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A Stacked Deck is a puzzle in Professor Layton and the Unwound Future.

Puzzle

There are 52 cards in the deck below--26 black and 26 red--and no jokers.

After shuffling the deck and randomly cutting it in two, you count 23 cards in the stack on the left.

So, what's the difference between the number of red cards in the left stack and the number of black cards in the right stack?

Hints




Click a Tab to reveal the Hint.

Don't let the fact that this is a number problem confuse you.

You should be able to figure out the answer using basic arithmetic if you can figure out what to look for.

The quickest way to the answer is to try out some placeholder numbers. There are 23 cards in the left pile. Pretend that there are 10 red cards and 13 black cards. There are 52 cards in a deck, so there are 29 cards in the other pile. Try to divide the piles up like so.

Continuing on from Hint Two, you can calculate the color of the cards in the right stack based on how many red and black cards are in the left stack.

So, subtract 10 from 26, and you get 16 red cards. Then take 13 from 26, and you get 13 black cards. You now know the difference between the number of red cards in the left stack and black cards in the right! Now try a different set of numbers to see what you get.

Keep plugging in different numbers. If the left stack has five red cards and 18 black, the right stack will have 21 red cards and eight black.

Now compare this result with the one from Hint Three. Look at that! The difference is the same no matter how many of each color there are!


Solution

Correct

You aced it!

There will always be three more black cards in the pile on the right than there are red cards on the left.

You can use an equation to solve this puzzle, but it's also fun to just plug in some random numbers and figure it out that way. Once you start noticing that there's a consistent difference no matter what numbers you pick, it's really exciting!

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A big thanks to http://professorlayton3walkthrough.blogspot.com