Perms and Combs! and some induction..

gAr · 2011-05-31 17:31:24

Hi,

Okay.
This one is confusing me, let me see.

gAr · 2011-06-01 05:25:10

Hi bobbym,

What I think about 3rd case is :

Pick a card from 1 suit : 13
Pick next card from 2nd suit : 12
Pick next from 3rd suit : 11
Pick last card, which is same as one of the above suits and one of the values : 6 possible cards
The 3 suits can be chosen in 4C3 ways.
Shuffle the cards chosen : 4!
Hence total : 13*12*11*6*4*4! = 988416 ways.

My doubt is whether I have overcounted, the total can't be greater than that.

bobbym · 2011-06-01 08:35:39

Hi gAr;

Thanks for providing that.
As usual I enjoy working with you. Someone else pointed out that the two answers are in a ratio of 4:5. I notice that my answer is 10296 greater than yours which is the number of just 1 pair. I showed your ideas to someone else and this is what he had to say.

Anyhow, it's completely clear that the method you attribute to your friend finds sets of four cards of the form aA aB bA cC (here lowercase letters represent suits and capital letters represent ranks, or vice-versa) but not of the form aA aB bC cC, i.e., when he or she chooses four cards, the pair of the same suit and the pair of the same number always have a card in common. Just ask your friend to show how his or her method leads to the hand of cards you gave in the first post, 2s 3h 2c 10h

He is waiting for me to ask him nicely for his solution. I have humbled myself and asked, I also would like to hear your thoughts on his comments.

gAr · 2011-06-01 16:05:57

Hi bobbym,

...finds sets of four cards of the form aA aB bA cC (here lowercase letters represent suits)

No, it finds sets of four cards of the form aA aB bB cC.

...but not of the form aA aB bC cC

We are not supposed to find this! It breaks the rule: any of the 3 cards must be of different suit and different rank.

2s 3h 2c 10h

We discard such a pair.

bobbym · 2011-06-01 17:09:44

Hi gAr;

2s 3h 2c 10h

We discard such a pair.

I am not following you here. That has 3 different cards {2, 3 10} and 3 different suits {s, h, c}, is that not a 3 card hand?

gAr · 2011-06-01 17:24:13

Hi,

OP had written this:

Ok so basically you are dealt 4 cards, out of the 4 cards, 3 of them have different suits and different values but the last one is either the same suit/value as one of the three. What are the odds of this?

So the 3 cards with different values and suits are from one combination.

For 2s 3h 2c 10h, we can find any combination of 3 cards with all three having different suits and different ranks.

bobbym · 2011-06-01 17:48:56

Hi gAr;

I think I am seeing the problem. It is in the way I am defining a 3 card.

Which of these are three card hands that you would count.

A♠ 5♦ 9♦ 9♥
2♠ 3♠ 4♦ 7♥
A♣ 2♠ 2♣ J♦
2♠ 3♠ 4♦ 7♥
4♠ 5♠ 6♦ K♥
5♦ 7♣ K♣ K♥
A♣ 2♠ 3♦ 3♥
J♥, J♣, 8♣, 8♥

gAr · 2011-06-01 18:02:55

Hi bobbym,

These are the cards to be counted :

2♠ 3♠ 4♦ 7♥
2♠ 3♠ 4♦ 7♥
4♠ 5♠ 6♦ K♥
A♣ 2♠ 3♦ 3♥

(First 2 are same, aren't they?)

bobbym · 2011-06-01 18:07:15

Hi gAr;

The problem is that he did not describe the rules of badugi correctly.

A♠ 5♦ 9♦ 9♥ is a 3 hand.

http://en.wikipedia.org/wiki/Badugi

Almost half way down A♠ 5♦ 9♦ 9♥ - > A59 a 3 hand and should be counted.

gAr · 2011-06-01 18:28:47

Hmmm, yes.
There would have been no confusion if the word badugi wasn't used at all!
The description is the most important thing before attempting to solve. We all spent our time solving different problems!

I'll take a little break, see you later.

bobbym · 2011-06-01 18:32:30

Hi gAr;

Thanks so much for helping me understand why. You have a lot of patience. Take a little break and recharge.

