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153 - An Extra Block154 - A Stacked Deck155 - Three More Blocks

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

Puzzle

US Version

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?

UK Version

There are 52 cards in the deck below, 26 black and 26 red. No jokers.

After shuffling the deck and randomly cutting it in half, 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.

US Version

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

UK Version

You should be able to work out the answer using simple arithmetic if you know what to look for.

US Version

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.

UK Version

The quickest way is to come up with trial numbers.

There are 23 cards in the left-hand stack. Since there are 52 cards in a deck, that means 29 cards in the other stack.

Now imagine that the left-hand stack is made up of 10 red cards and 13 black cards. How many cards of each colour remain in the right-hand stack?

US Version

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.

UK Version

After following Hint 2, you can work out the colour of the cards in the right-hand stack based on how many red and black cards are in the left stack. 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 and see what you get.

US Version

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!

UK Version

Keep trying out 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 3. Look at that! The difference is the same no matter how many of each colour there are!


Solution

Incorrect

Too bad!

US Version

It's clear this is a math problem of sorts, but it's hard to figure out what you're supposed to calculate.

Try plugging in some numbers, and see if you don't stumble upon something...

UK Version

It's clear that this is a maths problem of sorts, but it's hard to work out what you're supposed to calculate.

Experiment with some numbers and you might notice something...

Correct

You aced it!

US Version

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!

UK Version

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

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

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