face up, face down

February 27, 2012

Posed by Punit Rathore:

A blind man is handed a deck of 52 cards and told that exactly 10 of these cards are facing up. How can he divide the cards into two piles, not necessarily of equal size, with each pile having the same number of cards facing up?

Solution posted in comment 1.


One Response to “face up, face down”

  1. Ramesh Says:

    Let us say there are N up cards in the pile of 52 cards.

    1. Split them in to 2 piles of N (pile 1) and 52-N (pile 2) cards.
    2. Let us say that in pile 1 there are M up cards, then
    pile 1 will have N-M down cards;
    pile 2 has N-M up cards (because pile 1 has M up cards and there are only total N up cards)
    3. Flip the cards in pile 1. pile 1 has N-M up cards now and so does pile 2.

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