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In a hypothetical game, 2 numbers of nine wins. If I want to increase my chances, I would use combinations of 3. There is 84 combinations of 9 numbers (1 to 9) 3 to 3, but only 12 combinations of 3 groups all combinations of 9 2 to 2: 1 2 3, 1 4 7, 1 5 9, 1 6 8, 2 4 9, 2 5 8, 2 6 7, 3 4 8, 3 5 7, 3 6 9, 4 5 6, 7 8 9,

There is some method, algorithm, technique, whatever, that I can use to list all 8407 combinations of 50 numbers (1 to 50) taken 10 to 10, where 5 numbers wins? There is 2118760 combinations of 50 5 to 5, but only 8407 combinations of 50 10 to 10, to hit 5. Can anyone please help me to LIST the combinations?

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    Could you please explain more clearly how this hypothetical game works? From what I understand you want to construct a set of triples from $\{1, \ldots, 9\}$ such that every pair $\{x, y\}$ occurs together in one of these triples.2011-09-07
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    That´s right! In my question, I list all 12 combinations, but how to do if I have much more numbers, as a lottery with 50 numbers where 5 wins? I want to try some combination of 50 10 to 10 to win 5, to increase chances...2011-09-07
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    This is a *[lottery wheel](http://en.wikipedia.org/wiki/Lottery_Wheeling)* or *cover design*. You can find some rather old links [here](http://thelotteryinstitute.tripod.com/wheels.htm)2011-09-07

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