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Flipping cards

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You’re given a regular deck of 52 playing cards.  In the pile you’re given, 13 cards face up and the rest face down.  You are to separate the given cards into two piles, such that the number of face-up cards in each pile is the same.  In separating the cards, you’re allowed to flip cards over.  The catch:  you have to do this in a dark room where you cannot determine whether a card is face up or face down.

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ronret45 Expert Asked on 1st August 2015 in Microsoft Interview Puzzles.
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    • 1 Answer(s)

    Take any 13 cards and flip them all. Rest 39 cards will make another pile. These two piles will have the same number of cards facing up. Why? Well, say out of those 13 selected 0 \leq n \leq 13 cards are facing up.  Which means that in the pile with 39 cards there will be 13-n cards facing up. When you flip all 13 cards, number of cards facing up now becomes 13-n which is equal to what the other pile have.

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    SherlockHolmes Expert Answered on 8th August 2015.
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