not set, 2 bytes.\nRepeat 3 If set, the next byte specifies the number of additional times this set of flags is to be repeated. In this way, the number of flags listed can be smaller than the number of points in a character.\nThis x is same\n(Positive x-Short Vector) 4 This flag has two meanings, depending on how the x-Short Vector flag is set. If x-Short Vector is set, this bit describes the sign of the value, with 1 equalling positive and 0 negative. If the x-Short Vector bit is not set and this bit is set, then the current x-coordinate is the same as the previous x-coordinate. If the x-Short Vector bit is not set and this bit is also not set, the current x-coordinate is a signed 16-bit delta vector.\nThis y is same\n(Positive y-Short Vector) 5 This flag has two meanings, depending on how the y-Short Vector flag is set. If y-Short Vector is set, this bit describes the sign of the value, with 1 equalling positive and 0 negative. If the y-Short Vector bit is not set and this bit is set, then the current y-coordinate is the same as the previous y-coordinate. If the y-Short Vector bit is not set and this bit is also not set, the current y-coordinate is a signed 16-bit delta vector.\nReserved 6 This bit is reserved. Set it to zero.\nReserved 7 This bit is reserved. Set it to zero.\n\n----------------\n\nThe 'loca' table stores the offsets to the locations of the glyphs in the font relative to the beginning of the 'glyf' table. Its purpose is to provide quick access to the data for a particular character. For example, in the standard Macintosh glyph or
774675
the code for the prg is\n\nmain()\n{\nint no1,no2,min,max,i;\nscanf("%d %d", &no1,&no2);\nif (no1<no2)\n{\nmin=no1;\nmax=no2;\n}\nelse\n{\nmin=no2;\nmax=no1;\n}\n\nfor(i=min;i<=max;i++)\nprintf ("%d&#92;n",i);\n\n}
378294
http://www.maa.org/mathland/mathtrek_11_27_00.html
225834
Here it is check it out ...\n\nhttp://www.gnttype.org/
803702
Check out this web page: http://mathworld.wolfram.com/Net.html
997626
http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP?Res=150\n\nhttp://www.math.sfu.ca/~cbm/aands/subj.htm\n\nhttp://clusterfie.epn.edu.ec/ibernal/html/CURSOS/AbrilAgosto06/Metodos/Libros/Fundamentals%20Of%20Numerical%20Computing%20-%201997%20-Wiley%20%20(By%20Laxxuss).pdf
847707
Those who said googolplex are WAY, WAY off.\nThe largest number ever seriously used in a mathematical proof (and thus has its own name) is Graham's number, which is far, far bigger than a googolplex.\nMoser's number and Skewes' number are also bigger than a googolplex, although not nearly as big as Graham's.\n\nhttp://en.wikipedia.org/wiki/Graham%27s_number\n\nIts value is 3  ↑^g(63) 3.  (You will need to read the article if you dont understand this notation.  It is so large that it cannot even be written in scientific notation!)\n\nOf course, as there is no largest number, there probably will come a time when an even bigger number is named.
722679
60\n\nThe Babylonian sexagesimal number system, all Pythagorean triples have the property that the product of the 3 sides is a multiple of 60. I lived at a house which was no 60 in its street. And I am now 60.
406697
Googolplex is the number .\n\nIt can also be written as 10googol, or as a 1 followed by a googol (10 to the 100th power) zeroes. Note that  is the same as  because exponentiation works from the top down. The term googol was coined by Milton Sirotta, nephew of mathematician Edward Kasner. Googolplex was coined by Kasner to define an especially large number by extension from his nephew's idea.
1071520
there are formatting standards (no dashes, use spaces to separate numbers)\n\na good summary is here:\nhttp://www.geocities.com/dtmcbride/reference/tel-fmt.html
467967
this is probably not a perfect answer but this site may give you some clues.\n\nhttp://www.gomath.com/Questions/question.php?question=4751\n\naltrnatively type 'prove v*v = 2gr*r/s+v0*v0-2gr' into a search engine and see what comes up.
