Problem 369

[Eventhorizon]

Having trouble making sure I understand a Badugi, because I can't match the 5 card example. My understanding:

Regardless the number of cards in the hand (from 4 to 13), I must be able to form at least one set of 4 cards with the following property: Each card in the set of 4 has a different rank and a different suit.

The question says no pairs and no two of the same suit. I have assumed that means no 3 of a kind, 4 of a kind, no 3 of same suit and no 4 of same suit. But I am afeared of ass-u-me ing!

[TripleM]

That's right.

[ldesnogu]

The question says no pairs and no two of the same suit. I have assumed that means no 3 of a kind, 4 of a kind, no 3 of same suit and no 4 of same suit. But I am afeared of ass-u-me ing!

Hmm, I find assumption hard to read It looks like you're missing some exclusions.

[Eventhorizon]

Still not getting it ... so two questions

1) 5 cards, all different ranks, obviously 2 of same suit, e.g 2H, 6H, 3S, 4D, 5C. Does this only count as 1 badugi-containing hand, even though I can form 2 different badugis: 2H, 3S, 4D, 5C AND 6H, 3S, 4D, 5C?

2) 5 cards containing 1 badugi, can the fifth card be any of the remaining 48 without restriction e.g. 2H, 3S, 4D, 5C, RS (R - any rank, S - any suit, not already used)?

I am coming up with too many for the 5 card example 823,680 vs 514,800 given in the question. Is there some restriction on the 5th card that is implied in the question, but I am missing? If not, there must be some restriction on the badugi I am not counting. Grrr.

[TripleM]

1) and 2) are both correct, taken individually. Your problem lies with 1) and 2) when combined.

[jbiesnecker]

1) and 2) are both correct, taken individually. Your problem lies with 1) and 2) when combined.

I think I've figured out that part (the whole "why is card #5 card #5? because it's not one of the others" thing that narrows down the possible cards that it could be), but I'm still off (504,504 vs. 514,800). I know I'm still missing something stupid (and apparently quite small) but I can't for the life of me figure it out.

[Eventhorizon]

Thank you TripleM, your hint was understood - I see the source of my double-counting!

Of course, that doesn't mean I can solve the problem!

May I suggest if anyone else is having the same problem as me, simplify the deck to ranks 1-3 and suits H and S, and define a badugi' as 2 cards of different rank and suit. Enumerate all the possible Badugi' - containing hands for a hand of 3 cards.

I hope this would not be considered a spoiler.

[ScoopyPuppy2]

I really thought I had it, but no. There are already 99 people who solved it, so I guess this won't be my first one-in-a-hundred problem

Still, I'd like to check some other values of f, would that be OK? For instance, we know f(5) = 514800, I'd like to check my f(6).

Thanks in advance!

[thundre]

Still, I'd like to check some other values of f, would that be OK? For instance, we know f(5) = 514800, I'd like to check my f(6).

If you PM me your value for f(6), I'll tell you whether it's right or not.

[thkang]

hi,

can you tell me true/false of following n and f(n):

4 : 17160
5 : 514800
6 : 7207200
7 : 67095600
8 : 471330288
9 : 2657521152
10 : 12571072800
11 : 51136072416
12 : 182018076240

[Marcus_Andrews]

4 and 5 = OK. 6 onward = incorrect.

[DeatH_StaR]

My math might be crooked, by if you want to choose 5 cards out of a 52 deck, you can choose a card and have 52 possibilities, then the second with 51 possibilities, the third with 50, fourth with 49 and fifth with 48, so 52*51*50*49*48=311875200, and not 2598960 as you said. What am I doing wrong?

[v6ph1]

Are {1,2,3,4,5} and {2,3,4,5,1} different sets?