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Red and Black Cards is a puzzle in Professor Layton and the Curious Village.

Puzzle

US Version

A jokerless deck of 52 cards sits on the table. The cards are shuffled thoroughly and divided into two stacks of 26 cards labeled A and B.

If you divide the cards as described above and check the contents of each pile 1,000 times, how many times could you expect the number of red cards in one pile to match the number of black cards in the other?

UK Version

You have a jokerless deck of 52 cards, which have been shuffled thoroughly. You take the cards and divide them into two stacks of 26 cards each, labelled A and B.

If you divide the cards as described above and check the contents of each pile 1,000 times, how many times could you expect the number of red cards in one pile to match the number of black cards in the other?

Hints




Click a Tab to reveal the Hint.

How many red cards and black cards are there in a deck of 52 cards?

There are a total of 26 black cards and 26 red cards in a 52-card deck..

The number of red cards in pile A is equal to 26 minus the number of black cards in pile A.

You can also reverse this statement and apply it to the black cards, so...


Solution

Incorrect

Give it another shot.

Correct

You can expect a corresponding number of red and black cards to show up between the piles 1,000 times out of 1,000 tries.

US Version

There are 26 cards of each color in a 52-card deck. If you form two piles of 26 randomly selected cards from this deck, the number of red cards in pile A is equal to 26 cards minus the number of black cards in pile A. In pile B, the situation is reversed. No matter how the cards are divided, the number of red cards in pile A will be equal to the number of black cards in pile B, and vice versa.

UK Version

There are 26 cards of each colour in a 52-card deck. If you form two piles of 26 randomly selected cards from this deck, the number of red cards in pile A is equal to 26 cards minus the number of black cards in pile A. In pile B, the situation is reversed. No matter how the cards are divided, the number of red cards in pile A will be equal to the number of black cards in pile B and vice versa.

CV118S

A big thanks to http://professorlaytonwalkthrough.blogspot.com

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