679205
GD is a full featured graphics library written in C\n\nhttp://www.boutell.com/gd/
856921
There are precisely three answers:\nABCDEFGHJ\n267835149\n267953148\n678413259\n\n(slightly offtopic, how can you spend 30 minutes on a question that was asked 8 minutes before you answered ;) Just kidding.)\n\nTry each one and check that it works :) Unless you didn't mean  F(G*H) as F*(G*H), and meant the digit F followed by the answer G*H.. in which case I'll try solving it again. If you did mean it like that, there is indeed a unique answer:\n\n589736142\n\nAhha, third question change. Now it becomes 256973148.
409909
Symbols: LIHRY,FCX,GLG AND GG.
797722
AARGHHH!!  I withdraw my earlier attempt.  It must be dementia, I'm afraid.  It's still asking about 1000! (1000 factorial), of course, but a careful accounting is needed, not only of the effect of all numbers ending in: \n\nA. 1, 2, 3, ... 9 (I did this by a variety of ways, always coming up with a final non-zero digit of 6 for the product of all such sets), \n\nbut also of the following two other types of number, which I regrettably neglected the first time around:\n\nB. 10, 20, 30 ...90 (as often as sets of numbers like that occur), and finally, of types:\n\nC. 100, 200, 300, ... 900 (this set occurs but once).  The final, unique 4-digit number (1000) only adds three zeros at the end and doesn't affect the final non-zero digit.\n\nO.K., here goes:\n\nNumbers of Type A.\n\n1 x 2 x 3 x ... x 9 = 362880; final non-zero digit is 8.\n\nThere are 100 such "basic sets" of type A altogether.  \nMultiplying them together, set after set, we get the \nfollowing repeated cycle of non-zero ending digits \n(top row is # of basic sets used so far; bottom row is the corresponding final digit.)\n\n1   2   3   4   5   6   7   8   9 ...\n8   4   2   6   8   4   2   6   8 ...\n\nNotice that after every four basic sets have been used, we end up with 6 as the final non-zero digit.  Since there are exactly 100 such sets (a multiple of 4), we end up with that same last non-zero digit for the product of ALL numbers of type A.  (But we're not done yet.) \n\nNumbers of Type B.\n\nThere are exactly 10 sets of numbers of Type B, i.e. ending with  exactly one (but not two or three) zeros.\n\nMultiplying just these sets together, we'll have the following analogous results:\n\n1   2   3   4   5   6   7   8   9  10  \n8   4   2   6   8   4   2   6   8     4   \n\nSo, the last non-zero digit in these "10's products" is 4 for this lot.\n\nNumbers of Type C.\n\nWe have just one set of "100's".  For this, the last non-zero digit is 8 (it's just our "basic set" with a large number of zeros following it); only the last non-zero digit is of interest.\n\nSo, to summarize, the different sets we've divided our numbers into, when multiplied together, give us final non-zero digits as follows:\n\nType A:   6\nType B:   4\nType C:   8 \n\nFinally, then, the last non-zero digit of the product of everything is the last digit of:\n\n6 x 4 x 8, or 2.  (PHEW!!)\n\nWell, it's now the value of 2 (as reported by zanti3 from the 100 factorial website at:\n\nhttp://www.justinwhite.com/big-calc/1000.html)\n\n(Finish off this URL with 1000.html, instead of 1000... The Yahoo site would not reproduce the full URL from my draft.  Alternatively, just go to Yahoo or Google with 1000 factorial 1000 - this worked for me.) \n\nBoy; what a problem!  Evidently the jury is still out on the question of my impending dementia.  (See zanti3's kind words, below about my earlier fiasco.) \n\nThanks again to zanti3 for bringing the existence of a (1000 factorial) web site to my attention.\n\nLive long and prosper, everyone.