Tricky Min/Max Problem

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tarunjohri: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Mon May 28, 2012 6:18 pm

by tarunjohri » Sat Jun 15, 2013 11:50 pm

In a deck of 52 cards, each card is one of 4 different colors and there are 13 cards of each color. If cards are to be selected at random from the deck, what is the least number of cards that must be selected to ensure that these are at least 3 cards of each color among selected?

42

Please Explain the Solution.

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Source: Beat The GMAT — Problem Solving | Sat Jun 15, 2013 11:50 pm

aaggar7: Master | Next Rank: 500 Posts; Posts: 124; Joined: Sun Mar 11, 2012 8:48 pmFollowed by: 1 member; Thanked: 9 times

by aaggar7 » Sun Jun 16, 2013 12:32 am

Let the four colors be A,B,C,D.

and each (A,B,C,D) has 13 cards from (1 to 13).

To ensure we select 3 cards of each colour = 3 * 13 + 3 = 42 is the min number of cards to be selected.

A - 1 2 3 4 5 6 7 8 9 10 11 12 13
B - 1 2 3 4 5 6 7 8 9 10 11 12 13
C - 1 2 3 4 5 6 7 8 9 10 11 12 13
D - 1 2 3 4 5 6 7 8 9 10 11 12 13

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tarunjohri: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Mon May 28, 2012 6:18 pm

by tarunjohri » Sun Jun 16, 2013 1:07 am

Thanks a lot for your explanation.

aaggar7 wrote:Let the four colors be A,B,C,D.

and each (A,B,C,D) has 13 cards from (1 to 13).

To ensure we select 3 cards of each colour = 3 * 13 + 3 = 42 is the min number of cards to be selected.

A - 1 2 3 4 5 6 7 8 9 10 11 12 13
B - 1 2 3 4 5 6 7 8 9 10 11 12 13
C - 1 2 3 4 5 6 7 8 9 10 11 12 13
D - 1 2 3 4 5 6 7 8 9 10 11 12 13

Like this post

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