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Tuesday, July 29, 2008

Cards with Crosses

You have a stack of 23 cards. Each card has an image of a cross on one side, and an image of a circle on the other side. You know that 14 cards in the stack are laying with the cross up, and therefore 9 cards are with the circle up. But you don't know in which order the cards are. Moreover, you are in a completely dark room, so you can't see anything.

The Question: How can you, without seeing anything, divide the stack of cards in two smaller stacks, in such a way that both stacks have the same number of cards with a cross up?

Hint: You can turn cards round.


Answer: Take 14 cards from the stack. Of these 14 cards, k cards are with the cross up, and therefore 14-k cards are with the circle up. In the remaining stack of 9 cards are 14-k cards with a cross up.

Then turn the stack of 14 cards round. Now there are 14-k cards with a cross up in both stacks.

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