Cards in the dark
You are in a dark room with a deck of 52 cards on the table. The deck has been prepared so that 42 cards are face down and the other 10 are face up. The deck is shuffled, and you don't know where the face-up cards are because of the darkness. Your job is to divide the deck into two (in the darkness) in such a way that each group has the same number of face-up cards. To achieve your goal, you are allowed to turn over as many cards as you wish before or after you cut the deck.
After careful thinking, you divide the deck into two and then turn over some cards. The lights come on and, indeed, you've created two decks with the same number of face-up cards!
How many cards did you turn over?
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1 solution
You take out 10 cards and turn them all. If there are N reversed cards in that group, after turning them there will be 10-N of them. And the original deck also has 10-N reversed cars (you have just removed N from the original 10).