Written on 19 February 2003 (3 WE).
• Combinations.exe version 19 February 2003.
The version number is a digital dedication to my daughter Amy's birthday. On February 19, 2003 she reaches the U.S. legal age of gambling. When she was two she had plenty of fun fooling around with my soccer pool tickets. Nobody in the current Universe will ever say more sweetly 1, X, 2! My wish now is to invite her to a casino to gamble alongside her tati (daddy). Tati must burn his head to be able to cover all expenses. Partially on a genetic basis, she should appreciate how highly intelligent a human endeavor gambling is. Life is a streak-combination of success-failure, or win-loss in terms of theory of games. A father might encounter an unexpectedly long streak of father-failures. But a streak is what it is essentially because it has an end. Assuredly impossible, but how terrible would life be as an infinite win-streak?
”Our greatest glory consists not in never falling, but rising every time we fall.” (Confucius)
If I were an English-speaking Confucius, I would have replaced falling by failing and would have also discovered the Fundamental Formula of Gambling (FFG).
Combinations.exe is the universal lotto, lottery combinations generator. Assuredly the concept has merit based on Internet searching and emailing to this writer. The merit is the reason I release this application and make the special dedication. To my knowledge, no other piece of software can accurately generate universal 'N taken M at a time' combinations. Most certainly, no other program can generate lotto combinations 'in steps'.
The program also covers the Powerball-type of games (sets of numbers where the last number can be equal to any of the preceding numbers).
The day after. Combinations.exe must be that good! I received a ton of virus-infected emails! I mean, attempts of emails. My email providers scan the emails for viruses and warn me. At the same time, I do not open the downloaded messages automatically. What a day! Never seen more vicious attempts in a single day!
The initial version of the program did not function properly. It had some wheeling code which is not meant to be released. The standard sets of numbers (N,M) gave incorrect results. The program is now perfect for the task. I added error-checking routines as well. Invalid entries are spotted immediately; i.e . cases where M is greater than N or negative entries.
Ion Saliu
Combinations.exe generates combinations of any 'N taken M at a time' in 'steps' from 1 to C(N,M). The program looks at all the combinations in the set, in lexicographical order. For example, in a 10/6 "lotto" game, there are 210 combinations, C(10,6); if step=90, then only the combinations index #1, #91 and #181 will be generated. The generation always starts at index #1. The default step is 1: no skipping; i.e. all the combinations in the set will be generated.
Here is a sample of a 10/6 set combinations in steps of 100 lotto combinations:
1: 1 2 3 4 5 6
101: 1 3 5 6 9 10
201: 3 4 6 8 9 10
1: 1 2 3 4 5 1
1001: 1 4 5 9 10 1
2001: 3 4 5 7 8 1
The definitive version is date stamped: February 17, 2003 (02-17-03).
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