You are very right about getting the terms of the problem correctly. I should have asked him to show me exactly what he wanted.

gAr · 2011-06-01 19:19:20

Hi bobbym,

A lot of patience? Hmmm, I hope I don't lose any!
After all, it's a prerequisite to do math.

Yes, for such problems we must ask the poster to give some examples for all the cases which he/she considers right or wrong.

bobbym · 2011-06-01 19:56:35

Hi gAr;

I hope I can remember that next time. Actually your solution is what he wanted. I did not pay enough attention to his question. I went to the badugi sites and ended up setting up my solution based on them and not on his question.

gAr · 2011-06-01 20:30:23

And I never attempted to know badugi's rules and only concentrated on his question

bobbym · 2011-06-01 20:37:56

Anyway I found these symbols for the suits:
♠ ♦ ♣ ♥

gAr · 2011-06-01 21:17:39

Hi bobbym,

That's cool.
I was wondering whether there are unicodes for colored cards, then I found out!

bobbym · 2011-06-01 21:25:30

Hi;

That is one of the great things about wikipedia. You can just copy lots of it to this forum. If you highlight and copy math from there it is already in latex!

gAr · 2011-06-01 21:32:12

Yes, that's really a nice thing!

bobbym · 2011-06-01 21:39:00

Did you know that you can copy their pages as PDF's?

gAr · 2011-06-01 21:56:46

"Download as PDF" hyperlink?
Just now I saw it, I never paid attention to the contents there!

bobbym · 2011-06-02 05:12:41

They even have a way to make books out of them.

gAr · 2011-06-02 05:25:15

Ok, do you use that option?

bobbym · 2011-06-02 05:26:27

Not yet, I have been downloading the ones I like singularly.

Congratulations on your new status of super member!

careless25 · 2011-06-04 07:32:42

Wow guys! Sorry for the confusion...this was how the problem was stated to us and it was very confusing!!!
Thanks for the help! I appreciate it, was busy for the last few days so I couldn't get back to you guys but looks like you figured it out.

bobbym · 2011-06-04 09:33:52

Hi;

No problem, I had a good time working on it!

Math Is Fun Forum

#76 2011-05-31 17:31:24

Re: Perms and Combs! and some induction..

#77 2011-06-01 05:25:10

Re: Perms and Combs! and some induction..

#78 2011-06-01 08:35:39

Re: Perms and Combs! and some induction..

#79 2011-06-01 16:05:57

Re: Perms and Combs! and some induction..

#80 2011-06-01 17:09:44

Re: Perms and Combs! and some induction..

#81 2011-06-01 17:24:13

Re: Perms and Combs! and some induction..

#82 2011-06-01 17:48:56

Re: Perms and Combs! and some induction..

#83 2011-06-01 18:02:55

Re: Perms and Combs! and some induction..

#84 2011-06-01 18:07:15

Re: Perms and Combs! and some induction..

#85 2011-06-01 18:28:47

Re: Perms and Combs! and some induction..

#86 2011-06-01 18:32:30

Re: Perms and Combs! and some induction..

#87 2011-06-01 19:19:20

Re: Perms and Combs! and some induction..

#88 2011-06-01 19:56:35

Re: Perms and Combs! and some induction..

#89 2011-06-01 20:30:23

Re: Perms and Combs! and some induction..

#90 2011-06-01 20:37:56

Re: Perms and Combs! and some induction..

#91 2011-06-01 21:17:39

Re: Perms and Combs! and some induction..

#92 2011-06-01 21:25:30

Re: Perms and Combs! and some induction..

#93 2011-06-01 21:32:12

Re: Perms and Combs! and some induction..

#94 2011-06-01 21:39:00

Re: Perms and Combs! and some induction..

#95 2011-06-01 21:56:46

Re: Perms and Combs! and some induction..

#96 2011-06-02 05:12:41

Re: Perms and Combs! and some induction..

#97 2011-06-02 05:25:15

Re: Perms and Combs! and some induction..

#98 2011-06-02 05:26:27

Re: Perms and Combs! and some induction..

#99 2011-06-04 07:32:42

Re: Perms and Combs! and some induction..

#100 2011-06-04 09:33:52

Re: Perms and Combs! and some induction..

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