How Many Millions of Lottery Tickets Should we Buy?

[@charlesmarshall7045]

I do not know why a dude talking while he writes on a piece of paper with markers is interesting and informative. Keep it up!

[@kyay10]

6:50 Good thing to mention is that this works because your function preserves the ordering of elements, i.e. given an ordered tuple, the resulting set elements are ordered the same way. This wouldn't happen if e.g. you used `-1`, `-2`, etc. The things you're adding being ordered is what matters here. 5:10 Adding distinct things to distinct things doesn't always result in distinct things though For example: g() = { a + 4, b + 2 } g() = { 5 } So it's that you're adding distinct things that have the same ordering as the other distinct things. This probably follows from some lemma like: if a < b and c

[@vampire_catgirl]

I love wasting money, so this is super helpful, thank you!

[@megapussi]

my answer before having watched the video is that most people should buy 0 millions of lottery tickets

[@WrathofMath]

That's reasonable

[@chemicalbrother5743]

5:00 not quite, we know they r distinct when we add 1,...,5 because we add distinct *bigger* numbers to distinct *bigger* numbers.

[@robertobuenafe]

Wait, I have to replay since I'm lost. If we're just going for the jackpot only, then shouldn't the combinations formula already suffice?

[@WrathofMath]

There might be something about the rules of the game you have mixed up. The winning number that needs to be matched is a multiset of numbers in [100], so ordinary combinations will not work because they don't count multisets. For examples, {1, 10, 99, 99, 1} may be the winning combination, and that combo will not be counted by the traditional combination formula.

[@HarshitKumar-dj4ev]

I though the multisets can easily be found by n^k Since for each of the k number, we have n choices. So, n * n * n (....k times). What am I missing here?

[@hredger]

If I'm not wrong, that wouldn't work because in this case the order of the elements doesn't matter, and the calculation 100^5 would count for example the numbers (1, 1, 1, 1, 2) and (2, 1, 1, 1, 1) as distinct cases, even though they are the same thing in this case.

[@thedarkfairy3473]

I don’t know either. I had the same thoughts. Shouldn’t the answer be 100^5, therefore 100 * 100 * 100 * 100 * 100, and therefore 10,000,000,000? That covers the independent numbers being drawn. Though I’m realizing now, that will be more than the problem outlines, since it includes a lot of duplicates. It includes all the following; 1: 1,1,1,1,2 2:1,1,1,2,1 3:1,1,2,1,1 4:1,2,1,1,1 5:2,1,1,1,1

[@vikingursigurdsson]

You would be counting a few sets multiple times, so you'd need to compensate for them first