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.
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.
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.