# Million-to-one lottery game **URL:** \ **Category:** Factual Questions\ **Created:** [March 31, 2011, 4:04pm UTC](https://boards.straightdope.com/t/million-to-one-lottery-game/576643 "2011-03-31T16:04:07Z")\ **Posts on this page:** 6\ **Page:** 2
**Author:** ![Triskadecamus](https://avatars.discourse-cdn.com/v4/letter/t/b19c9b/32.png) [@Triskadecamus](https://boards.straightdope.com/u/Triskadecamus)\ **Post date:** [March 31, 2011, 7:14pm UTC](https://boards.straightdope.com/t/million-to-one-lottery-game/576643/21 "2011-03-31T19:14:08Z")
Lottery runs until won. Random selection only. Assigned selection removed electronically from the numeric pool. Pay 1 dollar. On the day the millionth number is purchased, random number selected with ten sets of 0-9 balls, ten different tumblers, sequence matters. New Lottery starts immediately, or on the following day. Payout limited to $40,000 per year, for twenty-five payments, commencing that day, and that date each year. No other prizes. State gets to keep the reducing balance as an interest free loan. Of course it is a hideously regressive tax on stupidity, but what we have now is as well. Tris ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [March 31, 2011, 7:36pm UTC](https://boards.straightdope.com/t/million-to-one-lottery-game/576643/22 "2011-03-31T19:36:20Z")
> [@Johnny\_L.A](#): > > Alas! > > From the reference I found earlier: If you’re complaining my answer isn’t exactly 1 in 1 million, I know that – that’s exactly why I wrote “I don’t think you’ll find anything that meets your requirements.” It’s not so much “I don’t think,” but _if my summary of my understanding of the question is correct_, there is no n choose k = 1000000, such that n and k are both integers and both “reasonable” numbers by your definition. Now, I’m sure there must be a clever way to come up with some sort of solution to this question, but in the _standard_ lotto format, I can’t see how there could be, without choosing a single ball from a pool of a million, choosing 999,999 balls from a million, or doing the six balls 0-9 (either chosen from 6 pools of balls or chosen with replacement) way. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [March 31, 2011, 7:55pm UTC](https://boards.straightdope.com/t/million-to-one-lottery-game/576643/23 "2011-03-31T19:55:52Z")
That’s why I said, ‘Alas!’ ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [March 31, 2011, 8:20pm UTC](https://boards.straightdope.com/t/million-to-one-lottery-game/576643/24 "2011-03-31T20:20:43Z")
How about 3 parameters: N balls, pick k, m must match. Of course you’d have to deal with the super bonus prize for matching more than m. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [March 31, 2011, 9:19pm UTC](https://boards.straightdope.com/t/million-to-one-lottery-game/576643/25 "2011-03-31T21:19:46Z")
> [@Johnny\_L.A](#): > > That’s why I said, ‘Alas!’ Oh, gotcha. Completely misunderstood the nature of the quote–thought you were quoting yourself, but now I see it’s Pratchett. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [March 31, 2011, 9:23pm UTC](https://boards.straightdope.com/t/million-to-one-lottery-game/576643/26 "2011-03-31T21:23:09Z")
> [@](#): > > there is no n choose k = 1000000, such that n and k are both integers and both “reasonable” Yup. Unique prime factorization theorem. Prime factors of one million are 2 and 5. Any combination requires the multiplication of consecutive integers in the calculation of the answer. All such numbers need to be multiples of only 2 and/or 5. Pretty quickly you find that choosing one from one million is the only one that works. [Previous page](https://boards.straightdope.com/t/million-to-one-lottery-game/576643.md?page=1)