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### Card Riddle

Card Riddle - 2 April

I have mixed 13 decks of cards.

What is the minimum number of cards must be taken out from the above mixed cards to guarantee at least one 'four of a kind'.

1. For a single pack of card we need to draw 39+1=40 cards to certainly get at least one of each kind.
Since 13 packs are MIXED, so we need to draw 13x39+1 = 508 cards to certainly get at least one of each kind.

2. You can't get more than 3 of each card (39) without getting a fourth, no matter how many decks you shuffle.

So, 40.

1. How so funny? Did you not understand me? There are 13 "kinds" - Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King.

Suits are never mentioned; they are not important.

When you have 3 of each "kind" (i.e. 39 cards), the next card MUST make a 4th of one kind, no matter what it is.

(I am guessing that the answers of 508 come from people who have misread the question, and assumed it says "What is the minimum number of cards must be taken out from the above mixed cards to guarantee at least one 'four of a kind', where all four suits are represented".)

2. A per you, the number of decks is irrelevant.

Lets take this case:

50 DECKS of cards are mixed togather. Now if one draws 50 cards and all of them can be King of Hearts.
For example, one draws First 50 cards and all of them can be King of hearts (there are 50 king of hearts when we Mix 50 Decks). In such case HOW one will get 4 of a kind by drawing 40 cards? Answer this.

Are u getting now : Its true that there are 13 kinds. But after drawing 39 cards u may not have 3 kinds. Thats the point. Hence the 40th card will not give u 4 of a kind.

In case of 20 DECKs are mixed, it is possible that u may draw 20 Ace, then 20 Jacks and then 20 queens. In such extreme cases even after drawing 60 cards u have only 3 kinds (Jack,Queen and Ace,even if u do not consider the suits).

3. But if you draw 20 Ace, then you have 4 aces?

4 of a kind doesn't specify 4 of *which* kind. If you don't have 3 of each after 39 cards, then you have 4 of one, and thus you have got there in *less* than 40 cards - 40 is the maximum.

3. This comment has been removed by the author.

4. 508 may be the right answer

U have got it totally wrong.

Just take the simple example : Two Decks of cards are mixed:

Now in these mixed cards you have-

26 Club (Ace to King)
26 Hearts (Ace to King)
26 Diamond (Ace to King)

Fastest way is to get one of each kind is 4 cards.
But slowest way will be :
If you first draw all 26 spades, then 26 Club, then 26 hearts. Till now you do not get any of diamonds. That means after drawing 78 (26+26+26) cards you do not have each of one kind. So number of decks in NOT irrelevant. Because you have MIXED the decks (not kept them separately).

I am a Faculty of Statistics.

Do not MISGUIDE people.Now remove your WRONG ans.

Thanks.

1. The solution of 40 is correct. It didn't say ANYWHERE that the 4-of-a-kind had to have a representative of each suit.

AH AH AH AH is just as valid as AH AS AD AC

2. (In your example, you say 26 of each of three suits - that's 6 of a kind, not 3 of a kind, because 26 cards is two of each)

Oh, and "I am a Faculty of Statistics." is a logical fallacy - it's Argument from Authority, and has no place here.

3. U r really idiot. The question says 4 of a kind. That means One of Heart, Spade, Club and Diamond. Don't u understand that u can draw 26 spades and then 26 hearts and then 26 clubs and then u may get diamond. Its not about the Ace or king. Ur logic is totally wrong. I hate such wrong things. If u u have the guts just call me .. 09738426856. If u do not call I will assume that u do not understand the problem.

And Admin. Do not just sleep. Put the correct ans.

4. If you interpret the question as being one heart, club, spade, diamond you are indeed correct. But that is not the question as given - 4 of a kind doesn't care about suits.

I understand you. You're just correctly answering a question that wasn't asked. Do you understand *me*?

5. (Oh, and I'm not making an international call just to correct someone who is wrong on the internet. They don't pay maths teachers enough for that!)

6. 40 ans is correct

4 of a kind example is like "4 ace or 4 kinds"

6. A per you, the number of decks is irrelevant.

Lets take this case:

50 DECKS of cards are mixed togather. Now if one draws 50 cards and all of them can be King of Hearts.
For example, he draws First 50 cards and all of them can be King of hearts (there are 50 king of hearts when we Mix 50 Decks). In such case how one will get 4 of a kind by drawing 40 cards? Answer this.

1. If all of them are King of Hearts then you have 4 kings in 4 cards.

There is no way to draw more than 39 cards without having 4 the same "kind" (where the 13 kinds are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King).

Every example you give has 4 of a kind in much fewer cards. And then you call *me* an idiot? You have a nerve. Oh, and "Ad hominem" is another logical fallacy, just like appealing to authority.

2. I got your point. U have considered only the numbers. Not relating to specific colors. Then obviously we will get in 40 cards.