BMAD 65 Posted March 23, 2013 Report Share Posted March 23, 2013 In five decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind? Quote Link to post Share on other sites

0 Solution superprismatic 11 Posted March 23, 2013 Solution Report Share Posted March 23, 2013 40 Quote Link to post Share on other sites

0 Prime 15 Posted March 23, 2013 Report Share Posted March 23, 2013 Assuming 52-deck card (no Jokers): 196 Quote Link to post Share on other sites

0 Prime 15 Posted March 23, 2013 Report Share Posted March 23, 2013 What I meant in the previous post was proper four of a kind, where you have 4 cards of the same rank and different suits. Quote Link to post Share on other sites

0 BMAD 65 Posted March 25, 2013 Author Report Share Posted March 25, 2013 Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter. Quote Link to post Share on other sites

0 Prime 15 Posted March 25, 2013 Report Share Posted March 25, 2013 Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter. In that case, like Sp said. And the number of decks does not matter. Quote Link to post Share on other sites

0 BMAD 65 Posted March 25, 2013 Author Report Share Posted March 25, 2013 Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter. In that case, like Sp said. And the number of decks does not matter. well this is embarrassing but for some reason i am getting a higher number, what am i missing? Quote Link to post Share on other sites

0 ThunderCloud 5 Posted March 25, 2013 Report Share Posted March 25, 2013 Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter. In that case, like Sp said. And the number of decks does not matter. well this is embarrassing but for some reason i am getting a higher number, what am i missing? There are 13 types of card in each suit. If you draw 39 cards and still do not have four of a kind, then you must have exactly 3 of each type. The 40th card will match with one of the sets of 3 you already have, making four of a kind. Quote Link to post Share on other sites

0 BMAD 65 Posted March 25, 2013 Author Report Share Posted March 25, 2013 Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter. In that case, like Sp said. And the number of decks does not matter. well this is embarrassing but for some reason i am getting a higher number, what am i missing? There are 13 types of card in each suit. If you draw 39 cards and still do not have four of a kind, then you must have exactly 3 of each type. The 40th card will match with one of the sets of 3 you already have, making four of a kind. Oops. for some reason i had it in my head that there were 14 card types... oopsies Quote Link to post Share on other sites

0 Prime 15 Posted March 25, 2013 Report Share Posted March 25, 2013 Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter. In that case, like Sp said. And the number of decks does not matter. well this is embarrassing but for some reason i am getting a higher number, what am i missing? Do your decks have Jokers? (Wouldn't matter, anyway, since Joker helps making 4 of a kind.) I assume, standard deck is 52 cards 2 - 10, J, Q, K, A. 13 different ranks. You can pick 3 cards of each rank. 3*13 = 39. The 40th card will match in rank one of the 3-of-a-kind that you already have. If the above assumptions are correct, but the answer is still wrong, I give up and would like to see a list of more cards than Sp posted not having at least 1 four of a kind. Quote Link to post Share on other sites

0 BMAD 65 Posted March 25, 2013 Author Report Share Posted March 25, 2013 Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter. In that case, like Sp said. And the number of decks does not matter. well this is embarrassing but for some reason i am getting a higher number, what am i missing? Do your decks have Jokers? (Wouldn't matter, anyway, since Joker helps making 4 of a kind.) I assume, standard deck is 52 cards 2 - 10, J, Q, K, A. 13 different ranks. You can pick 3 cards of each rank. 3*13 = 39. The 40th card will match in rank one of the 3-of-a-kind that you already have. If the above assumptions are correct, but the answer is still wrong, I give up and would like to see a list of more cards than Sp posted not having at least 1 four of a kind. 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A (13 cards) 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A (13 cards) 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A (13 cards) then any card would make a 4th copy and thus a 4 of a kind. This is highly improbable for them to be drawn like this but still possible so this would be the max amount you need to draw, 40 cards, to guarantee a 4 of a kind. Quote Link to post Share on other sites

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## BMAD 65

In five 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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