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You are a card shark, thrown in jail after you were caught dealing from the bottom of a deck. The sheriff, who has a reputation for being honest, has told you the swinging judge is on his way to town for the trial. You plead for him to let you out promising never to return to his territory again.He says, "Sure, but let's see how lucky you truly are."

He shows you a special deck with 23 cards in it. One side of each cards has an X, while the other side has on O. He throws the cards behind you (you cannot turn around and look, yet). He tells you 14 of them have landed with the X side up (which means the other nine landed with the O up).

He pushes you into the cell and closes the door, leaving you without any light at all. Calling through the door, he sets the challenge. "Put the cards into two stacks, so that both stacks have the same number of X's facing up! I'll be back in one hour."

You can hear him laughing as he walks away.

You spend the next 55 minutes gathering the cards together. One had fallen behind the cot's leg, making it especially hard to find in the dark. You made sure not to flip any of them over so that there are still 14 cards with the X side up, assuming the sheriff wasn't lying to you about that.

You have five minutes left to meet the challenge. What do you do?

Lay 1 random pack of 10 cards and 1 random pack of 11 cards on their side so that the edges touch the ground (Neither side is facing up). Put 1 of the remaining cards on the first deck and 1 on the second deck. This would give you the best chance of having both decks with X facing up.

ReplyDeleteThat's all I could think of, there's probably some mathematical thing you can do by turning cards over or bending them but I couldn't think of anything.

Split the cards into a stack of 9, and a stack of 14. Turn the stack of 14 over.

ReplyDeleteThe two stacks will now have the same number of Xs face up.

Explanation:

Imagine the 9-stack has x Xs face up.

Then the 14-stack has 14-x Xs face up, and so x Os face up.

When you turn the 14-stack over, it will have x Xs face up, the same as the 9-stack.

I love this question. It just seems so counterintuitive you can come up with a simple answer.

ReplyDelete