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Card Puzzle

Card Puzzle - 21 February

In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?

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  1. Forty.

    The number of decks is irrelevant; the answer is the same if one or one-hundred decks are used.

    Any card drawn will be a A,2,3,4,5,6,7,8,9,10,J,Q, or K, so there are 13 possibilities each time a card is drawn.

    The fastest way to draw a four of a kind is if the first four cards all have the same "value." The slowest way, which provides the solution, is to first draw 13 three of a kinds, and then one more card.

    Since 13 x 3 + 1 = 40, if 40 cards are drawn it is guaranteed that those forty cards contain at least one four of a kind.

  2. Hey how about 79. Is it correct? ?? 79 is my ans. Bcoz i believe fourofakind means all four shapes of a given no. So in day way forty is rong

  3. I too agree that 79 cards to be drawn to get all of the four shapes. (if the two decks are mixed togather. Otherwise we can choose one deck and start drawing from that deck only. Then it will be 40. )