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: : Combination Lexicographical Order, Rank, Index.T This is the comprehensive and lightning-fast algorithm. There has always been a great interest in 'combination sequence number' or lexicographical order. There is a branch of mathematics named 'combinatorics'. The lottery and many other gambling businesses rely on combinatorics or the 'mathematics of combinations'. Theory of probability itself wouldn't have been possible without the science of combinations. I wrote the computer program SEQUENCE.EXE. I presented the core of my algorithm in the message: 348.html "Combination sequence number" or "Lexicographical Order" Fast Algorithm. My algorithm did not cover an important combinatorics field: PowerBall. It is a different and difficult lotto game. It draws 5 or 6 numbers like in any regular lotto game. Then it draws separately a so-called 'power ball' that can be equal to or less than any regular number previously drawn. The two major issues were so difficult that nobody came even close to solving them. The PowerBall algorithm didn't work out in the first day. If I can't come out with a solution the first day, chances are there is no solution. Almighty Number grants us one unit of Light and one unit of Darkness to carry out important tasks. It was minutes after the end of the Darkness period. I "saw' the invisible PowerBall algorithm in a late dream. I tried to implement it several times, to no avail. It was a hot summer morning. Every line of code was melting down soon after its inception. The ice cubes did nothing but add fuel to the fire. The mathematics of combinations: combinatorics. Description: "Combination Lexicographical ORDER", version 1.00, lexicographic, lex. Don't ask me to give you the source code! I ain't no googoo; nor am I googol. There are so many bastards out there. They live only to steal and be asskicked by JAQK Fowuru. The masochists enjoy that, I dunno why. I want first to offer my algorithm to reputable repositories. I offered my previous algorithm to netlib.org. I don't know what was with them. I don't know how they handled my source code. Are there bastards everywhere, in any imaginable place? How can be some so stupid in their quest to satisfy their sick egos? So, the source code can be had only from a reputable repository. Until then, use COLORDER.EXE. I verified the algorithm with many cases. I believe the procedure is 100% accurate. But, if you think you discovered a miscalculation, please let me know. Document the error as detailed and as clearly as possible. I believe I can fix the errors – if any. The correct formula should take into consideration differences in lotto games formats. One fundamental element of a lotto game format is its largest number. Thus, in a lotto 49/6 game, the CSN for combination 6-7-16-20-28-47 is 6,991,908 (exactly the mid-point in the combination set). The same combination 6-7-16-20-28-47 has an index (CSN) of 45,148,858 in a lotto 69/6 game (PA lottery). Your formulae do not lead to these results, the only correct results. Although not a general-purpose formula, the algorithm I presented a few days ago represents the easiest way to calculate the indexes of any lotto combinations. The algorithm is for the BASIC language, but it can be converted to any programming language. I compiled NTHINDEX.EXE with PowerBasic, especially because of increased speed of execution. strange as it apparently seems to some I too use the ID in my lotto programs. Combinatorial mathematics: The very first rule they learn is this: "In combinations of N elements taken M at a time, M must be less than or equal to N. For it is absurd to try combining 2 elements taken them 3 at a time, or 0 elements 6 at a time." If one has only 2 elements, how can one combine them 3 at a time? One particular value that M can take is 0. "The number of combinations of any N elements taken 0 at a time is 1." But "0 elements taken N at a time is an absurdity." I presented earlier this month of July 2001 an algorithm to calculate the index, or rank, or lexicographical order, or combination sequence number (CSN). The algorithm was 100% precise. It had one problem, however. The speed of execution left much to be desired for monster-odds games, such as Keno (80/20, 70/20, even 70/10). The speed was acceptable for many other lotto games. Even a big game such as the 55/5/42 PowerBall required less than half a minute to determine the CSN. Nevertheless, running the algorithm for Keno games took an eternity! I came back to the original "B.P. Buckles and M. Lybanon" algorithm (algorithm "ACM #515"). I was able to add to it the reverse task: calculate the CSN for any lotto game, but the PowerBall. Later, the PowerBall will be added to the procedure. I recompiled NTHINDEX.EXE to SEQUENCE.EXE, the program that uses the new algorithm. Here is the main algorithm. Listed is also my function that calculates the number of combinations 'N taken M at a time': Combine (N, M). The program SEQUENCE.EXE was compiled with PowerBasic for DOS. Title: Algorithm Combination Lexicographic Order Rank Index. Mathematics, algorithm, formula, software, code to generate, calculate combination lexicographical order, index, rank, sequence, ordering. Combination, combinations, combinatorics, formula, formulas, formulae. Algorithm, algorithms, lexicographical order, Lexicographic order, lex, combination sequence number, index, rank, mathematics, math, maths. Lotto, lottery, generate combinations, programming, probability, software, freeware, free, program. Programs, source code, code, BASIC, PowerBasic, DOS, lottery, lotto, PowerBall, power ball, keno, binary search, nCr, C(N,M).